Odd-parity pairing and topological superconductivity in a strongly spin-orbit coupled semiconductor

Superconductivity in the High-Entropy Ceramics Ti0.2 Zr0.2 Nb0.2 Mo0.2 Ta0.2 Cx with Possible Nontrivial Band Topology

Topological superconductors have drawn significant interest from the scientific community due to the accompanying Majorana fermions. Here, the discovery of electronic structure and superconductivity (SC) in high-entropy ceramics Ti0.2 Zr0.2 Nb0.2 Mo0.2 Ta0.2 Cx (x = 1 and 0.8) combined with experiments and first-principles calculations is reported. The Ti0.2 Zr0.2 Nb0.2 Mo0.2 Ta0.2 Cx high-entropy ceramics show bulk type-II SC with Tc ≈ 4.00 K (x = 1) and 2.65 K (x = 0.8), respectively. The specific heat jump (∆C/γTc ) is equal to 1.45 (x = 1) and 1.52 (x = 0.8), close to the expected value of 1.43 for the BCS superconductor in the weak coupling limit. The high-pressure resistance measurements show a robust SC against high physical pressure in Ti0.2 Zr0.2 Nb0.2 Mo0.2 Ta0.2 C, with a slight Tc variation of 0.3 K within 82.5 GPa. Furthermore, the first-principles calculations indicate that the Dirac-like point exists in the electronic band structures of Ti0.2 Zr0.2 Nb0.2 Mo0.2 Ta0.2 C, which is potentially a topological superconductor. The Dirac-like point is mainly contributed by the d orbitals of transition metals M and the p orbitals of C. The high-entropy ceramics provide an excellent platform for the fabrication of novel quantum devices, and the study may spark significant future physics investigations in this intriguing material.

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.

Topological superconductivity and large spin Hall effect in the kagome family Ti6X4 (X = Bi, Sb, Pb, Tl, and In)

Topological superconductors (TSC) become a focus of research due to the accompanying Majorana fermions. However, the reported TSC are extremely rare. Recent experiments reported kagome TSC AV3Sb5 (A = K, Rb, and Cs) exhibit unique superconductivity, topological surface states (TSS), and Majorana bound states. More recently, the first titanium-based kagome superconductor CsTi3Bi5 with nontrivial topology was successfully synthesized as a perspective TSC. Given that Cs contributes little to electronic structures of CsTi3Bi5 and binary compounds may be easier to be synthesized, here, by first-principle calculations, we predict five stable nonmagnetic kagome compounds Ti6X4 (X = Bi, Sb, Pb, Tl, and In) which exhibit superconductivity with critical temperature Tc = 3.8 K - 5.1 K, nontrivialZ 2 band topology, and TSS close to the Fermi level. Additionally, large intrinsic spin Hall effect is obtained in Ti6X4, which is caused by gapped Dirac nodal lines due to a strong spin-orbit coupling. This work offers new platforms for TSC and spintronic devices.

Pattern-tunable synthetic gauge fields in topological photonic graphene

We propose a straightforward and effective approach to design, by pattern-tunable strain-engineering, photonic topological insulators supporting high quality factors edge states. Chiral strain-engineering creates opposite synthetic gauge fields in two domains resulting in Landau levels with the same energy spacing but different topological numbers. The boundary of the two topological domains hosts robust time-reversal and spin-momentum-locked edge states, exhibiting high quality factors due to continuous strain modulation. By shaping the synthetic gauge field, we obtain remarkable field confinement and tunability, with the strain strongly affecting the degree of localization of the edge states. Notably, the two-domain design stabilizes the strain-induced topological edge state. The large potential bandwidth of the strain-engineering and the opportunity to induce the mechanical stress at the fabrication stage enables large scalability for many potential applications in photonics, such as tunable microcavities, new lasers, and information processing devices, including the quantum regime.

