Experimental evidence for s-wave pairing symmetry in superconducting Cu(x)Bi2Se3 single crystals using a scanning tunneling microscope

Creation, stabilization, and investigation at ambient pressure of pressure-induced superconductivity in Bi0.5Sb1.5Te3

In light of breakthroughs in superconductivity under high pressure, and considering that record critical temperatures (Tcs) across various systems have been achieved under high pressure, the primary challenge for higher Tc should no longer solely be to increase Tc under extreme conditions but also to reduce, or ideally eliminate, the need for applied pressure in retaining pressure-induced or -enhanced superconductivity. The topological semiconductor Bi0.5Sb1.5Te3 (BST) was chosen to demonstrate our approach to addressing this challenge and exploring its intriguing physics. Under pressures up to ~50 GPa, three superconducting phases (BST-I, -II, and -III) were observed. A superconducting phase in BST-I appears at ~4 GPa, without a structural transition, suggesting the possible topological nature of this phase. Using the pressure-quench protocol (PQP) recently developed by us, we successfully retained this pressure-induced phase at ambient pressure and revealed the bulk nature of the state. Significantly, this demonstrates recovery of a pressure-quenched sample from a diamond anvil cell at room temperature with the pressure-induced phase retained at ambient pressure. Other superconducting phases were retained in BST-II and -III at ambient pressure and subjected to thermal and temporal stability testing. Superconductivity was also found in BST with Tc up to 10.2 K, the record for this compound series. While PQP maintains superconducting phases in BST at ambient pressure, both depressurization and PQP enhance its Tc, possibly due to microstructures formed during these processes, offering an added avenue to raise Tc. These findings are supported by our density-functional theory calculations.

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.

Emergent Majorana zero-modes in an intrinsic anti-ferromagnetic topological superconductor Mn2B2 monolayer

Topological superconductors (TSCs) are an exotic field due to the existence of Majorana zero-modes (MZM) in the edge states that obey non-Abelian statistics and can be used to implement topological quantum computations, especially for two-dimensional (2D) materials. Here we predict manganese diboride (Mn₂B₂) as an intrinsic 2D anti-ferromagnetic (AFM) TSC based on the magnetic and electronic structures of Mn and B atoms. Once Mn₂B₂ ML enters a superconducting state, MZM will be induced by the spin-polarized helical gapless edge states. The Z₂ topological non-trivial properties are confirmed by Wannier charge centers (WCC) and the platform of the spin Hall conductivity near the Fermi level. Phonon-electron coupling (EPC) implies s-wave superconductivity and the critical temperature (T_c) is 6.79 K.

Pressure-Induced Electronic Topological Transition and Superconductivity in Topological Insulator Bi2Te2.1Se0.9

One approach to discovering topological superconductors is establishing superconductivity based on well-identified topological insulators. However, the coexistence of superconductivity and a topological state is always arcane. In this paper, we report how pressure tunes the crystal structure, electronic structure, and superconductivity in topological insulator Bi₂Te_2.1Se_0.9. At ∼2.5 GPa, the abnormal changes in c/a and the full width at half-maximum of the A_1g¹ mode indicate the occurrence of an electronic topological transition. The pressure-induced superconductivity in Bi₂Te_2.1Se_0.9 pinned with an electronic topological transition presents at 2.4 GPa, which is far below the structural phase transition pressure of 8.4 GPa. These results suggest that the appearance of an electronic topological transition is closely correlated with superconductivity in the initial phase, where the topological surface state persists. Our work clarifies the complex electronic structure of Bi₂Te_2.1Se_0.9 and sheds light on the mechanism for superconductivity in topological insulators.

A millikelvin scanning tunneling microscope in ultra-high vacuum with adiabatic demagnetization refrigeration

We present the design and performance of an ultra-high vacuum scanning tunneling microscope (STM) that uses adiabatic demagnetization of electron magnetic moments for controlling its operating temperature ranging between 30 mK and 1 K with an accuracy of up to 7 μK rms. At the same time, high magnetic fields of up to 8 T can be applied perpendicular to the sample surface. The time available for STM experiments at 50 mK is longer than 20 h, at 100 mK about 40 h. The single-shot adiabatic demagnetization refrigerator can be regenerated automatically within 7 h while keeping the STM temperature below 5 K. The whole setup is located in a vibrationally isolated, electromagnetically shielded laboratory with no mechanical pumping lines penetrating its isolation walls. The 1 K pot of the adiabatic demagnetization refrigeration cryostat can be operated silently for more than 20 days in a single-shot mode using a custom-built high-capacity cryopump. A high degree of vibrational decoupling together with the use of a specially designed minimalistic STM head provides outstanding mechanical stability, demonstrated by the tunneling current noise, STM imaging, and scanning tunneling spectroscopy measurements, all performed on an atomically clean Al(100) surface.

