One dimensional edge localized YSR states in CrCl3 on NbSe2

Magnet/superconductor hybrid systems have been put forward as a platform for realizing topological superconductivity. We investigated the heterostructure of ferromagnetic monolayer CrCl3 and superconducting NbSe2. Using low-temperature scanning tunneling microscopy, we observe topologically trivial Yu-Shiba-Rusinov (YSR) states localized at the edge of CrCl3 islands. DFT simulations reveal that the Cr atoms at the edge have an enhanced d-orbital DOS close to E F . This leads to an exchange coupling between these atoms and the substrate that rationalizes the edge-localization of the YSR states.

Electrical Transport Interplay with Charge Density Waves, Magnetization, and Disorder Tuned by 2D van der Waals Interface Modification via Elemental Intercalation and Substitution in ZrTe3, 2H-TaS2, and Cr2Si2Te6 Crystals

Electrical transport in 2D materials exhibits unique behaviors due to reduced dimensionality, broken symmetries, and quantum confinement. It serves as both a sensitive probe for the emergence of coherent electronic phases and a tool to actively manipulate many-body correlated states. Exploring their interplay and interdependence is crucial but remains underexplored. This review integratively cross-examines the atomic and electronic structures and transport properties of van der Waals-layered crystals ZrTe3, 2H-TaS2, and Cr2Si2Te6, providing a comprehensive understanding and uncovering new discoveries and insights. A common observation from these crystals is that modifying the atomic and electronic interface structures of 2D van der Waals interfaces using heteroatoms significantly influences the emergence and stability of coherent phases, as well as phase-sensitive transport responses. In ZrTe3, substitution and intercalation with Se, Hf, Cu, or Ni at the 2D vdW interface alter phonon-electron coupling, valence states, and the quasi-1D interface Fermi band, affecting the onset of CDW and SC, manifested as resistance upturns and zero-resistance states. We conclude here that these phenomena originate from dopant-induced variations in the lattice spacing of the quasi-1D Te chains of the 2D vdW interface, and propose an unconventional superconducting mechanism driven by valence fluctuations at the van Hove singularity, arising from quasi-1D lattice vibrations. Short-range in-plane electronic heterostructures at the vdW interface of Cr2Si2Te6 result in a narrowed band gap. The sharp increase in in-plane resistance is found to be linked to the emergence and development of out-of-plane ferromagnetism. The insertion of 2D magnetic layers such as Mn, Fe, and Co into the vdW gap of 2H-TaS2 induces anisotropic magnetism and associated transport responses to magnetic transitions. Overall, 2D vdW interface modification offers control over collective electronic behavior, transport properties, and their interplays, advancing fundamental science and nanoelectronic devices.

Observation of edge and bulk states in a three-site Kitaev chain

A chain of quantum dots (QDs) in semiconductor-superconductor hybrid systems can form an artificial Kitaev chain hosting Majorana bound states (MBSs)1-3. These zero-energy states are expected to be localized on the edges of the chain4, at the outermost QDs. The remaining QDs, comprising the bulk, are predicted to host an excitation gap that protects the MBSs at the edges from local on-site perturbations. Here we demonstrate this connection between the bulk and edges in a minimal system, by engineering a three-site Kitaev chain in a two-dimensional electron gas. Through direct tunnelling spectroscopy on each site, we show that the appearance of stable zero-bias conductance peaks at the outer QDs is correlated with the presence of an excitation gap in the middle QD. Furthermore, we show that this gap can be controlled by applying a superconducting phase difference between the two hybrid segments and that the MBSs are robust only when the excitation gap is present. We find a close agreement between experiments and the original Kitaev model, thus confirming key predictions for MBSs in a three-site chain.

Spin-exchange induced spillover on poor man's Majoranas in minimal Kitaev chains

The 'poor man's Majoranas' (PMMs) (Leijnse and Flensberg 2012Phys. Rev. B86134528) devoid of topological protection can 'spill over' from one edge into another of the minimal Kitaev chain when perturbed electrostatically. As aftermath, this leads to a delocalized Majorana fermion (MF) at both the edges. Additionally, according to recent differential conductance measurements in a pair of superconducting and spinless quantum dots (QDs), such a PMM picture was brought to reality (Dviret al2023Nature614445; ten Haafet al2024Nature630329). Based on this scenario, we propose the spillover of the PMM when its QD is exchange coupled to a quantum spinS. We show that if this QD is perturbed by the exchange couplingJ, solely the half2S+1(2S+2)of the fine structure stays explicit for a fermionic (bosonic)S.Concurrently, the other half squeezes itself as the delocalized MF zero-mode. Particularly, turning-off the superconductivity the multiplicity2S+1holds regardless the spin statistics. Meanwhile, the PMM spillover induced byJbecomes a statistics dependent effect. Hence, our findings contribute to the comprehension of spin-phenomena interplay with superconductivity in minimal Kitaev chains, offering insights for future quantum computing devices hosting PMMs.

Metallated carbon nanowires for potential quantum computing applications via substrate proximity

The realization of next-generation quantum computing devices is hindered by the formidable challenge of detecting and manipulating Majorana zero mode (MZM). In this study, we study if MZM exist in metallated carbyne nanowires. Through optimizations of distinct types of metallated carbyne, we have achieved an average magnetic moment surpassing 1μB for the cases of Mo, Tc, and Ru metallated carbyne. where their local moments exceed 2μB. The magnetism of the Ru atom displays periodic variations with increasing carbyne length. associated with a strong average spin-orbital coupling of ∼140meV. When the ferromagnetic Ru metallated carbyne, coupled with a superconducting Ru substrate, could trigger band inversions at the gamma (G) point and M point, where spin-orbital coupling triggers the transition between the band inversion and the Dirac gap. Our findings present an exciting opportunity to realize carbon-based materials capable of hosting MZM.