Understanding Heterogeneities in Quantum Materials

Quantum materials are usually heterogeneous, with structural defects, impurities, surfaces, edges, interfaces, and disorder. These heterogeneities are sometimes viewed as liabilities within conventional systems; however, their electronic and magnetic structures often define and affect the quantum phenomena such as coherence, interaction, entanglement, and topological effects in the host system. Therefore, a critical need is to understand the roles of heterogeneities in order to endow materials with new quantum functions for energy and quantum information science applications. In this article, several representative examples are reviewed on the recent progress in connecting the heterogeneities to the quantum behaviors of real materials. Specifically, three intertwined topic areas are assessed: i) Reveal the structural, electronic, magnetic, vibrational, and optical degrees of freedom of heterogeneities. ii) Understand the effect of heterogeneities on the behaviors of quantum states in host material systems. iii) Control heterogeneities for new quantum functions. This progress is achieved by establishing the atomistic-level structure-property relationships associated with heterogeneities in quantum materials. The understanding of the interactions between electronic, magnetic, photonic, and vibrational states of heterogeneities enables the design of new quantum materials, including topological matter and quantum light emitters based on heterogenous 2D materials.

Superconductivity in In-doped AgSnBiTe3 with possible band inversion

We investigated the chemical pressure effects on structural and electronic properties of SnTe-based material using partial substitution of Sn by Ag_0.5Bi_0.5, which results in lattice shrinkage. For Sn_1-2x(AgBi)_xTe, single-phase polycrystalline samples were obtained with a wide range of x. On the basis of band calculations, we confirmed that the Sn_1-2x(AgBi)_xTe system is basically possessing band inversion and topologically preserved electronic states. To explore new superconducting phases related to the topological electronic states, we investigated the In-doping effects on structural and superconducting properties for x = 0.33 (AgSnBiTe₃). For (AgSnBi)_(1-y)/3In_yTe, single-phase polycrystalline samples were obtained for y = 0-0.5 by high-pressure synthesis. Superconductivity was observed for y = 0.2-0.5. For y = 0.4, the transition temperature estimated from zero-resistivity state was 2.4 K, and the specific heat investigation confirmed the emergence of bulk superconductivity. Because the presence of band inversion was theoretically predicted, and the parameters obtained from specific heat analyses were comparable to In-doped SnTe, we expect that the (AgSnBi)_(1-y)/3In_yTe and other (Ag, In, Sn, Bi)Te phases are candidate systems for studying topological superconductivity.

Unconventional Pressure Dependence of the Superfluid Density in the Nodeless Topological Superconductor α-PdBi_{2}

We investigated the superconducting properties of the topological superconductor α-PdBi_{2} at ambient and external pressures up to 1.77 GPa using muon spin rotation experiments. The ambient pressure measurements evince a fully gapped s-wave superconducting state in the bulk of the specimen. Alternating current magnetic susceptibility and muon spin rotation measurements manifest a continuous suppression of T_{c} with increasing pressure. In parallel, we observed a significant decrease of superfluid density by ∼20% upon application of external pressure. Remarkably, the superfluid density follows a linear relation with T_{c}, which was found before in some unconventional topological superconductors and hole-doped cuprates. This finding signals a possible crossover from Bose-Einstein to Bardeen-Cooper-Schrieffer like condensation in α-PdBi_{2}.

Thickness Dependence of Superconductivity in Layered Topological Superconductor β-PdBi2

We report a systematic study on the thickness-dependent superconductivity and transport properties in exfoliated layered topological superconductor β-PdBi2. The superconducting transition temperature Tc is found to decrease with the decreasing thickness. Below a critical thickness of 45 nm, the superconductivity is suppressed, but followed by an abrupt resistance jump near Tc, which is in opposite to the behavior in a superconductor. We attribute suppressed Tc to the enhanced disorder as the thickness decreases. The possible physical mechanisms were discussed for the origination of sharply increased resistance in thinner β-PdBi2 samples.

Observation of triplet superconductivity in CoSi2/TiSi2 heterostructures

Unconventional superconductivity and, in particular, triplet superconductivity have been front and center of topological materials and quantum technology research. Here, we report our observation of triplet pairing in nonmagnetic CoSi₂/TiSi₂ heterostructures on silicon. CoSi₂ undergoes a sharp superconducting transition at a critical temperature T _c ≃ 1.5 K, while TiSi₂ is a normal metal. We investigate conductance spectra of both two-terminal CoSi₂/TiSi₂ contact junctions and three-terminal T-shaped CoSi₂/TiSi₂ superconducting proximity structures. Below T _c, we observe (i) a narrow zero-bias conductance peak on top of a broad hump, accompanied by two symmetric side dips in the contact junctions, (ii) a narrow zero-bias conductance peak in T-shaped structures, and (iii) hysteresis in the junction magnetoresistance. These three independent and complementary observations point to chiral p-wave pairing in CoSi₂/TiSi₂ heterostructures. The excellent fabrication compatibility of CoSi₂ and TiSi₂ with present-day silicon-based integrated-circuit technology suggests their potential use in scalable quantum-computing devices.