Robust Zero Energy Modes on Superconducting Bismuth Islands Deposited on Fe(Te,Se)

Topological superconductivity is one of the frontier research directions in condensed matter physics. One of the unique elementary excitations in topological superconducting state is the Majorana Fermion (mode) which is its own antiparticle and obeys the non-Abelian statistics and is thus useful for constructing the fault-tolerant quantum computation. The evidence for Majorana Fermions (mode) in condensed matter is now quickly accumulated. We deposit Bi islands on the iron-based superconductors Fe(Te,Se) and find the easily achievable zero energy modes on the tunneling spectra on some Bi islands. The zero energy mode is robust and appears everywhere on the island. Temperature and magnetic field dependence of the zero energy mode are also investigated. We attribute these zero energy modes to the Majorana modes due to the proximity effect-induced topological superconductivity on the Bi islands with strong spin-orbit coupling effect.

Power-Law Temperature Dependence of the Penetration Depth in a Topological Superconductor Due to Surface States

We study the temperature dependence of the magnetic penetration depth in a 3D topological superconductor (TSC), incorporating the paramagnetic current due to the surface states. A TSC is predicted to host a gapless 2D surface Majorana fluid. In addition to the bulk-dominated London response, we identify a T^{3} power-law-in-temperature contribution from the surface, valid in the low-temperature limit. Our system is fully gapped in the bulk, and should be compared to bulk nodal superconductivity, which also exhibits power-law behavior. Power-law temperature dependence of the penetration depth can be one indicator of topological superconductivity.

Direction and symmetry transition of the vector order parameter in topological superconductors CuxBi2Se3

Topological superconductors have attracted wide-spreading interests for the bright application perspectives to quantum computing. Cu0.3Bi2Se3 is a rare bulk topological superconductor with an odd-parity wave function, but the details of the vector order parameter d and its pinning mechanism are still unclear. Here, we succeed in growing CuxBi2Se3 single crystals with unprecedented high doping levels. For samples with x  = 0.28, 0.36 and 0.37 with similar carrier density as evidenced by the Knight shift, the in-plane upper critical field Hc2 shows a two-fold symmetry. However, the angle at which the Hc2 becomes minimal is different by 90° among them, which indicates that the d-vector direction is different for each crystal likely due to a different local environment. The carrier density for x  = 0.46 and 0.54 increases substantially compared to x ≤ 0.37. Surprisingly, the in-plane Hc2 anisotropy disappears, indicating that the gap symmetry undergoes a transition from nematic to isotropic (possibly chiral) as carrier increases.

Visualizing pairing symmetry in nematic superconductors using spin-polarized spectroscopy of magnetic impurities

We study the spin-polarized spectral properties of Yu-Shiba-Rusinov resonance states induced by magnetic impurities in 2- and 3-dimensional nematic superconductors: few layer Bi₂Te₃ grown on FeTe_0.55Se_0.45 (2D) and Cu _x Bi₂Se₃ (3D). We focus on the relationship between pairing symmetry and the spatial structure of spin-polarized spectroscopy. We calculate the spin-polarized local density of states (SP LDOS) and the corresponding Fourier transformation using the T-matrix method for both the 2- and 3-dimensional materials. Various situations with different impurity orientations and different SP LDOSs have been investigated. We find that, like the quasiparticle interference spectrum, the spin-polarized spectroscopy can be applied to distinguish threefold rotation symmetric pairings, e.g. the plain s-wave pairing, chiral p -wave pairing, etc, and nematic pairings in these materials.

Superconductivity of Topological Surface States and Strong Proximity Effect in Sn1- x Pbx Te-Pb Heterostructures

Superconducting topological crystalline insulators are expected to form a new type of topological superconductors to host Majorana zero modes under the protection of lattice symmetries. The bulk superconductivity of topological crystalline insulators can be induced through chemical doping and the proximity effect. However, only conventional full gaps are observed, so the existence of topological superconductivity in topological crystalline insulators is still controversial. Here, the successful fabrication of atomically flat lateral and vertical Sn_{1- x} Pb_x Te-Pb heterostructures by molecular beam epitaxy is reported. The superconductivity of the Sn_{1- x} Pb_x Te-Pb heterostructures can be directly investigated by scanning tunneling spectroscopy. Unconventional peak-dip-hump gap features and fourfold symmetric quasiparticle interference patterns taken at the zero energy in the superconducting gap support the presence of the topological superconductivity in superconducting Sn_{1- x} Pb_x Te. Strong superconducting proximity effect and easy preparation of various constructions between Sn_{1- x} Pb_x Te and Pb make the heterostructures to be a promising candidate for topological superconducting devices to detect and manipulate Majorana zero modes in the future.

Superconductivity in Cu Co-Doped SrxBi2Se3 Single Crystals

In this study, we grew Cu co-doped single crystals of a topological superconductor candidate SrxBi2Se3, and studied their structural and transport properties. We reveal that the addition of even as small an amount of Cu co-dopant as 0.6 atomic %, completely suppresses superconductivity in SrxBi2Se3. Critical temperature (∼2.7 K) is rather robust with respect to co-doping. We show that Cu systematically increases the electron density and lattice parameters a and c. Our results demonstrate that superconductivity in SrxBi2Se3-based materials is induced by significantly lower Sr doping level x<0.02 than commonly accepted x∼0.06, and it strongly depends on the specific arrangement of Sr atoms in the host matrix. The critical temperature in superconductive Sr-doped Bi2Se3 is shown to be insensitive to carrier density.