Charging of Single Molecules Mediated by the Quantum Phase of Molecular Orbitals

Enriching the observable consequences of quantum phases has been a long-standing pursuit for quantum frontiers. Here, we demonstrate that the quantum phases of molecular orbitals can be manifested from the charging process of single NTCDA molecules. The self-assembled monolayer molecules form moiré patterns with the underlying Pb(111) substrate. The moiré pattern modulates the energy alignment between the molecule orbitals and the substrate Fermi level, resulting in three types of molecules. Scanning tunneling microscopy measurements indicate that all types of molecules can be gated by the tip electric field to incur charge state transitions but with different threshold fields. Intriguingly, the charge rings surrounding individual molecules exhibit intensity variations and even reversals with pertinent directional dependence. Such an observation is ascribed to the antisymmetric quantum phase of the charged molecular orbital, resulting in destructive tunneling along its highly symmetric molecular axis. This work opens up a new platform for utilizing the quantum phase of molecular orbitals in the control of charge transport in molecular junctions.

Enhanced Majorana stability in a three-site Kitaev chain

Majorana zero modes are non-Abelian quasiparticles predicted to emerge at the edges of topological superconductors. A one-dimensional topological superconductor can be realized with the Kitaev model-a chain of spinless fermions coupled via p-wave superconductivity and electron hopping-which becomes topological in the long-chain limit. Here we realize a three-site Kitaev chain using semiconducting quantum dots coupled by superconducting segments in a hybrid InSb/Al nanowire. We investigate the robustness of Majorana zero modes under varying coupling strengths and electrochemical potentials, comparing two- and three-site chains realized within the same device. We observe that extending the chain to three sites enhances the stability of the zero-energy modes, especially against variations in the coupling strengths. This experiment lacks superconducting phase control, yet numerical conductance simulations with phase averaging align well with our observations. Our results demonstrate the scalability of quantum-dot-based Kitaev chains and its benefits for Majorana stability.

Signatures of Amorphous Shiba State in FeTe0.55Se0.45

The iron-based superconductor FeTe0.55Se0.45 is a peculiar material: it hosts surface states with a Dirac dispersion, is a putative topological superconductor hosting Majorana modes in vortices, and has an unusually low Fermi energy. The superconducting state is generally characterized by three gaps in different bands, with the homogeneous, spatially extended Bogoliubov excitations─in this work, we uncover evidence that it is instead of a very different nature. Our scanning tunneling spectroscopy data show several peaks in the density of states above a full gap, and by analyzing their spatial and junction-resistance dependence, we conclude the peaks above the first one are not coherence peaks from different bands. Instead, comparisons with our simulations indicate they originate from generalized Shiba states that are spatially overlapping. This can lead to an amorphous state of Bogoliubov quasiparticles, reminiscent of impurity bands in semiconductors. We discuss the origin and implications of this new state.

Current-Driven Magnetization Switching for Superconducting Diode Memory

Stacking superconductors (SC) with ferromagnetic materials (FM) significantly impact superconductivity, enabling the emergence of spin-triplet states and topological superconductivity. The tuning of superconductivity in SC-FM heterostructure is also reflected in the recently discovered superconducting diode effect, characterized by nonreciprocal electric transport when time and inversion symmetries are broken. Notably, in SC-FM systems, a time reversal operation reverses both current and magnetization, leading to the conceptualization of superconducting magnetization diode effect (SMDE). In this variant, while the current direction remains fixed, the critical currents shall be different when reversing the magnetization. Here, the existence of SMDE in SC-FM heterostructures is demonstrated. SMDE uniquely maps magnetization states onto superconductivity by setting the read current between two critical currents for the positive and negative magnetization directions, respectively. Thus, the magnetization states can be read by measuring the superconductivity, while the writing process is accomplished by manipulating magnetization states through current-driven spin-orbit torque to switch the superconductivity. The proposed superconducting diode magnetoresistance in SC-FM heterostructures with an ideally infinite on/off ratio resolves the limitations of tunneling magnetoresistance in the magnetic tunneling junctions, thereby contributing to the advancement of superconducting spintronics.

Proximity-Induced Superconductivity in Ferromagnetic Fe3GeTe2 and Josephson Tunneling through a van der Waals Heterojunction

Synergy between superconductivity and ferromagnetism may offer great opportunities in nondissipative spintronics and topological quantum computing. Yet at the microscopic level, the exchange splitting of the electronic states responsible for ferromagnetism is inherently incompatible with the spin-singlet nature of conventional superconducting Cooper pairs. Here, we exploit the recently discovered van der Waals ferromagnets as enabling platforms with marvelous controllability to unravel the myth between ferromagnetism and superconductivity. We report unambiguous experimental evidence of superconductivity in few-layer ferromagnetic Fe3GeTe2 (FGT) proximity coupled to a superconducting NbSe2 overlayer through an insulating spacer, demonstrating coexistence of these two seemingly antagonistic orderings. Our transport measurements reveal a sudden resistance drop to zero in FGT below the superconducting critical temperature of NbSe2 and detect a Josephson supercurrent through the NbSe2/insulator/FGT van der Waals junction. Furthermore, using anomalous Hall effect and magnetic force microscopy characterizations, we confirm that FGT preserves its ferromagnetism in the superconducting regime. Our central findings reveal the microscopic harmony between ferromagnetism and superconductivity and render these systems immense technological potentials.

Stripe charge order and its interaction with Majorana bound states in 2M-WS2 topological superconductors

To achieve logic operations via Majorana braiding, positional control of the Majorana bound states (MBSs) must be established. Here we report the observation of a striped surface charge order coexisting with superconductivity and its interaction with the MBS in the topological superconductor 2M-WS2, using low-temperature scanning tunneling microscopy. By applying an out-of-plane magnetic field, we observe that MBSs are absent in vortices in the region with stripe order. This is in contrast to adjacent underlaying layers without charge order, where vortex-bound MBSs are observed. Via theoretical simulations, we show that the surface stripe order does not destroy the bulk topology, but it can effectively modify the spatial distribution of MBSs, i.e. it pushes them downward, away from the 2M-WS2 surface. Our findings demonstrate that the interplay of charge order and topological superconductivity can potentially be used to tune the positions of MBSs, and to explore new states of matter.