Unusual upper critical fields of the topological nodal-line semimetal candidate SnxNbSe2-δ

We report superconductivity in Sn_xNbSe_2-δ, a topological nodal-line semimetal candidate with a noncentrosymmetric crystal structure. The superconducting transition temperatureT_cof this compound is extremely sensitive to Sn concentrationxand Se deficiencyδ, 5.0 K for Sn_0.13NbSe_1.70and 8.6 K for Sn_0.14NbSe_1.71and Sn_0.15NbSe_1.69. In all samples, the temperature dependence of the upper critical fieldH_c2(T) differs from the prediction of the Werthamer-Helfand-Hohenberg theory. While the zero-temperature value of the in-plane upper critical field of Sn_xNbSe_2-δwith the higherT_cis lower than the BCS Pauli paramagnetic limitH_P, that of the lowerT_csample exceedsH_Pby a factor of ∼2. Our observations suggest that a possible odd-parity contribution dominates the superconducting gap function of Sn_xNbSe_2-δ, and it can be fine-tuned by the Sn concentration and Se deficiency.

Multiple In-Gap States Induced by Topological Surface States in the Superconducting Topological Crystalline Insulator Heterostructure Sn_{1-x}Pb_{x}Te-Pb

Superconducting topological crystalline insulators (TCIs) have been proposed to be a new type of topological superconductor where multiple Majorana zero modes may coexist under the protection of lattice symmetries. The bulk superconductivity of TCIs has been realized, but it is quite challenging to detect the superconductivity of topological surface states inside their bulk superconducting gaps. Here, we report high-resolution scanning tunneling spectroscopy measurements on lateral Sn_{1-x}Pb_{x}Te-Pb heterostructures using superconducting tips. Both the bulk superconducting gap and the multiple in-gap states with energy differences of ∼0.3  meV can be clearly resolved on TCI Sn_{1-x}Pb_{x}Te at 0.38 K. Quasiparticle interference measurements further confirm the in-gap states are gapless. Our work demonstrates that the unique topological superconductivity of a TCI can be directly distinguished in the density of states, which helps to further investigate the multiple Dirac and Majorana fermions inside the superconducting gap.

Robust Majorana edge modes with low frequency multiple time periodic driving

Floquet Majorana edge modes capture the topological features of periodically driven p-wave superconductors. We present a Kitaev chain with multiple time periodic driving terms. Our results demonstrate how multiple driving will affect Floquet bands in frequency space, leading to more robust Floquet Majorana edge modes against driving frequencyωin comparison with the single driving scenario. Meanwhile, we have proposed how to predict Majorana edge modes via the Zak phase of Floquet bands. Besides, in contrast to the cases with single driving term, where the constant phase can be gauged out by properly choosing the initial time, we have shown the relative phase between multiple driving can not be gauged out and will play a dominant role in deciding topological phase transitions. For the sake of completeness, we also investigate the high frequency limit. Analytical results on effective Hamiltonian can be obtained via Magnus expansion and relative phase induced topological transitions can be shown explicitly.

Development of topological insulator and topological crystalline insulator nanostructures

Topological insulators (TIs), a class of quantum materials with time reversal symmetry protected gapless Dirac-surface states, have attracted intensive research interests due to their exotic electronic properties. Topological crystalline insulators (TCIs), whose gapless surface states are protected by the crystal symmetry, have recently been proposed and experimentally verified as a new class of TIs. With high surface-to-volume ratio, nanoscale TI and TCI materials such as nanowires and nanoribbons can have significantly enhanced contribution from surface states in carrier transport and are thus ideally suited for the fundamental studies of topologically protected surface state transport and nanodevice fabrication. This article will review the synthesis and transport device measurements of TIs and TCIs nanostructures.

Evolution of Electronic States and Emergence of Superconductivity in the Polar Semiconductor GeTe by Doping Valence-Skipping Indium

GeTe is a chemically simple IV-VI semiconductor which bears a rich plethora of different physical properties induced by doping and external stimuli. Here, we report a superconductor-semiconductor-superconductor transition controlled by finely-tuned In doping. Our results reveal the existence of a critical doping concentration x_{c}=0.12 in Ge_{1-x}In_{x}Te, where various properties, including structure, resistivity, charge carrier type, and the density of states, take either an extremum or change their character. At the same time, we find indications of a change in the In-valence state from In^{3+} to In^{1+} with increasing x by core-level photoemission spectroscopy, suggesting that this system is a new promising playground to probe valence fluctuations and their possible impact on structural, electronic, and thermodynamic properties of their host.