Layer-Stacking, Defects, and Robust Superconductivity on the Mo-Terminated Surface of Ultrathin Mo2C Flakes Grown by CVD

Materials can exhibit exotic properties when they approach the two-dimensional (2D) limit. Because of promising applications in catalysis and energy storage, 2D transition-metal carbides (TMCs) have attracted considerable attention in recent years. Among these TMCs, ultrathin crystalline α-Mo₂C flakes have been fabricated by chemical vapor deposition on Cu/Mo bilayer foils, and their 2D superconducting property was revealed by transport measurements. Herein, we studied the ultrathin α-Mo₂C flakes by atomic-resolved scanning tunneling microscopy/spectroscopy (STM/S). Strain-related structural modulation and the coexistence of different layer-stacking modes are observed on the Mo-terminated surface of α-Mo₂C flakes as well as various lattice defects. Furthermore, an enhanced superconductivity with shorter correlation length was observed by STS technique, and such superconductivity is very robust despite the appearance of the defects. A mechanism of superconducting enhancement is proposed based on the strain-induced strong coupling and the increased disordering originated from lattice defects. Our results provide a comprehensive understanding of the correlations between atomic structure, defects, and enhanced superconductivity of this emerging 2D material.

Topological quantum states of matter in iron-based superconductors: from concept to material realization

We review recent progress in the exploration of topological quantum states of matter in iron-based superconductors. In particular, we focus on the non-trivial topology existing in the band structures and superconducting states of iron's 3d orbitals. The basic concepts, models, materials and experimental results are reviewed. The natural integration between topology and high-temperature superconductivity in iron-based superconductors provides great opportunities to study topological superconductivity and Majorana modes at high temperature.

Conductance Spectroscopy of Exfoliated Thin Flakes of Nb xBi2Se3

We study unconventional superconductivity in exfoliated single crystals of a promising three-dimensional (3D) topological superconductor candidate, Nb-doped Bi₂Se₃ through differential conductance spectroscopy and magneto-transport. The strong anisotropy of the critical field along the out-of-plane direction suggests that the thin exfoliated flakes are in the quasi-2D limit. Normal metal-superconductor (NS) contacts with either high or low transparencies made by depositing gold leads onto Nb-doped Bi₂Se₃ flakes both show significant enhancement in zero bias conductance and coherence dips at the superconducting energy gap. Such behavior is inconsistent with conventional Blonder-Tinkham-Klapwijk theory. Instead, we discuss how our results are consistent with p-wave pairing symmetry, supporting the possibility of topological superconductivity in Nb-doped Bi₂Se₃. Finally, we observe signatures of multiple superconducting energy gaps, which could originate from multiple Fermi surfaces reported earlier in bulk crystals.

A scanning tunneling microscope for spectroscopic imaging below 90 mK in magnetic fields up to 17.5 T

We describe the development and performance of an ultra-high vacuum scanning tunneling microscope working under combined extreme conditions of ultra-low temperatures and high magnetic fields. We combined a top-loading dilution refrigerator and a standard bucket dewar with a bottom-loading superconducting magnet to achieve 4.5 days operating time, which is long enough to perform various spectroscopic-imaging measurements. To bring the effective electron temperature closer to the mixing-chamber temperature, we paid particular attention to filtering out radio-frequency noise, as well as enhancing the thermal link between the microscope unit and the mixing chamber. We estimated the lowest effective electron temperature to be below 90 mK by measuring the superconducting-gap spectrum of aluminum. We confirmed the long-term stability of the spectroscopic-imaging measurement by visualizing superconducting vortices in the cuprate superconductor Bi₂Sr₂CaCu₂O_8+δ .

Evidence for Majorana bound states in an iron-based superconductor

The search for Majorana bound states (MBSs) has been fueled by the prospect of using their non-Abelian statistics for robust quantum computation. Two-dimensional superconducting topological materials have been predicted to host MBSs as zero-energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron-based superconductor FeTe_0.55Se_0.45, we observed a sharp zero-bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temperature, and tunneling barrier is consistent with the tunneling to a nearly pure MBS, separated from nontopological bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temperature.

Superconductivity with twofold symmetry in Bi2Te3/FeTe0.55Se0.45 heterostructures

Topological superconductors are an interesting and frontier topic in condensed matter physics. In the superconducting state, an order parameter will be established with the basic or subsidiary symmetry of the crystalline lattice. In doped Bi₂Se₃ or Bi₂Te₃ with a basic threefold symmetry, it was predicted, however, that bulk superconductivity with order parameters of twofold symmetry may exist because of the presence of odd parity. We report the proximity effect-induced superconductivity in the Bi₂Te₃ thin film on top of the iron-based superconductor FeTe_0.55Se_0.45. By using the quasiparticle interference technique, we demonstrate clear evidence of twofold symmetry of the superconducting gap. The gap minimum is along one of the main crystalline axes following the so-called Δ_4y notation. This is also accompanied by the elongated vortex shape mapped out by the density of states within the superconducting gap. Our results provide an easily accessible platform for investigating possible topological superconductivity in Bi₂Te₃/FeTe_0.55Se_0.45 heterostructures.