Individual Assembly of Radical Molecules on Superconductors: Demonstrating Quantum Spin Behavior and Bistable Charge Rearrangement

High-precision molecular manipulation techniques are used to control the distance between radical molecules on superconductors. Our results show that the molecules can host single electrons with a spin 1/2. By changing the distance between tip and sample, a quantum phase transition from the singlet to doublet ground state can be induced. Due to local screening and charge redistribution, we observe either charged or neutral molecules, which couple in a sophisticated way, showing quantum spin behavior that deviates from the classical spins. Dimers at different separations show multiple Yu-Shiba-Rusinov peaks in tunneling spectroscopy of varying intensity, which are in line with the superconducting two-impurity Anderson model, where singlet (S = 0) and doublet (S = 1/2) ground states are found. The assembly of chains of 3, 4, and 5 molecules shows alternating charge patterns, where the edge molecules always host a charge/spin. The tetramer is observed in two configurations, where the neutral site is moved by one position. We show that these two configurations can be switched by the action of the probing tip in a nondestructive manner, demonstrating that the tetramer is an information unit, based on single-electron charge reorganization.

Charge-Density-Wave Control by Adatom Manipulation and Its Effect on Magnetic Nanostructures

Charge-density waves (CDWs) are correlated states of matter, in which the electronic density is modulated periodically due to electronic and phononic interactions. Often, CDW phases coexist with other correlated states, such as superconductivity, spin-density waves, or Mott insulators. Controlling CDW phases may, therefore, enable the manipulation of the energy landscape of these interacting states. The transition metal dichalcogenide 2H-NbSe2 hosts both CDW order and superconductivity, with the incommensurate CDW phase resulting in different CDW-to-lattice alignments at the atomic scale. Using scanning tunneling microscopy, we position adatoms on the surface to induce reversible CDW domain switching. We show that the domain structure critically affects other local interactions, particularly the hybridization of Yu-Shiba-Rusinov states, which emerge from exchange interactions of magnetic Fe atoms with the superconductor. Our results suggest that CDW manipulation could also be used to introduce domain walls into coupled spin chains on superconductors, potentially impacting topological superconductivity.

Chirality-Induced Majorana Zero Modes and Majorana Polarization

Realizing Majorana Fermions has always been regarded as a crucial and formidable task in topological superconductors. In this work, we report a physical mechanism and a material platform for realizing Majorana zero modes (MZMs). This material platform consists of open circular helix molecule (CHM) proximity coupled with an s-wave superconductor (under an external magnetic field) or interconnected-CHM chain coupled with a phase-bias s-wave superconducting heterostructure (without any external magnetic field). MZMs generated here are tightly associated with the structural chirality in CHMs. Notably, the left- and right-handedness results in completely opposite Majorana polarization (MP), leading us to refer to this phenomenon as chirality-induced MP (CIMP). Importantly, the local CIMP is closely linked to chirality-induced spin polarization, providing us with an effective way to regulate MZMs through the chirality-induced spin selectivity (CISS) effect. Furthermore, MZMs can be detected by the spin-polarized current measurements related to the CISS in chiral materials.

Emergence of Exotic Spin Texture in Supramolecular Metal Complexes on a 2D Superconductor

Designer heterostructures have offered a very powerful strategy to create exotic superconducting states by combining magnetism and superconductivity. In this Letter, we use a heterostructure platform combining supramolecular metal complexes (SMCs) with a quasi-2D van der Waals superconductor NbSe_{2}. Our scanning tunneling microscopy measurements demonstrate the emergence of Yu-Shiba-Rusinov bands arising from the interaction between the SMC magnetism and the NbSe_{2} superconductivity. Using x-ray absorption spectroscopy and x-ray magnetic circular dichroism measurements, we show the presence of antiferromagnetic coupling between the SMC units. These result in the emergence of an unconventional 3×3 reconstruction in the magnetic ground state that is directly reflected in real space modulation of the Yu-Shiba-Rusinov bands. The combination of flexible molecular building blocks, frustrated magnetic textures, and superconductivity in heterostructures establishes a fertile starting point to fabricating tunable quantum materials, including unconventional superconductors and quantum spin liquids.

Construction of topological quantum magnets from atomic spins on surfaces

Artificial quantum systems have emerged as platforms to realize topological matter in a well-controlled manner. So far, experiments have mostly explored non-interacting topological states, and the realization of many-body topological phases in solid-state platforms with atomic resolution has remained challenging. Here we construct topological quantum Heisenberg spin lattices by assembling spin chains and two-dimensional spin arrays from spin-1/2 Ti atoms on an insulating MgO film in a scanning tunnelling microscope. We engineer both topological and trivial phases of the quantum spin model and thereby realize first- and second-order topological quantum magnets. We probe the many-body excitations of the quantum magnets by single-atom electron spin resonance with an energy resolution better than 100 neV. Making use of the atomically localized magnetic field of the scanning tunnelling microscope tip, we visualize various many-body topological bound modes including topological edge states, topological defects and higher-order corner modes. Our results provide a bottom-up approach for the simulation of exotic quantum many-body phases of interacting spins.

Observation of Yu-Shiba-Rusinov-like states at the edge of CrBr3/NbSe2 heterostructure

The hybrid ferromagnet-superconductor heterostructures have attracted extensive attention as they potentially host topological superconductivity. Relevant experimental signatures have recently been reported in CrBr3/NbSe2 ferromagnet-superconductor heterostructure, but controversies remain. Here, we reinvestigate CrBr3/NbSe2 by an ultralow temperature scanning tunneling microscope with higher spatial and energy resolutions. We find that the single-layer CrBr3 film is insulating and acts likely as a vacuum barrier, the measured superconducting gap and vortex state on it are nearly the same as those of NbSe2 substrate. Meanwhile, in-gap features are observed at the edges of CrBr3 island, which display either a zero-energy conductance peak or a pair of particle-hole symmetric bound states. They are discretely distributed at the edges of CrBr3 film, and their appearance is found closely related to the atomic lattice reconstruction near the edges. By increasing tunneling transmissivity, the zero-energy conductance peak quickly splits, while the pair of nonzero in-gap bound states first approach each other, merge, and then split again. These behaviors are unexpected for Majorana edge modes, but in consistent with the conventional Yu-Shiba-Rusinov states. Our results provide critical information for further understanding the interfacial coupling in CrBr3/NbSe2 heterostructure.