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.

Majorana Multipole Response of Topological Superconductors

In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensed-matter systems may have electromagnetic multipoles. We developed a general theory of magnetic multipoles for helical MFs on time-reversal-invariant superconductors. The results show that the multipole response is governed by crystal symmetry, and that a one-to-one correspondence exists between the symmetry of Cooper pairs and the representation of magnetic multipoles under crystal symmetry. The latter property provides a way to identify unconventional pairing symmetry via the magnetic response of helical MFs. We also find that most helical MFs exhibit a magnetic-dipole response, but those on superconductors with spin-3/2 electrons may display a magnetic-octupole response in leading order, which uniquely characterizes high-spin superconductors. Detection of such an octupole response provides direct evidence of high-spin superconductivity, such as in half-Heusler superconductors.

Signatures of Topological Superconductivity in Bulk-Insulating Topological Insulator BiSbTe1.25Se1.75 in Proximity with Superconducting NbSe2

The combination of superconductivity and spin-momentum locking at the interface between an s-wave superconductor and a three-dimensional topological insulator (3D-TI) is predicted to generate exotic p-wave topological superconducting phases that can host Majorana Fermions. However, large bulk conductivities of previously investigated 3D-TI samples and Fermi level mismatches between 3D bulk superconductors and 2D topological surface states have thwarted significant progress. Here, we employ bulk-insulating topological insulators in proximity with two-dimensional superconductor NbSe₂ assembled via van der Waals epitaxy. Experimentally measured differential conductance yields unusual features including a double-gap spectrum, an intrinsic asymmetry that vanishes with small in-plane magnetic fields, and differential conductance ripples at biases significantly larger than the superconducting gap. We explain our results on the basis of proximity-induced superconductivity of topological surface states, while also considering possibilities of topologically trivial superconductivity arising from Rashba-type surface states. Our work demonstrates the possibility of obtaining p-wave superconductors by proximity effects on bulk-insulating TIs.

Weak-link Josephson Junctions Made from Topological Crystalline Insulators

We report on the fabrication of Josephson junctions using the topological crystalline insulator Pb_{0.5}Sn_{0.5}Te as the weak link. The properties of these junctions are characterized and compared to those fabricated with weak links of PbTe, a similar material yet topologically trivial. Most striking is the difference in the ac Josephson effect: junctions made with Pb_{0.5}Sn_{0.5}Te exhibit a rich subharmonic structure consistent with a skewed current-phase relation. This structure is absent in junctions fabricated from PbTe. A discussion is given on the origin of this effect as an indication of novel behavior arising from the topologically nontrivial surface state.

The Property, Preparation and Application of Topological Insulators: A Review

Topological insulator (TI), a promising quantum and semiconductor material, has gapless surface state and narrow bulk band gap. Firstly, the properties, classifications and compounds of TI are introduced. Secondly, the preparation and doping of TI are assessed. Some results are listed. (1) Although various preparation methods are used to improve the crystal quality of the TI, it cannot reach the industrialization. Fermi level regulation still faces challenges; (2) The carrier type and lattice of TI are affected by non-magnetic impurities. The most promising property is the superconductivity at low temperature; (3) Magnetic impurities can destroy the time-reversal symmetry of the TI surface, which opens the band gap on the TI surface resulting in some novel physical effects such as quantum anomalous Hall effect (QAHE). Thirdly, this paper summarizes various applications of TI including photodetector, magnetic device, field-effect transistor (FET), laser, and so on. Furthermore, many of their parameters are compared based on TI and some common materials. It is found that TI-based devices exhibit excellent performance, but some parameters such as signal to noise ratio (S/N) are still lower than other materials. Finally, its advantages, challenges and future prospects are discussed. Overall, this paper provides an opportunity to improve crystal quality, doping regulation and application of TI.

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.

