Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator

Intercalates of Bi2Se3 studied in situ by time-resolved powder X-ray diffraction and neutron diffraction

Intercalation of lithium and ammonia into the layered semiconductor Bi₂Se₃ proceeds via a hyperextended (by >60%) ammonia-rich intercalate, to eventually produce a layered compound with lithium amide intercalated between the bismuth selenide layers which offers scope for further chemical manipulation.

New lithium amide/ammonia intercalates of Bi₂Se₃ are revealed using in situ X-ray powder diffraction.

Hybrid Symmetry Epitaxy of the Superconducting Fe(Te,Se) Film on a Topological Insulator

It is challenging to grow an epitaxial 4-fold compound superconductor (SC) on a 6-fold topological insulator (TI) platform due to the stringent lattice-matching requirement. Here, we demonstrate that Fe(Te,Se) can grow epitaxially on a TI (Bi2Te3) layer due to accidental, uniaxial lattice match, which is dubbed as "hybrid symmetry epitaxy". This new growth mode is critical to stabilizing robust superconductivity with TC as high as 13 K. Furthermore, the superconductivity in this FeTe1-xSex/Bi2Te3 system survives in the Te-rich phase with Se content as low as x = 0.03 but vanishes at Se content above x = 0.56, exhibiting a phase diagram that is quite different from that of the conventional Fe(Te,Se) systems. This unique heterostructure platform that can be formed in both TI-on-SC and SC-on-TI sequences opens a route to unprecedented topological heterostructures.

Tip-induced superconductivity

It is widely believed that topological superconductivity, a hitherto elusive phase of quantum matter, can be achieved by inducing superconductivity in topological materials. In search of such topological superconductors, certain topological insulators (like, Bi₂Se₃) were successfully turned into superconductors by metal-ion (Cu, Pd, Sr, Nb etc) intercalation. Superconductivity could be induced in topological materials through applying pressure as well. For example, a pressure-induced superconducting phase was found in the topological insulator Bi₂Se₃. However, in all such cases, no conclusive signature of topological superconductivity was found. In this review, we will discuss about another novel way of inducing superconductivity in a non-superconducting topological material-by creating a mesoscopic interface on the material with a non-superconducting, normal metallic tip where the mesoscopic interface becomes superconducting. Such a phase is now known as a tip-induced superconducting (TISC) phase. This was first realized on Cd₃As₂in India. Following that, a large number of other topological materials were shown to display TISC. Since the TISC phase emerges only at a confined region under a mesoscopic point contact, traditional bulk tools for characterizing superconductivity cannot be employed to detect/confirm such a phase. On the other hand, such a point contact geometry is ideal for probing the possible existence of a temperature and magnetic field dependent superconducting energy gap and a temperature and magnetic field dependent critical current. We will review the details of the experimental signatures that can be used to prove the existence of superconductivity even when the 'text-book' tests for detecting superconductivity cannot be performed. Then, we will review various systems where a TISC phase could be realized.

Observation of topological superconductivity in a stoichiometric transition metal dichalcogenide 2M-WS2

Topological superconductors (TSCs) are unconventional superconductors with bulk superconducting gap and in-gap Majorana states on the boundary that may be used as topological qubits for quantum computation. Despite their importance in both fundamental research and applications, natural TSCs are very rare. Here, combining state of the art synchrotron and laser-based angle-resolved photoemission spectroscopy, we investigated a stoichiometric transition metal dichalcogenide (TMD), 2M-WS₂ with a superconducting transition temperature of 8.8 K (the highest among all TMDs in the natural form up to date) and observed distinctive topological surface states (TSSs). Furthermore, in the superconducting state, we found that the TSSs acquired a nodeless superconducting gap with similar magnitude as that of the bulk states. These discoveries not only evidence 2M-WS₂ as an intrinsic TSC without the need of sensitive composition tuning or sophisticated heterostructures fabrication, but also provide an ideal platform for device applications thanks to its van der Waals layered structure.

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.

Fermi surfaces of the topological semimetal CaSn3probed through de Haas van Alphen oscillations

In the search of topological superconductors, nailing down the Fermiology of the normal state is as crucial a prerequisite as unraveling the superconducting pairing symmetry. In particular, the number of time-reversal-invariant momenta (TRIM) in the Brillouin zone enclosed by Fermi surfaces is closely linked to the topological class of time-reversal-invariant systems, and can experimentally be investigated. We report here a detailed study of de Haas van Alphen quantum oscillations in single crystals of the topological semimetal CaSn₃with torque magnetometry in high magnetic fields up to 35 T. In conjunction with density functional theory based calculations, the observed quantum oscillations frequencies indicate that the Fermi surfaces of CaSn₃enclose an odd number of TRIM, satisfying one of the proposed criteria to realize topological superconductivity. Nonzero Berry phases extracted from the magnetic oscillations also support the nontrivial topological nature of CaSn₃.