Surface superconductivity in the topological Weyl semimetal t-PtBi2

Topological superconductivity is a promising concept for generating fault-tolerant qubits. Early experimental studies looked at hybrid systems and doped intrinsic topological or superconducting materials at very low temperatures. However, higher critical temperatures are indispensable for technological exploitation. Recent angle-resolved photoemission spectroscopy results have revealed that superconductivity in the type-I Weyl semimetal-trigonal PtBi2 (t-PtBi2)-is located at the Fermi-arc surface states, which renders the material a potential candidate for intrinsic topological superconductivity. Here we show, using scanning tunnelling microscopy and spectroscopy, that t-PtBi2 presents surface superconductivity at elevated temperatures (5 K). The gap magnitude is elusive: it is spatially inhomogeneous and spans from 0 to 20 meV. In particular, the large gap value and the shape of the quasiparticle excitation spectrum resemble the phenomenology of high-Tc superconductors. To our knowledge, this is the largest superconducting gap so far measured in a topological material. Moreover, we show that the superconducting state at 5 K persists in magnetic fields up to 12 T.

High-Resolution Spectroscopy of the Intermediate Impurity States near a Quantum Phase Transition

The intermediate behavior near a quantum phase transition is crucial for understanding the quantum criticality of various competing phases and their separate origins, yet it remains unexplored for the multiple Yu-Shiba-Rusinov (YSR) states. Here, we investigated the detailed spectroscopic change of the exchange-coupling-dependent YSR states near a quantum phase transition. The initially developed one pair of YSR states, induced by the Fe vacancy in monolayer Fe(Te,Se) superconductor, are clearly resolved with high resolution showing an evolution into two pairs of YSR peaks yet with dichotomy in their spectral features as they enter the quantum phase transition region. Spectral-weight analysis suggests that the double YSR pairs occur as a result of field splitting by the magnetic anisotropy. Our findings unveil the intermediate region of a quantum phase transition with a magnetic anisotropy-induced splitting of the YSR resonance, and highlight a prospect for developing functional electronics based on the flexibly controllable multiple quantum states.

Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge

The Majorana fermion offers fascinating possibilities such as non-Abelian statistics and nonlocal robust qubits, and hunting it is one of the most important topics in current condensed matter physics. Most of the efforts have been focused on the Majorana bound state at zero energy in terms of scanning tunneling spectroscopy searching for the quantized conductance. On the other hand, a chiral Majorana edge channel appears at the surface of a three-dimensional topological insulator when engineering an interface between proximity-induced superconductivity and ferromagnetism. Recent advances in microwave spectroscopy of topological edge states open a new avenue for observing signatures of such Majorana edge states through the local optical conductivity. As a guide to future experiments, we show how the local optical conductivity and density of states present distinct qualitative features depending on the symmetry of the superconductivity, that can be tuned via the magnetization and temperature. In particular, the presence of the Majorana edge state leads to a characteristic nonmonotonic temperature dependence achieved by tuning the magnetization.

Topological superconductivity from unconventional band degeneracy with conventional pairing

We present a new scheme for Majorana modes in systems with nonsymmorphic-symmetry-protected band degeneracy. We reveal that when the gapless fermionic excitations are encoded with conventional superconductivity and magnetism, which can be intrinsic or induced by proximity effect, topological superconductivity and Majorana modes can be obtained. We illustrate this outcome in a system which respects the space group P4/nmm and features a fourfold-degenerate fermionic mode at (π,  π) in the Brillouin zone. We show that in the presence of conventional superconductivity, different types of topological superconductivity, i.e., first-order and second-order topological superconductivity, with coexisting fragile Wannier obstruction in the latter case, can be generated in accordance with the different types of magnetic orders; Majorana modes are shown to exist on the boundary, at the corner and in the vortices. To further demonstrate the effectiveness of our approach, another example related to the space group P4/ncc based on this scheme is also provided. Our study offers insights into constructing topological superconductors based on bulk energy bands and conventional superconductivity and helps to find new material candidates and design new platforms for realizing Majorana modes.

Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states

Kitaev chains in quantum dot-superconductor arrays are a promising platform for the realization of topological superconductivity. As recently demonstrated, even a two-site chain can host Majorana zero modes known as "poor man's Majorana". Harnessing the potential of these states for quantum information processing, however, requires increasing their robustness to external perturbations. Here, we form a two-site Kitaev chain using Yu-Shiba-Rusinov states in proximitized quantum dots. By deterministically tuning the hybridization between the quantum dots and the superconductor, we observe poor man's Majorana states with a gap larger than 70 μeV. The sensitivity to charge fluctuations is also greatly reduced compared to Kitaev chains made with non-proximitized dots. The systematic control and improved energy scales of poor man's Majorana states realized with Yu-Shiba-Rusinov states will benefit the realization of longer Kitaev chains, parity qubits, and the demonstration of non-Abelian physics.

Altermagnetic Routes to Majorana Modes in Zero Net Magnetization

We propose heterostructures that realize first and second order topological superconductivity with vanishing net magnetization by utilizing altermagnetism. Such platforms may offer a significant improvement over conventional platforms with uniform magnetization since the latter suppresses the superconducting gap. We first introduce a 1D semiconductor-superconductor structure in proximity to an altermagnet that realizes end Majorana zero modes (MZMs) with vanishing net magnetization. Additionally, a coexisting Zeeman term provides a tuning knob to distinguish topological and trivial zero modes. We then propose 2D altermagnetic platforms that can realize chiral Majorana fermions or higher order corner MZMs. Our Letter paves the way toward realizing Majorana boundary states with an alternative source of time-reversal breaking and zero net magnetization.

Quasiperiodic disorder induced critical phases in a periodically driven dimerized p-wave Kitaev chain

The intricate relationship between topology and disorder in non-equilibrium quantum systems presents a captivating avenue for exploring localization phenomenon. Here, we look for a suitable platform that enables an in-depth investigation of the topic. To this end, we delve into the nuanced analysis of the topological and localization characteristics exhibited by a one-dimensional dimerized Kitaev chain under periodic driving and perform detailed analyses of the Floquet Majorana modes. Such a non-equilibrium scenario is made further interesting by including a spatially varying quasiperiodic potential with a temporally modulated amplitude. Apriori, the motivation is to explore an interplay between dimerization and a quasiperiodic disorder in a topological setting which is also known to demonstrate unique (re-entrant) localization properties. While the topological properties of the driven system confirm the presence of zero and π Majorana modes, the phase diagram obtained by constructing a pair of topological invariants ( Z × Z ), also referred to as the real space winding numbers, at different driving frequencies reveal intriguing features that are distinct from the static scenario. In particular, at either low or intermediate frequency regimes, the phase diagram concerning the zero mode involves two distinct phase transitions, one from a topologically trivial to a non-trivial phase, and another from a topological phase to an Anderson localized phase. On the other hand, the study of the Majorana π mode unveils the emergence of a unique topological phase, characterized by complete localization of both the bulk and the edge modes, which may be called as the Floquet topological Anderson phase. Moreover, different frequency regimes showcase distinct localization features which can be examined via the localization toolbox, namely, the inverse and the normalized participation ratios. Specifically, the low and high-frequency regimes demonstrate the existence of completely extended and localized phases, respectively. While at intermediate frequencies, we observe the critical (multifractal) phase of the model which is further investigated via a finite-size scaling analysis of the fractal dimension. Finally, to add depth into our study, we have performed a mean level spacing analyses and computed the Hausdorff dimension which yields specific characteristics inherent to the critical phase, offering profound insights into its underlying properties.