Pressure induced superconductivity in the antiferromagnetic Dirac material BaMnBi2

The so-called Dirac materials such as graphene and topological insulators are a new class of matter different from conventional metals and (doped) semiconductors. Superconductivity induced by doing or applying pressure in these systems may be unconventional, or host mysterious Majorana fermions. Here, we report a successfully observation of pressure-induced superconductivity in an antiferromagnetic Dirac material BaMnBi₂ with T_c of ~4 K at 2.6 GPa. Both the higher upper critical field, μ₀H_c2(0) ~ 7 Tesla, and the measured current independent of T_c precludes that superconductivity is ascribed to the Bi impurity. The similarity in ρ_ab(B) linear behavior at high magnetic fields measured at 2 K both at ambient pressure (non-superconductivity) and 2.6 GPa (superconductivity, but at the normal state), as well as the smooth and similar change of resistivity with pressure measured at 7 K and 300 K in zero field, suggests that there may be no structure transition occurred below 2.6 GPa, and superconductivity observed here may emerge in the same phase with Dirac fermions. Our findings imply that BaMnBi₂ may provide another platform for studying SC mechanism in the system with Dirac fermions.

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.

Disorder-induced topological phase transitions in two-dimensional spin-orbit coupled superconductors

Normal superconductors with Rashba spin-orbit coupling have been explored as candidate systems of topological superconductors. Here we present a comparative theoretical study of the effects of different types of disorder on the topological phases of two-dimensional Rashba spin-orbit coupled superconductors. First, we show that a topologically trivial superconductor can be driven into a chiral topological superconductor upon diluted doping of isolated magnetic disorder, which close and reopen the quasiparticle gap of the paired electrons in a nontrivial manner. Secondly, the superconducting nature of a topological superconductor is found to be robust against Anderson disorder, but the topological nature is not, converting the system into a topologically trivial state even in the weak scattering limit. These topological phase transitions are distinctly characterized by variations in the topological invariant. We discuss the central findings in connection with existing experiments, and provide new schemes towards eventual realization of topological 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.

Influence of an embedded quantum dot on the Josephson effect in the topological superconducting junction with Majorana doublets

One Majorana doublet can be realized at each end of the time-reversal-invariant Majorana nanowires. We investigate the Josephson effect in the Majorana-doublet-presented junction modified by different inter-doublet coupling manners. It is found that when the Majorana doublets couple indirectly via a non-magnetic quantum dot, only the normal Josephson effect occurs, and the fermion parity in the system just affects the current direction and amplitude. However, one magnetic field applied on the dot can induce the fractional Josephson effect in the odd-parity case. Next if the direct and indirect couplings between the Majorana doublets coexist, no fractional Josephson effect takes place, regardless of the presence of magnetic field. Instead, there almost appears the π-period-like current in some special cases. All the results are clarified by analyzing the influence of the fermion occupation in the quantum dot on the parity conservation in the whole system. We ascertain that this work will be helpful for describing the dot-assisted Josephson effect between the Majorana doublets.

Evolution of Density of States and a Spin-Resolved Checkerboard-Type Pattern Associated with the Majorana Bound State

In terms of the Bogoliubov-de Gennes approach, we investigate the Majorana bound state (MBS) in a vortex of proximity-induced superconductivity on the surface of a topological insulator. Mapping out the local density of states (LDOS) of quasiparticle excitations as a function of energy and distance from the vortex center, it is found that the spectral distribution evolves from a V shape to a Y shape with the emergence of a MBS upon variation of the chemical potential, consistent with the STM/STS measurement in a very recent experiment [Xu et al., Phys. Rev. Lett. 114, 017001 (2015)] on a Bi(2)Te(3) thin layer on the top of NbSe(2). Moreover, we demonstrate that there is a checkerboard-type pattern in the relative LDOS between the spin-up and -down channels, where the quantum mechanical wave function of the MBS manifests itself clearly as a single quantum state. Therefore, a spin-resolved STM/STS technique is expected to be able to provide phase-sensitive evidence for a MBS in the vortex core of a topological superconductor.

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.

Engineering topological superconductors using surface atomic-layer/molecule hybrid materials

Surface atomic-layer (SAL) superconductors consisting of epitaxially grown metal adatoms on a clean semiconductor surface have been recently established. Compared to conventional metal thin films, they have two important features: (i) space-inversion symmetry-breaking throughout the system and (ii) high sensitivity to surface adsorption of foreign species. These potentially lead to manifestation of the Rashba effect and a Zeeman field exerted by adsorbed magnetic organic molecules. After introduction of the archetypical SAL superconductor Si(111)-(√7 × √3)-In, we describe how these features are utilized to engineer a topological superconductor with Majorana fermions and discuss its promises and expected challenges.