Mechanism for Unconventional Superconductivity in the Hole-Doped Rashba-Hubbard Model

Motivated by the recent resurgence of interest in topological superconductivity, we study superconducting pairing instabilities of the hole-doped Rashba-Hubbard model on the square lattice with first- and second-neighbor hopping. Within the random phase approximation, we compute the spin-fluctuation-mediated pairing interactions as a function of filling. Rashba spin-orbit coupling splits the spin degeneracies of the bands, which leads to two van Hove singularities at two different fillings. We find that, for a doping region in between these two van Hove fillings, the spin fluctuations exhibit a strong ferromagnetic contribution. Because of these ferromagnetic fluctuations, there is a strong tendency towards spin-triplet f-wave pairing within this filling region, resulting in a topologically nontrivial phase.

Fermiology and Superconductivity of Topological Surface States in PdTe_{2}

We study the low-energy surface electronic structure of the transition-metal dichalcogenide superconductor PdTe_{2} by spin- and angle-resolved photoemission, scanning tunneling microscopy, and density-functional theory-based supercell calculations. Comparing PdTe_{2} with its sister compound PtSe_{2}, we demonstrate how enhanced interlayer hopping in the Te-based material drives a band inversion within the antibonding p-orbital manifold well above the Fermi level. We show how this mediates spin-polarized topological surface states which form rich multivalley Fermi surfaces with complex spin textures. Scanning tunneling spectroscopy reveals type-II superconductivity at the surface, and moreover shows no evidence for an unconventional component of its superconducting order parameter, despite the presence of topological surface states.

Observation of topological superconductivity on the surface of an iron-based superconductor

Topological superconductors are predicted to host exotic Majorana states that obey non-Abelian statistics and can be used to implement a topological quantum computer. Most of the proposed topological superconductors are realized in difficult-to-fabricate heterostructures at very low temperatures. By using high-resolution spin-resolved and angle-resolved photoelectron spectroscopy, we find that the iron-based superconductor FeTe_1-x Se _x (x = 0.45; superconducting transition temperature T_c = 14.5 kelvin) hosts Dirac-cone-type spin-helical surface states at the Fermi level; the surface states exhibit an s-wave superconducting gap below T_c Our study shows that the surface states of FeTe_0.55Se_0.45 are topologically superconducting, providing a simple and possibly high-temperature platform for realizing Majorana states.

Growth and structural characterisation of Sr-doped Bi2Se3 thin films

We grew Sr-doped Bi2Se3 thin films using molecular beam epitaxy, and their high quality was verified using transmission electron microscopy. The thin films exhibited weak antilocalisation behaviours in magneto-resistance measurements, a typical transport signature of topological insulators, but were not superconducting. In addition, the carrier densities of the non-superconducting thin-film samples were similar to those of their superconducting bulk counterparts. Atom-by-atom energy-dispersive X-ray mapping also revealed similar Sr doping structures in the bulk and thin-film samples. Because no qualitative distinction between non-superconducting thin-film and superconducting bulk samples had been found, we turned to a quantitative statistical analysis, which uncovered a key structural difference between the bulk and thin-film samples. The separation between Bi layers in the same quintuple layer was compressed whereas that between the closest Bi layers in two neighbouring quintuple layers was expanded in the thin-film samples compared with the separations in pristine bulk Bi2Se3. In marked contrast, the corresponding changes in the bulk doped samples showed opposite trends. These differences may provide insight into the absence of superconductivity in doped topological insulator thin films.

Topological Phase Transitions in Multicomponent Superconductors

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology, and energetics, we show that for a generic normal state band structure, the phase transition occurs via extended intermediate phases in which even- and odd-parity pairing components coexist. For inversion-symmetric systems, the coexistence phase spontaneously breaks time-reversal symmetry. For noncentrosymmetric superconductors, the low-temperature intermediate phase is time-reversal breaking, while the high-temperature phase preserves time-reversal symmetry and has topologically protected line nodes. Furthermore, with approximate rotational invariance, the system has an emergent U(1)×U(1) symmetry, and novel topological defects, such as half vortex lines binding Majorana fermions, can exist. We analytically solve for the dispersion of the Majorana fermion and show that it exhibits small and large velocities at low and high energies. Relevance of our theory to superconducting pyrochlore oxide Cd_{2}Re_{2}O_{7} and half-Heusler materials is discussed.

Full-gap superconductivity in spin-polarised surface states of topological semimetal β-PdBi2

A bulk superconductor possessing a topological surface state at the Fermi level is a promising system to realise long-sought topological superconductivity. Although several candidate materials have been proposed, experimental demonstrations concurrently exploring spin textures and superconductivity at the surface have remained elusive. Here we perform spectroscopic-imaging scanning tunnelling microscopy on the centrosymmetric superconductor β-PdBi2 that hosts a topological surface state. By combining first-principles electronic-structure calculations and quasiparticle interference experiments, we determine the spin textures at the surface, and show not only the topological surface state but also all other surface bands exhibit spin polarisations parallel to the surface. We find that the superconducting gap fully opens in all the spin-polarised surface states. This behaviour is consistent with a possible spin-triplet order parameter expected for such in-plane spin textures, but the observed superconducting gap amplitude is comparable to that of the bulk, suggesting that the spin-singlet component is predominant in β-PdBi2.Although several materials have been proposed as topological superconductors, spin textures and superconductivity at the surface remain elusive. Here, Iwaya et al. determine the spin textures at the surface of a superconductor β-PdBi2 and find the superconducting gap opening in all spin-polarised surface states.