The pressure-enhanced superconducting phase of Sr[Formula: see text]-Bi[Formula: see text]Se[Formula: see text] probed by hard point contact spectroscopy

The superconducting systems emerging from topological insulators upon metal ion intercalation or application of high pressure are ideal for investigation of possible topological superconductivity. In this context, Sr-intercalated Bi[Formula: see text]Se[Formula: see text] is specially interesting because it displays pressure induced re-entrant superconductivity where the high pressure phase shows almost two times higher [Formula: see text] than the ambient superconducting phase ( [Formula: see text] K). Interestingly, unlike the ambient phase, the pressure-induced superconducting phase shows strong indication of unconventional superconductivity. However, since the pressure-induced phase remains inaccessible to spectroscopic techniques, the detailed study of the phase remained an unattained goal. Here we show that the high-pressure phase can be realized under a mesoscopic point contact, where transport spectroscopy can be used to probe the spectroscopic properties of the pressure-induced phase. We find that the point contact junctions on the high-pressure phase show unusual response to magnetic field supporting the possibility of unconventional superconductivity.

Two-Dimensional 2M-WS2 Nanolayers for Superconductivity

Recently, a newly discovered VIB group transition metal dichalcogenide (TMD) material, 2M-WS₂, has attracted extensive attention due to its interesting physical properties such as topological superconductivity, nodeless superconductivity, and anisotropic Majorana bound states. However, the techniques to grow high-quality 2M-WS₂ bulk crystals and the study of their physical properties at the nanometer scale are still limited. In this work, we report a new route to grow high-quality 2M-WS₂ single crystals and the observation of superconductivity in its thin layers. The crystal structure of the as-grown 2M-WS₂ crystals was determined by X-ray diffraction (XRD) and scanning tunneling microscopy (STM). The chemical composition of the 2M-WS₂ crystals was determined by energy dispersive X-ray spectroscopy (EDS) analysis. At 77 K, we observed the spatial variation of the local tunneling conductance (dI/dV) of the 2M-WS2 thin flakes by scanning tunneling spectroscopy (STS). Our low temperature transport measurements demonstrate clear signatures of superconductivity of a 25 nm-thick 2M-WS₂ flake with a critical temperature (T _C) of ∼8.5 K and an upper critical field of ∼2.5 T at T = 1.5 K. Our work may pave new opportunities in studying the topological superconductivity at the atomic scale in simple 2D TMD materials.

Superconductivity in topological insulator-PdBi2under pressure

The topological insulator PdBi2exhibits two different crystal phases at ambient pressure, i.e., 'α-PdBi2' and ' -PdBi2'. The pressure dependence of crystal structure and superconductivity of α-PdBi2has been fully elucidated thus far. However, the physical properties of β-PdBi2crystals under pressure have not been sufficiently investigated. In this study, we fully investigate the crystal structure and superconductivity of β-PdBi2under pressure based on synchrotron x-ray diffraction (XRD) patterns. The temperature dependence of β-PdBi2indicates its superconductivity with a superconducting transition temperature (Tc) as high as 4.10 K, and its crystal structure is tetragonal [space group ofI4/mmm(no. 139)]. The XRD patterns at 0-22.0 GPa indicate no structural phase transitions, and the unit cell volume shrinks monotonically with pressure, unlike the behavior of α-PdBi2. Furthermore, α-PdBi2transformed to β-PdBi2under pressure. This suggests that β-PdBi2is stable under pressure. The superconductivity is clearly observed at 0-11.8 GPa, and the value ofTcis almost constant at ∼4.4 K. The temperature dependence of the upper critical field at ambient pressure and 10.7 GPa indicates that the superconductivity is not attributed to a simples-wave dirty limit but ans-wave clean orp-wave polar model. This is the first systematic study of superconductivity of topological insulator β-PdBi2under pressure.

Time-Domain Investigations of Coherent Phonons in van der Waals Thin Films

Coherent phonons can be launched in materials upon localized pulsed optical excitation, and be subsequently followed in time-domain, with a sub-picosecond resolution, using a time-delayed pulsed probe. This technique yields characterization of mechanical, optical, and electronic properties at the nanoscale, and is taken advantage of for investigations in material science, physics, chemistry, and biology. Here we review the use of this experimental method applied to the emerging field of homo- and heterostructures of van der Waals materials. Their unique structure corresponding to non-covalently stacked atomically thin layers allows for the study of original structural configurations, down to one-atom-thin films free of interface defect. The generation and relaxation of coherent optical phonons, as well as propagative and resonant breathing acoustic phonons, are comprehensively discussed. This approach opens new avenues for the in situ characterization of these novel materials, the observation and modulation of exotic phenomena, and advances in the field of acoustics microscopy.