Signatures of hybridization of multiple Majorana zero modes in a vortex

Majorana zero modes (MZMs) are emergent zero-energy topological quasiparticles that are their own antiparticles1,2. Detected MZMs are spatially separated and electrically neutral, so producing hybridization between MZMs is extremely challenging in superconductors3,4. Here, we report the magnetic field response of vortex bound states in superconducting topological crystalline insulator SnTe (001) films. Several MZMs were predicted to coexist in a single vortex due to magnetic mirror symmetry. Using a scanning tunnelling microscope equipped with a three-axis vector magnet, we found that the zero-bias peak (ZBP) in a single vortex exhibits an apparent anisotropic response even though the magnetic field is weak. The ZBP can robustly extend a long distance of up to approximately 100 nm at the (001) surface when the magnetic field is parallel to the ( 1 1 ¯ 0 )-type mirror plane, otherwise it displays an asymmetric splitting. Our systematic simulations demonstrate that the anisotropic response cannot be reproduced with trivial ZBPs. Although the different MZMs cannot be directly distinguished due to the limited energy resolution in our experiments, our comparisons between experimental measurements and theoretical simulations strongly support the existence and hybridization of symmetry-protected multiple MZMs. Our work demonstrates a way to hybridize different MZMs by controlling the orientation of the magnetic field and expands the types of MZM available for tuning topological states.

Observation of In-Gap States in a Two-Dimensional CrI2/NbSe2 Heterostructure

Low-dimensional magnetic structures coupled with superconductors are promising platforms for realizing Majorana zero modes, which have potential applications in topological quantum computing. Here, we report a two-dimensional (2D) magnetic-superconducting heterostructure consisting of single-layer chromium diiodide (CrI2) on a niobium diselenide (NbSe2) superconductor. Single-layer CrI2 nanosheets, which hold antiferromagnetic (AFM) ground states by our first-principles calculations, were epitaxially grown on the layered NbSe2 substrate. Using scanning tunneling microscopy/spectroscopy, we observed robust in-gap states spatially located at the edge of the nanosheets and defect-induced zero-energy peaks inside the CrI2 nanosheets. Magnetic-flux vortices induced by an external field exhibit broken 3-fold rotational symmetry of the pristine NbSe2 superconductor, implying the efficient modulation of the interfacial superconducting states by the epitaxial CrI2 layer. A phenomenological model suggests the existence of chiral edge states in a 2D AFM-superconducting hybrid system with an even Chern number, providing a qualitatively plausible understanding for our experimental observation.

Charged Black-Hole-Like Electronic Structure Driven by Geometric Potential of 2D Semiconductors

One of the exotic expectations in the 2D curved spacetime is the geometric potential from the curvature of the 2D space, still possessing unsolved fundamental questions through Dirac quantization. The atomically thin 2D materials are promising for the realization of the geometric potential, but the geometric potential in 2D materials is not identified experimentally. Here, the curvature-induced ring-patterned bound states are observed in structurally deformed 2D semiconductors and formulated the modified geometric potential for the curvature effect, which demonstrates the ring-shape bound states with angular momentum. The formulated modified geometric potential is analogous to the effective potential of a rotating charged black hole. Density functional theory and tight-binding calculations are performed, which quantitatively agree well with the results of the modified geometric potential. The modified geometric potential is described by modified Gaussian and mean curvatures, corresponding to the curvature-induced changes in spin-orbit interaction and band gap, respectively. Even for complex structural deformation, the geometric potential solves the complexity, which aligns well with experimental results. The understanding of the modified geometric potential provides us with an intuitive clue for quantum transport and a key factor for new quantum applications such as valleytronics, spintronics, and straintronics in 2D semiconductors.

Resonant exchange of chiral Majorana Fermions modulated by two parallel quantum dots

Resonant exchange of the chiral Majorana fermions (MFs) that is coupled to two parallel Majorana zero modes (MZMs) or two parallel quantum dots (QDs) is investigated. We find that, in the two QDs coupling case, the resonant exchange for the chiral MFs is analogous to that in the MZM coupling case. We further propose a circuit based on topological superconductor, which is formed by the proximity coupling of a quantum anomalous Hall insulator and a s-wave superconductor, to observe the resonant exchange of chiral MFs pairs. The numerical calculations show that the resonant transmission of the chiral MFs can be adjusted by varying the coupling parameters at superconductor phase differenceΔφ=π. It is particularly noteworthy that, by only modulating the coupling strength between the two QDs, the resonant exchange may be switched on or off. By adding another MZM, the non-Abelian braiding like operation can be realized. Therefore, our design scheme may provide another way for non-Abelian braiding operation of MFs and the findings may have potential application value in the realization of topological quantum computers.

Quantum spin driven Yu-Shiba-Rusinov multiplets and fermion-parity-preserving phase transition in K3C60

Magnetic impurities in superconductors are of increasing interest due to emergent Yu-Shiba-Rusinov (YSR) states and Majorana zero modes for fault-tolerant quantum computation. However, a direct relationship between the YSR multiple states and magnetic anisotropy splitting of quantum impurity spins remains poorly characterized. By using scanning tunneling microscopy, we systematically resolve individual transition-metal (Fe, Cr, and Ni) impurities induced YSR multiplets as well as their Zeeman effects in the K3C60 superconductor. The YSR multiplets show identical d orbital-like wave functions that are symmetry-mismatched to the threefold K3C60(1 1 1) host surface, breaking point-group symmetries of the spatial distribution of YSR bound states in real space. Remarkably, we identify an unprecedented fermion-parity-preserving quantum phase transition between ground states with opposite signs of the uniaxial magnetic anisotropy that can be manipulated by an external magnetic field. These findings can be readily understood in terms of anisotropy splitting of quantum impurity spins, and thus elucidate the intricate interplay between the magnetic anisotropy and YSR multiplets.