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.

Revealing Surface States in In-Doped SnTe Nanoplates with Low Bulk Mobility

Indium (In) doping in topological crystalline insulator SnTe induces superconductivity, making In-doped SnTe a candidate for a topological superconductor. SnTe nanostructures offer well-defined nanoscale morphology and high surface-to-volume ratios to enhance surface effects. Here, we study In-doped SnTe nanoplates, In(x)Sn(1-x)Te, with x ranging from 0 to 0.1 and show they superconduct. More importantly, we show that In doping reduces the bulk mobility of In(x)Sn(1-x)Te such that the surface states are revealed in magnetotransport despite the high bulk carrier density. This is manifested by two-dimensional linear magnetoresistance in high magnetic fields, which is independent of temperature up to 10 K. Aging experiments show that the linear magnetoresistance is sensitive to ambient conditions, further confirming its surface origin. We also show that the weak antilocalization observed in In(x)Sn(1-x)Te nanoplates is a bulk effect. Thus, we show that nanostructures and reducing the bulk mobility are effective strategies to reveal the surface states and test for topological superconductors.

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.

Turning a band insulator into an exotic superconductor

Understanding exotic, non-s-wave-like states of Cooper pairs is important and may lead to new superconductors with higher critical temperatures and novel properties. Their existence is known to be possible but has always been thought to be associated with non-traditional mechanisms of superconductivity where electronic correlations play an important role. Here we use a first principles linear response calculation to show that in doped Bi₂Se₃ an unconventional p-wave-like state can be favoured via a conventional phonon-mediated mechanism, as driven by an unusual, almost singular behaviour of the electron–phonon interaction at long wavelengths. This may provide a new platform for our understanding of superconductivity phenomena in doped band insulators.

Most superconductors that exhibit exotic pairing symmetries are derived from host materials that are Mott insulators. Xiangang Wan and Sergey Savrasov show that it may be possible to realize an exotic p-wave superconductor in doped Bi₂Se₃, which is a topological band insulator.

Evidence for topologically protected surface states and a superconducting phase in [Tl4](Tl(1-x)Sn(x))Te3 using photoemission, specific heat, and magnetization measurements, and density functional theory

We report the discovery of surface states in the perovskite superconductor [Tl4]TlTe3 (Tl5Te3) and its nonsuperconducting tin-doped derivative [Tl4](Tl0.4Sn0.6)Te3 as observed by angle-resolved photoemission spectroscopy. Density functional theory calculations predict that the surface states are protected by a Z2 topology of the bulk band structure. Specific heat and magnetization measurements show that Tl5Te3 has a superconducting volume fraction in excess of 95%. Thus Tl5Te3 is an ideal material in which to study the interplay of bulk band topology and superconductivity.

Inducing time-reversal-invariant topological superconductivity and fermion parity pumping in quantum wires

We propose a setup to realize time-reversal-invariant topological superconductors in quantum wires, proximity coupled to conventional superconductors. We consider a model of quantum wire with strong spin-orbit coupling and proximity coupling to two s-wave superconductors. When the relative phase between the two superconductors is ϕ=π a Kramers pair of Majorana zero modes appears at each edge of the wire. We study the robustness of the phase in the presence of both time-reversal-invariant and time-reversal-breaking perturbations. In addition, we show that the system forms a natural realization of a fermion parity pump, switching the local fermion parity of both edges when the relative phase between the superconductors is changed adiabatically by 2π.

Fermiology of the strongly spin-orbit coupled superconductor Sn(1-x)In(x)Te: implications for topological superconductivity

We have performed angle-resolved photoemission spectroscopy on the strongly spin-orbit coupled low-carrier density superconductor Sn(1-x)In(x)Te (x = 0.045) to elucidate the electronic states relevant to the possible occurrence of topological superconductivity, as recently reported for this compound based on point-contact spectroscopy. The obtained energy-band structure reveals a small holelike Fermi surface centered at the L point of the bulk Brillouin zone, together with a signature of a topological surface state, indicating that this material is a doped topological crystalline insulator characterized by band inversion and mirror symmetry. A comparison of the electronic states with a band-noninverted superconductor possessing a similar Fermi surface structure, Pb(1-x)Tl(x)Te, suggests that the anomalous behavior in the superconducting state of Sn(1-x)In(x)Te is related to the peculiar orbital characteristics of the bulk valence band and/or the presence of a topological surface state.