Soft-Mode-Phonon-Mediated Unconventional Superconductivity in Monolayer 1T^{'}-WTe_{2}

Recent experiments have tuned the monolayer 1T^{'}-WTe_{2} to be superconducting by electrostatic gating. Here, we theoretically study the phonon-mediated superconductivity in monolayer 1T^{'}-WTe_{2} via charge doping. We reveal that the emergence of soft-mode phonons with specific momentum is crucial to give rise to the superconductivity in the electron-doping regime, whereas no such soft-mode phonons and no superconductivity emerge in the hole-doping regime. We also find a superconducting dome, which can be attributed to the change of Fermi surface nesting conditions with electron doping. By taking into account the experimentally established strong anisotropy of temperature-dependent upper critical field H_{c2} between the in-plane and out-of-plane directions, we show that the superconducting state probably has the unconventional equal-spin-triplet pairing in the A_{u} channel of the C_{2h} point group. Our studies provide a promising understanding to the doping dependent superconductivity and strong anisotropy of H_{c2} in monolayer 1T^{'}-WTe_{2}, and can be extended to understand the superconductivity in other gated transition metal dichalcogenides.

Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering

Helium-atom scattering (HAS) spectroscopy from conducting surfaces has been shown to provide direct information on the electron–phonon interaction, more specifically the mass-enhancement factor λ from the temperature dependence of the Debye–Waller exponent, and the mode-selected electron–phonon coupling constants λQν from the inelastic HAS intensities from individual surface phonons. The recent applications of the method to superconducting ultra-thin films, quasi-1D high-index surfaces, and layered transition-metal and topological pnictogen chalcogenides are briefly reviewed.

Quantum oscillations with angular dependence in PdTe2single crystals

The layered transition-metal dichalcogenide PdTe₂has been discovered to possess bulk Dirac points as well as topological surface states. By measuring the magnetization (up to 7 T) and magnetic torque (up to 35 T) in single crystalline PdTe₂, we observe distinct de Haas-van Alphen (dHvA) oscillations. Eight frequencies are identified withH||c, with two low frequencies (F_α= 8 T andF_β= 117 T) dominating the spectrum. The effective masses obtained by fitting the Lifshitz-Kosevich (LK) equation to the data aremα*=0.059m0andmβ*=0.067m0wherem₀is the free electron mass. The corresponding Landau fan diagrams allow the determination of the Berry phase for these oscillations resulting in values of ∼0.67πfor the 3D α band (hole-type) (down to the 1st Landau level) and ∼0.23π-0.73πfor the 3D β band (electron-type) (down to the 3rd Landau level). By investigating the angular dependence of the dHvA oscillations, we find that the frequencies and the corresponding Berry phase (Φ_B) vary with the field direction, with a Φ_B∼ 0 whenHis 10°-30° away from theabplane for both α and β bands. The multiple band nature of PdTe₂is further confirmed from Hall effect measurements.

Spin-Orbit-Parity-Coupled Superconductivity in Topological Monolayer WTe_{2}

Recent experiments reported gate-induced superconductivity in the monolayer 1T^{'}-WTe_{2} which is a two-dimensional topological insulator in its normal state. The in-plane upper critical field B_{c2} is found to exceed the conventional Pauli paramagnetic limit B_{p} by one to three times. The enhancement cannot be explained by conventional spin-orbit coupling which vanishes due to inversion symmetry. In this Letter, we unveil some distinctive superconducting properties of centrosymmetric 1T^{'}-WTe_{2} which arise from the coupling of spin, momentum and band parity degrees of freedom. As a result of this spin-orbit-parity coupling (SOPC): (i) there is a first-order superconductor-metal transition at B_{c2} that is much higher than the Pauli paramagnetic limit B_{p}, (ii) spin-susceptibility is anisotropic with respect to in-plane directions and can result in possible anisotropic B_{c2}, and (iii) the B_{c2} exhibits a strong gate dependence as the spin-orbit-parity coupling is significant only near the topological band crossing points. The importance of SOPC on the topologically nontrivial inter-orbital pairing phase is also discussed. Our theory generally applies to centrosymmetric materials with topological band inversions.