Implementation of the Su-Schrieffer-Heeger Model in the Self-Assembly Si-In Atomic Chains on the Si(553)-Au Surface

Indium-decorated Si atomic chains on a stepped Si(553)-Au substrate are proposed as an extended Su-Schrieffer-Heeger (SSH) model, revealing topological end states. An appropriate amount of In atoms on the Si(553)-Au surface induce the self-assembly formation of trimer SSH chains, where the chain unit cell comprises one In atom and two Si atoms, confirmed by scanning tunneling microscopy images and density functional calculations. The electronic structure of the system, examined through scanning tunneling spectroscopy, manifests three electron bands within the Si-In chain, accompanied by additional midgap topological states exclusively appearing at the chain's end atoms. To elucidate the emergence of these topological states, a tight-binding model for a finite-length-extended SSH chain is proposed. Analysis of the energy spectra, density of states functions, and eigenfunctions demonstrates the topological nature of these self-assembled atomic chains.

Topologically trivial gap-filling in superconducting Fe(Se,Te) by one-dimensional defects

Structural distortions and imperfections are a crucial aspect of materials science, on the macroscopic scale providing strength, but also enhancing corrosion and reducing electrical and thermal conductivity. At the nanometre scale, multi-atom imperfections, such as atomic chains and crystalline domain walls have conversely been proposed as a route to topological superconductivity, whose most prominent characteristic is the emergence of Majorana Fermions that can be used for error-free quantum computing. Here, we shed more light on the nature of purported domain walls in Fe(Se,Te) that may host 1D dispersing Majorana modes. We show that the displacement shift of the atomic lattice at these line-defects results from sub-surface impurities that warp the topmost layer(s). Using the electric field between the tip and sample, we manage to reposition the sub-surface impurities, directly visualizing the displacement shift and the underlying defect-free lattice. These results, combined with observations of a completely different type of 1D defect where superconductivity remains fully gapped, highlight the topologically trivial nature of 1D defects in Fe(Se,Te).

Shaping Graphene Superconductivity with Nanometer Precision

Graphene holds great potential for superconductivity due to its pure 2D nature, the ability to tune its carrier density through electrostatic gating, and its unique, relativistic-like electronic properties. At present, still far from controlling and understanding graphene superconductivity, mainly because the selective introduction of superconducting properties to graphene is experimentally very challenging. Here, a method is developed that enables shaping at will graphene superconductivity through a precise control of graphene-superconductor junctions. The method combines the proximity effect with scanning tunnelling microscope (STM) manipulation capabilities. Pb nano-islands are first grown that locally induce superconductivity in graphene. Using a STM, Pb nano-islands can be selectively displaced, over different types of graphene surfaces, with nanometre scale precision, in any direction, over distances of hundreds of nanometres. This opens an exciting playground where a large number of predefined graphene-superconductor hybrid structures can be investigated with atomic scale precision. To illustrate the potential, a series of experiments are performed, rationalized by the quasi-classical theory of superconductivity, going from the fundamental understanding of superconductor-graphene-superconductor heterostructures to the construction of superconductor nanocorrals, further used as "portable" experimental probes of local magnetic moments in graphene.

Correlation between two distant quasiparticles in separate superconducting islands mediated by a single spin

Controlled coupling between distant particles is a key requirement for the implementation of quantum information technologies. A promising platform are hybrid systems of semiconducting quantum dots coupled to superconducting islands, where the tunability of the dots is combined with the macroscopic coherence of the islands to produce states with non-local correlations, e.g. in Cooper pair splitters. Electrons in hybrid quantum dots are typically not amenable to long-distance spin alignment as they tend to be screened into a localized singlet state by bound superconducting quasiparticles. However, two quasiparticles coming from different superconductors can overscreen the quantum dot into a doublet state, leading to ferromagnetic correlations between the superconducting islands. We present experimental evidence of a stabilized overscreened state, implying correlated quasiparticles over a micrometer distance. We propose alternating chains of quantum dots and superconducting islands as a novel platform for controllable large-scale spin coupling.

Topological band inversion and chiral Majorana mode in hcp thallium

The chiral Majorana fermion is an exotic particle that is its own antiparticle. It can arise in a one-dimensional edge of topological materials, and especially that in a topological superconductor can be exploited in non-Abelian quantum computation. While the chiral Majorana mode (CMM) remains elusive, a promising situation is realized when superconductivity coexists with a topologically non-trivial surface state. Here, we perform fully non-empirical calculation for the CMM considering superconductivity and surface relaxation, and show that hexagonal close-packed thallium (Tl) has an ideal electronic state that harbors the CMM. Thekz=0plane of Tl is a mirror plane, realizing a full-gap band inversion corresponding to a topological crystalline insulating phase. Its surface and hinge are stable and easy to make various structures. Another notable feature is that the surface Dirac point is very close to the Fermi level, so that a small Zeeman field can induce a topological transition. Our calculation indicates that Tl will provide a new platform of the Majorana fermion.

Chemical Bonding Induces One-Dimensional Physics in Bulk Crystal BiIr4Se8

One-dimensional (1D) systems persist as some of the most interesting because of the rich physics that emerges from constrained degrees of freedom. A desirable route to harness the properties therein is to grow bulk single crystals of a physically three-dimensional (3D) but electronically 1D compound. Most bulk compounds which approach the electronic 1D limit still field interactions across the other two crystallographic directions and, consequently, deviate from the 1D models. In this paper, we lay out chemical concepts to realize the physics of 1D models in 3D crystals. These are based on both structural and electronic arguments. We present BiIr4Se8, a bulk crystal consisting of linear Bi2+ chains within a scaffolding of IrSe6 octahedra, as a prime example. Through crystal structure analysis, density functional theory calculations, X-ray diffraction, and physical property measurements, we demonstrate the unique 1D electronic configuration in BiIr4Se8. This configuration at ambient temperature is a gapped Su-Schriefer-Heeger system, generated by way of a canonical Peierls distortion involving Bi dimerization that relieves instabilities in a 1D metallic state. At 190 K, an additional 1D charge density wave distortion emerges, which affects the Peierls distortion. The experimental evidence validates our design principles and distinguishes BiIr4Se8 among other quasi-1D bulk compounds. We thus show that it is possible to realize unique electronically 1D materials applying chemical concepts.