Highly tunable time-reversal-invariant topological superconductivity in topological insulator thin films

We study time-reversal-invariant topological superconductivity in topological insulator (TI) thin films including both intra- and inter-surface pairing. We find a nontrivial topology for multiple different configurations. For intra-surface pairing a π-phase difference between the intra-surface pairing states is required. We show that in this case the resulting topological phase is highly tunable by both an applied electric field and varied chemical potential. For spin-singlet inter-surface pairing, a sign-changing tunnel coupling present in many TI thin films is needed, and again, the topology can be tuned by electric field or doping. Notably, we find that the required inter-surface pairing strength for achieving nontrivial topology can still be subdominant compared to the intra-surface pairing. Finally, for spin-triplet inter-surface pairing we prove that the superconducting state is always topological nontrivial. We show that thin films of Cu-doped Bi₂Se₃ will likely host such spin-triplet inter-surface pairing. Taken together, these results show that time-reversal-invariant topological superconductivity is common in superconducting TI thin films and that the topological phase and its Kramers pair of Majorana edge modes is highly tunable with an applied electric field and varied chemical potential.

Proximity-effect-induced Superconducting Gap in Topological Surface States - A Point Contact Spectroscopy Study of NbSe2/Bi2Se3 Superconductor-Topological Insulator Heterostructures

Proximity-effect-induced superconductivity was studied in epitaxial topological insulator Bi2Se3 thin films grown on superconducting NbSe2 single crystals. A point contact spectroscopy (PCS) method was used at low temperatures down to 40 mK. An induced superconducting gap in Bi2Se3 was observed in the spectra, which decreased with increasing Bi2Se3 layer thickness, consistent with the proximity effect in the bulk states of Bi2Se3 induced by NbSe2. At very low temperatures, an extra point contact feature which may correspond to a second energy gap appeared in the spectrum. For a 16 quintuple layer Bi2Se3 on NbSe2 sample, the bulk state gap value near the top surface is ~159 μeV, while the second gap value is ~120 μeV at 40 mK. The second gap value decreased with increasing Bi2Se3 layer thickness, but the ratio between the second gap and the bulk state gap remained about the same for different Bi2Se3 thicknesses. It is plausible that this is due to superconductivity in Bi2Se3 topological surface states induced through the bulk states. The two induced gaps in the PCS measurement are consistent with the three-dimensional bulk state and the two-dimensional surface state superconducting gaps observed in the angle-resolved photoemission spectroscopy (ARPES) measurement.

Topological superconductors: a review

This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.

Experimental signature of topological superconductivity and Majorana zero modes on β-Bi2Pd thin films

The search for Majorana fermions in topological superconductors is one of paramount research targets in physics today. Using a cryogenic scanning tunneling microscopy, we here report the signature of topologically nontrivial superconductivity on a single material of β-Bi₂Pd films grown by molecular beam epitaxy. The superconducting gap associated with spinless odd-parity pairing opens on the surface and appears much larger than the bulk one due to the Dirac-fermion enhanced parity mixing of surface pair potential. Zero bias conductance peaks, probably from Majorana zero modes supported by such superconducting states, are identified at magnetic vortices. The superconductivity exhibits resistance to nonmagnetic defects, characteristic of time-reversal-invariant topological superconductors. Our study reveals β-Bi₂Pd as a prime platform to generate, manipulate and braid Majorana zero modes for quantum computation.

Patterning Superconductivity in a Topological Insulator

Topologically protected states in combination with superconductivity hold great promise for quantum computing applications, but the progress on electrical transport measurements in such systems has been impeded by the difficulty of fabricating devices with reliable electrical contacts. We find that superconductivity can be patterned directly into Bi₂Se₃ nanostructures by local doping with palladium. Superconducting regions are defined by depositing palladium on top of the nanostructures using electron beam lithography followed by in situ annealing. Electrical transport measurements at low temperatures show either partial or full superconducting transition, depending on the doping conditions. Structural characterization techniques indicate that palladium remains localized in the targeted areas, making it possible to pattern superconducting circuits of arbitrary shapes in this topological material.

Degradation of topological surface state by nonmagnetic S doping in SrxBi2Se3

Research on possible topological superconductivity has grown rapidly over the past several years, from fundamental studies to the development of next generation technologies. Recently, it has been reported that the Sr_xBi₂Se₃ exhibits superconductivity with topological surface state, making this compound a promising candidate for investigating possible topological superconductivity. However, whether or not the topological surface state is robust against impurities is not clear in this system. Here we report a detailed investigation on the lattice structure, electronic and magnetic properties, as well as the topological superconducting properties of Sr_xBi₂Se_3-yS_y samples. It is found that the superconducting transition temperature keeps nearly unchanged in all samples, despite of a gradual decrease of the superconducting shielding volume fraction with increasing S doping content. Meanwhile, the Shubnikov-de Hass oscillation results of the Sr_xBi₂Se_3-yS_y samples reveal that the topological surface states are destroyed in S doped samples, suggesting the topological character is degraded by nonmagnetic dopants.