Evidence for nematic superconductivity of topological surface states in PbTaSe2

Spontaneous symmetry breaking has been a paradigm to describe the phase transitions in condensed matter physics. In addition to the continuous electromagnetic gauge symmetry, an unconventional superconductor can break discrete symmetries simultaneously, such as time reversal and lattice rotational symmetry. In this work we report a characteristic in-plane 2-fold behaviour of the resistive upper critical field and point-contact spectra on the superconducting semimetal PbTaSe₂ with topological nodal-rings, despite its hexagonal lattice symmetry (or D_3h in bulk while C_3v on surface, to be precise). The 2-fold behaviour persists up to its surface upper critical field H_c2^R even though bulk superconductivity has been suppressed at its bulk upper critical field H_c2^HC≪H_c2^R, signaling its probable surface-only electronic nematicity. In addition, we do not observe any lattice rotational symmetry breaking signal from field-angle-dependent specific heat within the resolution. It is worth noting that such surface-only electronic nematicity is in sharp contrast to the observation in the topological superconductor candidate, Cu_xBi₂Se₃, where the nematicity occurs in various bulk measurements. In combination with theory, superconducting nematicity is likely to emerge from the topological surface states of PbTaSe₂, rather than the proximity effect. The issue of time reversal symmetry breaking is also addressed. Thus, our results on PbTaSe₂ shed new light on possible routes to realize nematic superconductivity with nontrivial topology.

Uniaxial-strain control of nematic superconductivity in SrxBi2Se3

Nematic states are characterized by rotational symmetry breaking without translational ordering. Recently, nematic superconductivity, in which the superconducting gap spontaneously lifts the rotational symmetry of the lattice, has been discovered. In nematic superconductivity, multiple superconducting domains with different nematic orientations can exist, and these domains can be controlled by a conjugate external stimulus. Domain engineering is quite common in magnets but has not been achieved in superconductors. Here, we report control of the nematic superconductivity and their domains of SrxBi2Se3, through externally-applied uniaxial stress. The suppression of subdomains indicates that it is the Δ4y state that is most favoured under compression along the basal Bi-Bi bonds. This fact allows us to determine the coupling parameter between the nematicity and lattice distortion. These results provide an inevitable step towards microscopic understanding and future utilization of the unique topological nematic superconductivity.

Chemical Vapor Deposition of IrTe2 Thin Films

Two-dimensional (2D) IrTe2 has a profound charge ordering and superconducting state, which is related to its thickness and doping. Here, we report the chemical vapor deposition (CVD) of IrTe2 films using different Ir precursors on different substrates. The Ir(acac)3 precursor and hexagonal boron nitride (h-BN) substrate is found to yield a higher quality of polycrystalline IrTe2 films. Temperature-dependent Raman spectroscopic characterization has shown the q1/8 phase to HT phase at ~250 K in the as-grown IrTe2 films on h-BN. Electrical measurement has shown the HT phase to q1/5 phase at around 220 K.

Vortex End Majorana Zero Modes in Superconducting Dirac and Weyl Semimetals

Time-reversal invariant Dirac and Weyl semimetals in three dimensions (3D) can host open Fermi arcs and spin-momentum locking Fermi loops on the surfaces. We find that when they become superconducting with s-wave pairing and the doping is lower than a critical level, straight π-flux vortex lines terminating at surfaces with Fermi arcs or spin-momentum locking Fermi loops can realize 1D topological superconductivity and harbor Majorana zero modes at their ends. Remarkably, we find that the vortex-generation-associated Zeeman field can open (when the surfaces have only Fermi arcs) or enhance the topological gap protecting Majorana zero modes, which is contrary to the situation in superconducting topological insulators. By studying the tilting effect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weyl semimetals in general have a much broader topological regime than type-II ones. Our findings build up a connection between time-reversal invariant Dirac and Weyl semimetals and Majorana zero modes in vortices.

Phonon softening and higher-order anharmonic effect in the superconducting topological insulator SrxBi2Se3

We report the anharmonic effect of the Raman-scattering spectrum in the low-carrier density superconductor SrxBi2Se3, which is dominated by the quartic term. Compared to the parent Bi2Se3, the superconducting SrxBi2Se3crystals show obvious phonon softening in the three optical phonon modesA1g1,Eg2, andA1g2. Based on the simulations by the Fano function, we present compelling evidence of the enhanced electron-phonon coupling in SrxBi2Se3for its smaller asymmetric parameterq. Moreover, an anomalous broadening and intensity antiresonance in the characteristic Raman peaks were observed as the temperature decreased to around 160 K. Thus, the superconducting topological material SrxBi2Se3represents a counterintuitive example where the electron-phonon interaction is strengthened by the accumulation of electron carriers.