Electrostatic potentials of atomic nanostructures at metal surfaces quantified by scanning quantum dot microscopy

The discrete and charge-separated nature of matter - electrons and nuclei - results in local electrostatic fields that are ubiquitous in nanoscale structures and relevant in catalysis, nanoelectronics and quantum nanoscience. Surface-averaging techniques provide only limited experimental access to these potentials, which are determined by the shape, material, and environment of the nanostructure. Here, we image the potential over adatoms, chains, and clusters of Ag and Au atoms assembled on Ag(111) and quantify their surface dipole moments. By focusing on the total charge density, these data establish a benchmark for theory. Our density functional theory calculations show a very good agreement with experiment and allow a deeper analysis of the dipole formation mechanisms, their dependence on fundamental atomic properties and on the shape of the nanostructures. We formulate an intuitive picture of the basic mechanisms behind dipole formation, allowing better design choices for future nanoscale systems such as single-atom catalysts.

Atomic Diffusion-Induced Polarization and Superconductivity in Topological Insulator-Based Heterostructures

The proximity effect at a highly transparent interface of an s-wave superconductor (S) and a topological insulator (TI) provides a promising platform to create Majorana zero modes in artificially designed heterostructures. However, structural and chemical issues pertinent to such interfaces have been poorly explored so far. Here, we report the discovery of Pd diffusion-induced polarization at interfaces between superconductive Pd1+x(Bi0.4Te0.6)2 (xPBT, 0 ≤ x ≤ 1) and Pd-intercalated Bi2Te3 by using atomic-resolution scanning transmission electron microscopy. Our quantitative image analysis reveals that nanoscale lattice strain and QL polarity synergistically suppress and promote Pd diffusion at the normal and parallel interfaces, formed between Te-Pd-Bi triple layers (TLs) and Te-Bi-Te-Bi-Te quintuple layers (QLs), respectively. Further, our first-principles calculations unveil that the superconductivity of the xPBT phase and topological nature of the Pd-intercalated Bi2Te3 phase are robust against the broken inversion symmetry. These findings point out the necessity of considering the coexistence of electric polarization with superconductivity and topology in such S-TI systems.

Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors

Majorana excitations are the quasiparticle analog of Majorana fermions in solid materials. Typical examples are the Majorana zero modes (MZMs) and the dispersing Majorana modes. When probed by scanning tunneling spectroscopy, the former manifest as a pronounced conductance peak locating precisely at zero-energy, while the latter behaves as constant or slowly varying density of states. The MZMs obey non-abelian statistics and are believed to be building blocks for topological quantum computing, which is highly immune to the environmental noise. Existing MZM platforms include hybrid structures such as topological insulator, semiconducting nanowire or 1D atomic chains on top of a conventional superconductor, and single materials such as the iron-based superconductors (IBSs) and 4Hb-TaS2. Very recently, ordered and tunable MZM lattice has also been realized in IBS LiFeAs, providing a scalable and applicable platform for future topological quantum computation. In this review, we present an overview of the recent local probe studies on MZMs. Classified by the material platforms, we start with the MZMs in the iron-chalcogenide superconductors where FeTe0.55Se0.45and (Li0.84Fe0.16)OHFeSe will be discussed. We then review the Majorana research in the iron-pnictide superconductors as well as other platforms beyond the IBSs. We further review recent works on ordered and tunable MZM lattice, showing that strain is a feasible tool to tune the topological superconductivity. Finally, we give our summary and perspective on future Majorana research.

Quantum Phase Transition in Magnetic Nanographenes on a Lead Superconductor

Quantum spins, also known as spin operators that preserve SU(2) symmetry, lack a specific orientation in space and are hypothesized to display unique interactions with superconductivity. However, spin-orbit coupling and crystal field typically cause a significant magnetic anisotropy in d/f shell spins on surfaces. Here, we fabricate atomically precise S = 1/2 magnetic nanographenes on Pb(111) through engineering sublattice imbalance in the graphene honeycomb lattice. Through tuning the magnetic exchange strength between the unpaired spin and Cooper pairs, a quantum phase transition from the singlet to the doublet state has been observed, consistent with the quantum spin models. From our calculations, the particle-hole asymmetry is induced by the Coulomb scattering potential and gives a transition point about kBTk ≈ 1.6Δ. Our work demonstrates that delocalized π electron magnetism hosts highly tunable magnetic bound states, which can be further developed to study the Majorana bound states and other rich quantum phases of low-dimensional quantum spins on superconductors.

Dirac-fermion-assisted interfacial superconductivity in epitaxial topological-insulator/iron-chalcogenide heterostructures

Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement. TSC can be created in electronic systems where the topological and superconducting orders coexist, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb)2Te3. By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer.

Intrinsic surface p-wave superconductivity in layered AuSn4

The search for topological superconductivity (TSC) is currently an exciting pursuit, since non-trivial topological superconducting phases could host exotic Majorana modes. However, the difficulty in fabricating proximity-induced TSC heterostructures, the sensitivity to disorder and stringent topological restrictions of intrinsic TSC place serious limitations and formidable challenges on the materials and related applications. Here, we report a new type of intrinsic TSC, namely intrinsic surface topological superconductivity (IS-TSC) and demonstrate it in layered AuSn4 with Tc of 2.4 K. Different in-plane and out-of-plane upper critical fields reflect a two-dimensional (2D) character of superconductivity. The two-fold symmetric angular dependences of both magneto-transport and the zero-bias conductance peak (ZBCP) in point-contact spectroscopy (PCS) in the superconducting regime indicate an unconventional pairing symmetry of AuSn4. The superconducting gap and surface multi-bands with Rashba splitting at the Fermi level (EF), in conjunction with first-principle calculations, strongly suggest that 2D unconventional SC in AuSn4 originates from the mixture of p-wave surface and s-wave bulk contributions, which leads to a two-fold symmetric superconductivity. Our results provide an exciting paradigm to realize TSC via Rashba effect on surface superconducting bands in layered materials.