Drive the Dirac electrons into Cooper pairs in SrxBi2Se3

Topological superconductors are a very interesting and frontier topic in condensed matter physics. Despite the tremendous efforts in exploring topological superconductivity, its presence is however still under heavy debate. The Dirac electrons have been proven to exist on the surface of a topological insulator. It remains unclear whether and how the Dirac electrons fall into Cooper pairing in an intrinsic superconductor with the topological surface states. Here we show the systematic study of scanning tunnelling microscope/spectroscopy on the possible topological superconductor Sr_xBi₂Se₃. We first demonstrate that only the intercalated Sr atoms can induce superconductivity. Then we show the full superconducting gaps without any in-gap density of states as expected theoretically for a bulk topological superconductor. Finally, we find that the surface Dirac electrons will simultaneously condense into the superconducting state within the superconducting gap. This vividly demonstrates how the surface Dirac electrons are driven into Cooper pairs.

Whether and how the Dirac electrons can be driven into superconducting state remains unclear. Here, Du et al. present systematic study to demonstrate the Dirac electrons condensing into Cooper pairs on the surface of a possible topological superconductor Sr_xBi₂Se₃.

A New Microfluidic Device for Classification of Microalgae Cells Based on Simultaneous Analysis of Chlorophyll Fluorescence, Side Light Scattering, Resistance Pulse Sensing

Fast on-site monitoring of foreign microalgae species carried by ship ballast water has drawn more and more attention. In this paper, we presented a new method and a compact device of classification of microalgae cells by simultaneous detection of three kinds of signals of single microalgae cells in a disposable microfluidic chip. The microfluidic classification device has advantages of fast detection, low cost, and portability. The species of a single microalgae cell can be identified by simultaneous detection of three signals of chlorophyll fluorescence (CF), side light scattering (SLS), and resistance pulse sensing (RPS) of the microalgae cell. These three signals represent the different characteristics of a microalgae cell. A compact device was designed to detect these three signals of a microalgae cell simultaneously. In order to demonstrate the performance of the developed system, the comparison experiments of the mixed samples of three different species of microalgae cells between the developed system and a commercial flow cytometer were conducted. The results show that three kinds of microalgae cells can be distinguished clearly by our developed system and the commercial flow cytometer and both results have good agreement.

Superconducting topological surface states in the noncentrosymmetric bulk superconductor PbTaSe2

The search for topological superconductors (TSCs) is one of the most urgent contemporary problems in condensed matter systems. TSCs are characterized by a full superconducting gap in the bulk and topologically protected gapless surface (or edge) states. Within each vortex core of TSCs, there exists the zero-energy Majorana bound states, which are predicted to exhibit non-Abelian statistics and to form the basis of the fault-tolerant quantum computation. To date, no stoichiometric bulk material exhibits the required topological surface states (TSSs) at the Fermi level (EF) combined with fully gapped bulk superconductivity. We report atomic-scale visualization of the TSSs of the noncentrosymmetric fully gapped superconductor PbTaSe2. Using quasi-particle scattering interference imaging, we find two TSSs with a Dirac point at E ≅ 1.0 eV, of which the inner TSS and the partial outer TSS cross EF, on the Pb-terminated surface of this fully gapped superconductor. This discovery reveals PbTaSe2 as a promising candidate for TSC.

Topological Superconductivity on the Surface of Fe-Based Superconductors

As one of the simplest systems for realizing Majorana fermions, the topological superconductor plays an important role in both condensed matter physics and quantum computations. Based on ab initio calculations and the analysis of an effective 8-band model with superconducting pairing, we demonstrate that the three-dimensional extended s-wave Fe-based superconductors such as Fe_{1+y}Se_{0.5}Te_{0.5} have a metallic topologically nontrivial band structure, and exhibit a normal-topological-normal superconductivity phase transition on the (001) surface by tuning the bulk carrier doping level. In the topological superconductivity (TSC) phase, a Majorana zero mode is trapped at the end of a magnetic vortex line. We further show that the surface TSC phase only exists up to a certain bulk pairing gap, and there is a normal-topological phase transition driven by the temperature, which has not been discussed before. These results pave an effective way to realize the TSC and Majorana fermions in a large class of superconductors.

Rotational symmetry breaking in the topological superconductor SrxBi2Se3 probed by upper-critical field experiments

Recently it was demonstrated that Sr intercalation provides a new route to induce superconductivity in the topological insulator Bi2Se3. Topological superconductors are predicted to be unconventional with an odd-parity pairing symmetry. An adequate probe to test for unconventional superconductivity is the upper critical field, Bc2. For a standard BCS layered superconductor Bc2 shows an anisotropy when the magnetic field is applied parallel and perpendicular to the layers, but is isotropic when the field is rotated in the plane of the layers. Here we report measurements of the upper critical field of superconducting SrxBi2Se3 crystals (Tc = 3.0 K). Surprisingly, field-angle dependent magnetotransport measurements reveal a large anisotropy of Bc2 when the magnet field is rotated in the basal plane. The large two-fold anisotropy, while six-fold is anticipated, cannot be explained with the Ginzburg-Landau anisotropic effective mass model or flux flow induced by the Lorentz force. The rotational symmetry breaking of Bc2 indicates unconventional superconductivity with odd-parity spin-triplet Cooper pairs (Δ4-pairing) recently proposed for rhombohedral topological superconductors, or might have a structural nature, such as self-organized stripe ordering of Sr atoms.