Z3-vestigial nematic order due to superconducting fluctuations in the doped topological insulators NbxBi2Se3 and CuxBi2Se3

A state of matter with a multi-component order parameter can give rise to vestigial order. In the vestigial phase, the primary order is only partially melted, leaving a remaining symmetry breaking behind, an effect driven by strong classical or quantum fluctuations. Vestigial states due to primary spin and charge-density-wave order have been discussed in iron-based and cuprate materials. Here we present the observation of a partially melted superconductivity in which pairing fluctuations condense at a separate phase transition and form a nematic state with broken Z3, i.e., three-state Potts-model symmetry. Thermal expansion, specific heat and magnetization measurements of the doped topological insulators NbxBi2Se3 and CuxBi2Se3 reveal that this symmetry breaking occurs at [Formula: see text] above [Formula: see text], along with an onset of superconducting fluctuations. Thus, before Cooper pairs establish long-range coherence at Tc, they fluctuate in a way that breaks the rotational invariance at Tnem and induces a crystalline distortion.

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.

Topological Semimetal Nanostructures: From Properties to Topotronics

Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.

Change in the electronic structure of the bismuth chalcogenide superconductor CsBi4-x Pb x Te6 by dissociation of the bismuth dimers

CsBi_4-x Pb _x Te₆ is synthesized and the superconductivity associated with the structural transition from Pb substitution is studied. Photoemission spectroscopy measurements are performed in order to elucidate the relationship between the electronic structure and the occurrence of the superconductivity. When Bi is substituted with Pb, an electron doping-like change in the electronic structure is directly observed which is contrary to the naive expectation of hole doping. This observation is consistent with band structure calculations and appears to be a unique characteristic of CsBi_4-x Pb _x Te₆ because of the dissociation of Bi dimers upon Pb substitution. These results indicate that it may be possible to control the electron and hole doping via manipulating the Bi dimers through Pb substitution.

Interfacial Superconductivity on the Topological Semimetal Tungsten Carbide Induced by Metal Deposition

Interfaces between materials with different electronic ground states have become powerful platforms for creating and controlling novel quantum states of matter, in which inversion symmetry breaking and other effects at the interface may introduce additional electronic states. Among the emergent phenomena, superconductivity is of particular interest. Here, by depositing metal films on a newly identified topological semimetal tungsten carbide (WC) single crystal, interfacial superconductivity is obtained, evidenced from soft point-contact spectroscopy. This very robust phenomenon is demonstrated for a wide range of metal/WC interfaces, involving both nonmagnetic and ferromagnetic films, and the superconducting transition temperatures are surprisingly insensitive to the magnetism of thin films. This method offers an opportunity to explore the long-sought topological superconductivity and has potential applications in topological-state-based spin devices.

High-Pressure Synthesis and Superconducting Properties of NaCl-Type In1−xPbxTe (x = 0–0.8)

We have investigated the Pb-substitution effect upon the superconductivity of NaCl-type In1−xPbxTe. Polycrystalline samples with x = 0–0.8 were synthesized using high-pressure synthesis. The lattice parameter was systematically increased by Pb substitution. For x ≤ 0.6, bulk superconductivity was observed, and the superconducting transition temperature increased from 3 K (for InTe) to 5 K by Pb substitutions. From analyses of specific heat jumps at the superconducting transition, conventional (phonon-mediated) weak-coupling pairing mechanisms were suggested for In1−xPbxTe.

Symmetry of Order Parameters in Multiband Superconductors LaRu_{4}As_{12} and PrOs_{4}Sb_{12} Probed by Local Magnetization Measurements

The temperature dependencies of the lower critical field H_{c1}(T) of several filled-skutterudite superconductors were investigated by local magnetization measurements. While LaOs_{4}As_{12} and PrRu_{4}As_{12} exhibit the H_{c1}(T) dependencies consistent with the single-band BCS prediction, for LaRu_{4}As_{12} (the superconducting temperature T_{c}=10.4  K) with a similar three-dimensional Fermi surface, we observe a sudden increase in H_{c1}(T) deep in a superconducting state below about 0.32T_{c}. Remarkably, a rapid rise of H_{c1}(T) at approximately the same reduced temperature 0.27T_{c} is also found for the heavy-fermion compound PrOs_{4}Sb_{12} (T_{c}≃1.78  K), in fair accord with the earlier macroscopic study. We attribute the unusual H_{c1}(T) dependencies of LaRu_{4}As_{12} and PrOs_{4}Sb_{12} to a kink structure in their superfluid densities due to different contributions from two nearly decoupled bands. Whereas LaRu_{4}As_{12} is established as a two-band isotropic s-wave superconductor, nonsaturating behavior of H_{c1}(T) is observed for PrOs_{4}Sb_{12}, indicative of an anisotropic structure of a smaller gap. For this superconductor with broken time-reversal symmetry, our findings suggest a superconducting state with multiple symmetries of the order parameters.