Emergent superconductivity in topological-kagome-magnet/metal heterostructures

Itinerant kagome lattice magnets exhibit many novel correlated and topological quantum electronic states with broken time-reversal symmetry. Superconductivity, however, has not been observed in this class of materials, presenting a roadblock in a promising path toward topological superconductivity. Here, we report that novel superconductivity can emerge at the interface of kagome Chern magnet TbMn6Sn6 and metal heterostructures when elemental metallic thin films are deposited on either the top (001) surface or the side surfaces. Superconductivity is also successfully induced and systematically studied by using various types of metallic tips on different TbMn6Sn6 surfaces in point-contact measurements. The anisotropy of the superconducting upper critical field suggests that the emergent superconductivity is quasi-two-dimensional. Remarkably, the interface superconductor couples to the magnetic order of the kagome metal and exhibits a hysteretic magnetoresistance in the superconducting states. Taking into account the spin-orbit coupling, the observed interface superconductivity can be a surprising and more realistic realization of the p-wave topological superconductors theoretically proposed for two-dimensional semiconductors proximity-coupled to s-wave superconductors and insulating ferromagnets. Our findings of robust superconductivity in topological-Chern-magnet/metal heterostructures offer a new direction for investigating spin-triplet pairing and topological superconductivity.

Evidence of Nodal Superconductivity in Monolayer 1H-TaS2 with Hidden Order Fluctuations

Unconventional superconductors represent one of the fundamental directions in modern quantum materials research. In particular, nodal superconductors are known to appear naturally in strongly correlated systems, including cuprate superconductors and heavy-fermion systems. Van der Waals materials hosting superconducting states are well known, yet nodal monolayer van der Waals superconductors have remained elusive. Here, using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) experiments, it is shown that pristine monolayer 1H-TaS2 realizes a nodal superconducting state. Non-magnetic disorder drives the nodal superconducting state to a conventional gapped s-wave state. Furthermore, many-body excitations emerge close to the gap edge, signalling a potential unconventional pairing mechanism. The results demonstrate the emergence of nodal superconductivity in a van der Waals monolayer, providing a building block for van der Waals heterostructures exploiting unconventional superconducting states.

Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices

Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.

Spin-polarized Majorana zero modes in proximitized superconducting penta-silicene nanoribbons

We theoretically propose penta-silicene nanoribbons (p-SiNRs) with induced p-wave superconductivity as a platform for the emergence of spin-polarized Majorana zero-modes (MZMs). The model explicitly considers the key ingredients of well-known Majorana hybrid nanowire setups: Rashba spin-orbit coupling, magnetic field perpendicular to the nanoribbon plane, and first nearest neighbor hopping with p-wave superconducting pairing. The energy spectrum of the system, as a function of chemical potential, reveals the existence of MZMs with a well-defined spin orientation localized at the opposite ends of both the top and bottom chains of the p-SiNR, associated with well-localized and nonoverlapping wave function profiles. Well-established experimental techniques enable the fabrication of highly ordered p-SiNRs, complemented by a thin lead film on top, responsible for inducing p-wave superconductivity through proximity effect. Moreover, the emergence of MZMs with explicit opposite spin orientations for some set of model parameters opens a new avenue for exploring quantum computing operations, which accounts for both MZMs and spin properties, as well as for new MZMs probe devices based on spin-polarized electronic transport mechanisms.

Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene

Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayer WSe_{2} revealed robust, ultraclean superconductivity coexisting with sizable induced spin-orbit coupling. Here, we propose BLG/WSe_{2} as a platform to engineer gate-defined planar topological Josephson junctions, where the normal and superconducting regions descend from a common material. More precisely, we show that if superconductivity in BLG/WSe_{2} is gapped and emerges from a parent state with intervalley coherence, then Majorana zero-energy modes can form in the barrier region upon applying weak in-plane magnetic fields. Our results spotlight a potential pathway for "internally engineered" topological superconductivity that minimizes detrimental disorder and orbital-magnetic-field effects.

Topological Superconductors from a Materials Perspective

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

Majorana Excitons in a Kitaev Chain of Semiconductor Quantum Dots in a Nanowire

We present here a theory of Majorana excitons, photo-excited conduction electron-valence band hole pairs, interacting with Majorana Fermions in a Kitaev chain of semiconductor quantum dots embedded in a nanowire. Using analytical tools and exact diagonalization methods, we identify the presence of Majorana zero modes in the nanowire absorption spectra.

Control of the Magnetic Interaction between Single-Molecule Magnet TbPc2 and Superconductor NbSe2 Surface by an Intercalated Co Atom

We demonstrate that an intercalated Co atom in superconductor NbSe2 could control the magnetic interaction between the adsorbed magnetic molecule of TbPc2 and the NbSe2 substrate. An intercalated Co atom enhances the magnetic interaction between the NbSe2 and the TbPc2 spin to cause Kondo resonance at the TbPc2 position, a spin-singlet state formed by the itinerary electron. By applying a surface-normal magnetic field, we change the molecule's spin direction from the initial one directed to the Co atom to the surface normal. The change appears as a split Kondo resonance at the TbPc2, one of which is enhanced at the Tb site, which disappears when the outer magnetic field normal to the surface is applied and never appears, even if we return B to 0 T. The phenomenon suggests that the intercalated magnetic atoms can control the magnetic interaction between a magnetic molecule and the superconductor NbSe2.

Full counting statistics, fluctuation relations, and linear response properties in a one-dimensional Kitaev chain

We analytically calculate the cumulant generating function of energy and particle transport in an open one-dimensional Kitaev chain at finite temperature by utilizing the Keldysh technique. The joint distribution of particle and energy currents satisfies different fluctuation relations in different regions of the parameter space as a result of U(1) symmetry breaking and energy conservation. Furthermore, we investigate the linear response behavior of the Kitaev chain within the framework of three-terminal systems, deriving the expressions for the Seebeck coefficient and thermal conductance. Notably, we observe a pronounced peak in the thermal conductance near the phase transition point, in agreement with previous predictions. Additionally, we prove that the peak value saturates at half of the thermal conductance quantum for finite-length chains at the zero temperature limit.