Electronic structure and relaxation dynamics in a superconducting topological material

Topological superconductors host new states of quantum matter which show a pairing gap in the bulk and gapless surface states providing a platform to realize Majorana fermions. Recently, alkaline-earth metal Sr intercalated Bi2Se3 has been reported to show superconductivity with a Tc ~ 3 K and a large shielding fraction. Here we report systematic normal state electronic structure studies of Sr0.06Bi2Se3 (Tc ~ 2.5 K) by performing photoemission spectroscopy. Using angle-resolved photoemission spectroscopy (ARPES), we observe a quantum well confined two-dimensional (2D) state coexisting with a topological surface state in Sr0.06Bi2Se3. Furthermore, our time-resolved ARPES reveals the relaxation dynamics showing different decay mechanism between the excited topological surface states and the two-dimensional states. Our experimental observation is understood by considering the intra-band scattering for topological surface states and an additional electron phonon scattering for the 2D states, which is responsible for the superconductivity. Our first-principles calculations agree with the more effective scattering and a shorter lifetime of the 2D states. Our results will be helpful in understanding low temperature superconducting states of these topological materials.

Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd3As2 crystals

Three-dimensional (3D) Dirac semimetals, which possess 3D linear dispersion in the electronic structure as a bulk analogue of graphene, have lately generated widespread interest in both materials science and condensed matter physics. Recently, crystalline Cd3As2 has been proposed and proved to be a 3D Dirac semimetal that can survive in the atmosphere. Here, by using point contact spectroscopy measurements, we observe exotic superconductivity around the point contact region on the surface of Cd3As2 crystals. The zero-bias conductance peak (ZBCP) and double conductance peaks (DCPs) symmetric around zero bias suggest p-wave-like unconventional superconductivity. Considering the topological properties of 3D Dirac semimetals, our findings may indicate that Cd3As2 crystals under certain conditions could be topological superconductors, which are predicted to support Majorana zero modes or gapless Majorana edge/surface modes in the boundary depending on the dimensionality of the material.

Odd-Parity Superconductivity in the Vicinity of Inversion Symmetry Breaking in Spin-Orbit-Coupled Systems

We study superconductivity in spin-orbit-coupled systems in the vicinity of inversion symmetry breaking. We find that, because of the presence of spin-orbit coupling, fluctuations of the incipient parity-breaking order generate an attractive pairing interaction in an odd-parity pairing channel, which competes with the s-wave pairing. We show that Coulomb repulsion or an external Zeeman field suppresses the s-wave pairing and promotes the odd-parity superconducting state. Our work provides a new mechanism for odd-parity pairing and opens a route to novel topological superconductivity.

Surface-Facet-Dependent Phonon Deformation Potential in Individual Strained Topological Insulator Bi2Se3 Nanoribbons

Strain is an important method to tune the properties of topological insulators. For example, compressive strain can induce superconductivity in Bi2Se3 bulk material. Topological insulator nanostructures are the superior candidates to utilize the unique surface states due to the large surface to volume ratio. Therefore, it is highly desirable to monitor the local strain effects in individual topological insulator nanostructures. Here, we report the systematical micro-Raman spectra of single strained Bi2Se3 nanoribbons with different thicknesses and different surface facets, where four optical modes are resolved in both Stokes and anti-Stokes Raman spectral lines. A striking anisotropy of the strain dependence is observed in the phonon frequency of strained Bi2Se3 nanoribbons grown along the ⟨112̅0⟩ direction. The frequencies of the in-plane Eg(2) and out-of-plane A1g(1) modes exhibit a nearly linear blue-shift against bending strain when the nanoribbon is bent along the ⟨112̅0⟩ direction with the curved {0001} surface. In this case, the phonon deformation potential of the Eg(2) phonon for 100 nm-thick Bi2Se3 nanoribbon is up to 0.94 cm(–1)/%, which is twice of that in Bi2Se3 bulk material (0.52 cm(–1)/%). Our results may be valuable for the strain modulation of individual topological insulator nanostructures.

Topologically protected surface states in a centrosymmetric superconductor β-PdBi2

The topological aspects of electrons in solids can emerge in real materials, as represented by topological insulators. In theory, they show a variety of new magneto-electric phenomena, and especially the ones hosting superconductivity are strongly desired as candidates for topological superconductors. While efforts have been made to develop possible topological superconductors by introducing carriers into topological insulators, those exhibiting indisputable superconductivity free from inhomogeneity are very few. Here we report on the observation of topologically protected surface states in a centrosymmetric layered superconductor, β-PdBi₂, by utilizing spin- and angle-resolved photoemission spectroscopy. Besides the bulk bands, several surface bands are clearly observed with symmetrically allowed in-plane spin polarizations, some of which crossing the Fermi level. These surface states are precisely evaluated to be topological, based on the Z₂ invariant analysis in analogy to three-dimensional strong topological insulators. β-PdBi₂ may offer a solid stage to investigate the topological aspect in the superconducting condensate.