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.

Conversion of a conventional superconductor into a topological superconductor by topological proximity effect

Realization of topological superconductors (TSCs) hosting Majorana fermions is a central challenge in condensed-matter physics. One approach is to use the superconducting proximity effect (SPE) in heterostructures, where a topological insulator contacted with a superconductor hosts an effective p-wave pairing by the penetration of Cooper pairs across the interface. However, this approach suffers a difficulty in accessing the topological interface buried deep beneath the surface. Here, we propose an alternative approach to realize topological superconductivity without SPE. In a Pb(111) thin film grown on TlBiSe₂, we discover that the Dirac-cone state of substrate TlBiSe₂ migrates to the top surface of Pb film and obtains an energy gap below the superconducting transition temperature of Pb. This suggests that a Bardeen-Cooper-Schrieffer superconductor is converted into a TSC by the topological proximity effect. Our discovery opens a route to manipulate topological superconducting properties of materials.

Realizing topological superconductivity is essential for applicable fault-tolerant quantum computation. Here, Trang et al. report migration of Dirac-cone from TlBiSe₂ substrate to top surface of superconducting Pb film due to topological proximity effect, suggesting realization of topological superconductivity.

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 in an organometallic compound

Organometallic compounds constitute a very large group of substances that contain at least one metal-to-carbon bond in which the carbon is part of an organic group. They have played a major role in the development of the science of chemistry. These compounds are used to a large extent as catalysts (substances that increase the rate of reactions without themselves being consumed) and as intermediates in the laboratory and in industry. Recently, novel quantum phenomena such as topological insulators and superconductors were also suggested in these materials. However, there has been no report on the experimental exploration of the topological state. Evidence for superconductivity from the zero-resistivity state in any organometallic compound has not been achieved yet, though much effort has been made. Here we report the experimental realization of superconductivity with a critical temperature of 3.6 K in a potassium-doped organometallic compound, i.e. tri-o-tolylbismuthine, with evidence of both the Meissner effect and the zero-resistivity state through dc and ac magnetic susceptibility measurements. The obtained superconducting parameters classify this compound as a type-II superconductor. The benzene ring is identified to be the essential superconducting unit in such a phenyl organometallic compound. The superconducting phase and its composition are determined by combined studies of X-ray diffraction and theoretical calculations as well as Raman spectroscopy measurements. These findings enrich the applications of organometallic compounds in superconductivity and add a new electron-acceptor family of organic superconductors. This work also points to a large pool for finding superconductors from organometallic compounds.

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.

Crystalline electric field study in a putative topologically trivial rare-earth doped YPdBi compound

Topological states of matter have attracted a lot of attention recently due to their intriguing physical properties and potential applications. In particular, the family of half-Heusler compounds [Formula: see text] (R  =  rare earth, M  =  Pt, Pd or Au, and T  =  Bi, Sb, Pb or Sn) has been predicted to display tunable topological properties via their cubic unit cell volume and/or the charges of the M and T atoms. In this work, we report electron spin resonance (ESR), along with complementary macroscopic experiments, in the putative topologically trivial rare-earth doped (Gd, Nd and Er) YPdBi. From magnetic susceptibility data analysis constrained by ESR results, we were able to extract the fourth (A ₄) and sixth (A ₆) order crystal field parameters (CFP) for YPdBi and compared them with those already reported to YPtBi, which is known as a topologically non-trivial compound. We observed that the sign of the CFP changes systematically from YPdBi to YPtBi, possibly due to the inversion of the valence and conduction bands at the Fermi level. The enhanced spin-orbit coupling in YPtBi, when compared to YPdBi, induces the band inversion that drives the system to a non-trivial topological state. This band inversion likely has an effect on the effective charges surrounding the magnetic dopants that are probed by the CFP.