Materials possessing topologically non-trivial electronic surface states are predicted to host exotic Majorana fermion excitations in the superconducting state. Here, the authors demonstrate the existence of topologically-protected surface states in the centrosymmetric layered superconductor β-PdBi2.

Superconductivity in the surface states of a Bi2X3 topological insulator: effects of a realistic model

Superconductivity in the topological surface states is essential to both the surface spectrum of bulk superconducting state and the proximity-induced superconductivity of Bi2X3 (X is Se or Te) topological insulators. While previous theories were mostly based on simplified models for the bulk topological insulator and the surface states, the accumulating experiments stimulate us to make an analysis using realistic model for the normal state electronic structures, incorporating terms responsible for particle–hole asymmetry and hexagonal warping. An effective low-energy model for the topological surface states is derived first. Then we identify all the bulk time-reversal-invariant superconducting pairings in the topological insulator that can open a gap in the topological surface states. Many more pairings are found to be able to gap the topological surface states as compared to conclusions based on simplified models. The number of proximity-induced pairing channels in the topological surface states increases by one as a result of the hexagonal warping term, but is not changed by the particle–hole asymmetry term.

Topological surface states in nodal superconductors

Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states.

Symmetry protected topological superfluid (3)He-B

Owing to the richness of symmetry and well-established knowledge of bulk superfluidity, the superfluid (3)He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of (3)He in a multifaceted manner, including symmetry considerations, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the (3)He-B confined in a slab geometry. The (3)He-B under a magnetic field is separated to two different sub-phases: the symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of the (3)He nucleus. It is also demonstrated that odd-frequency even-parity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt3 and Rashba superconductors as examples.

Effective low-energy theory for superconducting topological insulators

Candidate pairings of superconducting topological insulators support interesting surface Andreev bound states (SABSs) known as Majorana fermions. As these materials are described by a two-orbital Bernevig-Hughes-Zhang type model, a general understanding of the low-energy physics such as the possible kinds of SABSs are difficult. By virtue of an analogy between a topological insulator and a time reversal invariant topological superconductor, we propose a simple and intuitive method of constructing the low-energy effective models for superconducting topological insulators like CuxBi2Se3. Depending on the value of the chemical potential and for experimentally relevant model parameters, the low-energy properties of these superconductors are shown to be determined by one copy or two copies of single-orbital effective models. If the effective pairing potential shows sign reversal upon reflection by the surface, one Kramers' pair or two Kramers' pairs of SABSs are expected to appear. Explicit analytical calculations in terms of the effective low energy model reproduce the dispersions of the numerically confirmed two pairs of SABSs for a commonly studied pairing.

Electron-phonon coupling and its implication for the superconducting topological insulators

The recent observation of superconductivity in doped topological insulators has sparked a flurry of interest due to the prospect of realizing the long-sought topological superconductors. Yet the understanding of underlying pairing mechanism in these systems is far from complete. Here we investigate this problem by providing robust first-principles calculations of the role of electron-phonon coupling for the superconducting pairing in the prime candidate Cu_xBi₂Se₃. Our results show that electron-phonon scattering process in this system is dominated by zone center and boundary optical modes, with coexistence of phonon stiffening and softening. While the calculated electron-phonon coupling constant λ suggests that T_c from electron-phonon coupling is 2 orders smaller than the ones reported on bulk inhomogeneous samples, suggesting that superconductivity may not come from pure electron-phonon coupling. We discuss the possible enhancement of superconducting transition temperature by local inhomogeneity introduced by doping.

Photonic simulation of topological superconductor edge state and zero-energy mode at a vortex

Photonic simulations of quantum Hall edge states and topological insulators have inspired considerable interest in recent years. Interestingly, there are theoretical predictions for another type of topological states in topological superconductors, but debates over their experimental observations still remain. Here we investigate the photonic analogue of the p_x + ip_y model of topological superconductor. Two essential characteristics of topological superconductor, particle-hole symmetry and p_x + ip_y pairing potentials, are well emulated in photonic systems. Its topological features are presented by chiral edge state and zero-energy mode at a vortex. This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.

Scanning tunneling microscopy studies of topological insulators

Scanning tunneling microscopy (STM), with surface sensitivity, is an ideal tool to probe the intriguing properties of the surface state of topological insulators (TIs) and topological crystalline insulators (TCIs). We summarize the recent progress on those topological phases revealed by STM studies. STM observations have directly confirmed the existence of the topological surface states and clearly revealed their novel properties. We also discuss STM work on magnetic doped TIs, topological superconductors and crystalline symmetry-protected surface states in TCIs. The studies have greatly promoted our understanding of the exotic properties of the new topological phases, as well as put forward new challenges. STM will continue to play an important role in this rapidly growing field from the point view of both fundamental physics and applications.