Experimental evidence of anomalously large superconducting gap on topological surface state of β-Bi2Pd film

Connate topological superconductor (TSC) combines topological surface states with nodeless superconductivity in a single material, achieving effective p-wave pairing without interface complication. By combining angle-resolved photoemission spectroscopy and in-situ molecular beam epitaxy, we studied the momentum-resolved superconductivity in β-Bi₂Pd film. We found that the superconducting gap of topological surface state (Δ_TSS ∼ 3.8 meV) is anomalously enhanced from its bulk value (Δ_b ∼ 0.8 meV). The ratio of 2Δ_TSS/k_BT_c ∼ 16.3, is substantially larger than the BCS value. By measuring β-Bi₂Pd bulk single crystal as a comparison, we clearly observed the upward-shift of chemical potential in the film. In addition, a concomitant increasing of surface weight on the topological surface state was revealed by our first principle calculation, suggesting that the Dirac-fermion-mediated parity mixing may cause this anomalous superconducting enhancement. Our results establish β-Bi₂Pd film as a unique case of connate TSCs with a highly enhanced topological superconducting gap, which may stabilize Majorana zero modes at a higher temperature.

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.

Pressure-Induced Large Volume Collapse, Plane-to-Chain, Insulator to Metal Transition in CaMn2Bi2

In situ high pressure single crystal X-ray diffraction study reveals that the quantum material CaMn₂Bi₂ undergoes a unique plane to chain structural transition between 2 and 3 GPa, accompanied by a large volume collapse. Puckered Mn-Mn honeycomb layer converts to quasi-one-dimensional (1D) zigzag chains above the phase transition pressure. Single crystal measurements reveal that the pressure-induced structural transformation is accompanied by a dramatic 2 orders of magnitude drop of resistivity. Although the ambient pressure phase displays semiconducting behavior at low temperatures, metallic temperature dependent resistivity is observed for the high pressure phase, as surprisingly, are two resistivity anomalies with opposite pressure dependences, while one of them could be a magnetic transition and the other originates from Fermi surface instability. Assessment of the total energies for hypothetical magnetic structures for high pressure CaMn₂Bi₂ indicates that ferrimagnetism is thermodynamically favored.

Quasiparticle Evidence for the Nematic State above T_{c} in Sr_{x}Bi_{2}Se_{3}

In the electronic nematic state, an electronic system has a lower symmetry than the crystal structure of the same system. Electronic nematic states have been observed in various unconventional superconductors such as cuprate, iron-based, heavy-fermion, and topological superconductors. The relation between nematicity and superconductivity is a major unsolved problem in condensed matter physics. By angle-resolved specific heat measurements, we report bulk quasiparticle evidence of nematicity in the topological superconductor Sr_{x}Bi_{2}Se_{3}. The specific heat exhibited a clear twofold symmetry despite the threefold symmetric lattice. Most importantly, the twofold symmetry appeared in the normal state above the superconducting transition temperature. This is explained by the angle-dependent Zeeman effect due to the anisotropic density of states in the nematic phase. Such results highlight the interrelation between nematicity and unconventional superconductivity.

Nonlinear Planar Hall Effect

An intriguing property of a three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi_{2}Se_{3} film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a π/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of π/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time-reversal symmetry breaking, which also exists in a wide class of noncentrosymmetric materials with a large span of magnitude. It provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.

Discovery of Superconductivity in 2M WS2 with Possible Topological Surface States

Recently the metastable 1T'-type VIB-group transition metal dichalcogenides (TMDs) have attracted extensive attention due to their rich and intriguing physical properties, including superconductivity, valleytronics physics, and topological physics. Here, a new layered WS₂ dubbed "2M" WS₂ , is constructed from 1T' WS₂ monolayers, is synthesized. Its phase is defined as 2M based on the number of layers in each unit cell and the subordinate crystallographic system. Intrinsic superconductivity is observed in 2M WS₂ with a transition temperature T_c of 8.8 K, which is the highest among TMDs not subject to any fine-tuning process. Furthermore, the electronic structure of 2M WS₂ is found by Shubnikov-de Haas oscillations and first-principles calculations to have a strong anisotropy. In addition, topological surface states with a single Dirac cone, protected by topological invariant Z₂ , are predicted through first-principles calculations. These findings reveal that the new 2M WS₂ might be an interesting topological superconductor candidate from the VIB-group transition metal dichalcogenides.

Evidence for singular-phonon-induced nematic superconductivity in a topological superconductor candidate Sr0.1Bi2Se3

Superconductivity mediated by phonons is typically conventional, exhibiting a momentum-independent s-wave pairing function, due to the isotropic interactions between electrons and phonons along different crystalline directions. Here, by performing inelastic neutron scattering measurements on a superconducting single crystal of Sr0.1Bi2Se3, a prime candidate for realizing topological superconductivity by doping the topological insulator Bi2Se3, we find that there exist highly anisotropic phonons, with the linewidths of the acoustic phonons increasing substantially at long wavelengths, but only for those along the [001] direction. This observation indicates a large and singular electron-phonon coupling at small momenta, which we propose to give rise to the exotic p-wave nematic superconducting pairing in the MxBi2Se3 (M = Cu, Sr, Nb) superconductor family. Therefore, we show these superconductors to be example systems where electron-phonon interaction can induce more exotic superconducting pairing than the s-wave, consistent with the topological superconductivity.

Emergence of intrinsic superconductivity below 1.178 K in the topologically non-trivial semimetal state of CaSn3

Topological materials which are also superconducting are of great current interest, since they may exhibit a non-trivial topologically-mediated superconducting phase. Although there have been many reports of pressure-tuned or chemical-doping-induced superconductivity in a variety of topological materials, there have been few examples of intrinsic, ambient pressure superconductivity in a topological system having a stoichiometric composition. Here, we report that the pure intermetallic CaSn₃ not only exhibits topological fermion properties, but also has a superconducting phase at ~1.178 K under ambient pressure. The topological fermion properties, including the nearly zero quasi-particle mass and the non-trivial Berry phase accumulated in cyclotron motions, were revealed from the de Haas-van Alphen (dHvA) quantum oscillation studies of this material. Although CaSn₃ was previously reported to be superconducting with T _c  =  4.2 K, our studies show that the T _c  =  4.2 K superconductivity is extrinsic and caused by Sn on the degraded surface, whereas its intrinsic bulk superconducting transition occurs at 1.178 K. These findings make CaSn₃ a promising candidate for exploring new exotic states arising from the interplay between non-trivial band topology and superconductivity, e.g. topological superconductivity (TSC).

Formation of Fe-Te Nanostructures during in Situ Fe Heavy Doping of Bi2Te3

To study the in situ doping effect upon monotonically increasing dopant concentration, a Bi₂Te₃ layer doped with Fe up to ~6.9% along the growth direction was fabricated by the molecular beam epitaxy (MBE) technique. Its resistance versus temperature curve displays a superconductivity transition at about 12.3 K. Detailed structural and chemical analysis via X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy-dispersive X-ray spectroscopy (EDS) reveal that this layer consists of two types of unexpected Fe-Te nanostructures: one is FeTe thin layer formed near the surface, and the other is FeTe₂ nanorod embedded in the Bi₂Te₃ layer. Based on the results of further electrical and magnetotransport studies, it is likely that the observed superconductivity originates from the interface between the FeTe nanostructure and the neighboring Bi₂Te₃ layer. We have addressed the formation mechanisms of the observed nanostructures, which is attributed to the strong reaction between Fe and Te atoms during the growth process. The findings of this study also provide an unusual approach to synthesizing nanostructures via heavy doping if the dopant element is strongly reactive with an element in the host matrix.

Fermi level tuning of Ag-doped Bi2Se3 topological insulator

The temperature dependence of the resistivity (ρ) of Ag-doped Bi₂Se₃ (Ag_xBi_2−xSe₃) shows insulating behavior above 35 K, but below 35 K, ρ suddenly decreases with decreasing temperature, in contrast to the metallic behavior for non-doped Bi₂Se₃ at 1.5–300 K. This significant change in transport properties from metallic behavior clearly shows that the Ag doping of Bi₂Se₃ can effectively tune the Fermi level downward. The Hall effect measurement shows that carrier is still electron in Ag_xBi_2−xSe₃ and the electron density changes with temperature to reasonably explain the transport properties. Furthermore, the positive gating of Ag_xBi_2−xSe₃ provides metallic behavior that is similar to that of non-doped Bi₂Se₃, indicating a successful upward tuning of the Fermi level.

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.

Kondo Signatures of a Quantum Magnetic Impurity in Topological Superconductors

We study the Kondo physics of a quantum magnetic impurity in two-dimensional topological superconductors (TSCs), either intrinsic or induced on the surface of a bulk topological insulator, using a numerical renormalization group technique. We show that, despite sharing the p+ip pairing symmetry, intrinsic and extrinsic TSCs host different physical processes that produce distinct Kondo signatures. Extrinsic TSCs harbor an unusual screening mechanism involving both electron and orbital degrees of freedom that produces rich and prominent Kondo phenomena, especially an intriguing pseudospin Kondo singlet state in the superconducting gap and a spatially anisotropic spin correlation. In sharp contrast, intrinsic TSCs support a robust impurity spin doublet ground state and an isotropic spin correlation. These findings advance fundamental knowledge of novel Kondo phenomena in TSCs and suggest experimental avenues for their detection and distinction.

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.

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.