Intrinsic topological superconductors with p-wave pairing are rare in nature. Its underlying reason is due to the fact that it is usually difficult to change the relative strength between the singlet and triplet channels for the electron-electron interaction in material. Here we show that by considering superconductivity occurring on surfaces of topological insulators (TIs), the relative strength between the singlet and triplet channels can be changed by geometry and sizes of TIs. Specifically, we show that pairing of electrons at different locations on the surface of a topological insulator generally tends to favor the triplet pairing and can induce topological superconductivity by controlling the surface curvature and size of the topological insulator. We illustrate the effects in two configurations, thin film geometry and the spherical geometry with a sphere or a hemisphere, and find that topological superconductivity arises with the $p \pm ip$ pairing symmetry dominated in nanoscale size of the TI. As a consequence, vortices can spontaneously form on surfaces of topological insulators with roughness of appropriate curvature. These vortices support a Majorana zero mode inside each core and can be used as a platform to host Majorana zero modes without invoking real magnetic fields. Our theoretical discovery opens a new route to realize topological superconductivity in material.
Intrinsic and symmetry protected topological states have attracted lots of interest in condensed matter physics recently. In particular, time reversal symmetry protected fermion topological insulators have been theoretically predicted and experimentally verified. However despite considerable experimental and theoretical works, definitive evidence for time reversal invariant topological superconductivity is still lacking. Here we propose that upon electron doping the hydrogenated single bilayer Bi, namely BiH, will exhibit time reversal invariant topological superconductivity. If confirmed expe…
Using functional renormalization group method, we study the favorable condition for electronic correlation driven time reversal invariant topological superconductivity in symmetry class DIII. For non-centrosymmetric systems we argue that the proximity to ferromagnetic (or small wavevector magnetic) instability can be used as a guideline for the search of this type of superconductivity. This is analogous to the appearance of singlet unconventional superconductivity in the neighborhood of antiferromagnetic instability. We show three concrete examples where ferromagnetic-like fluctuation leads to…
Van der Waals materials like NbSe$_2$ or TaS$_2$ have demonstrated Ising superconductivity down to atomically thin layers. Due to the spin-orbit coupling, these superconductors have the in-plane upper critical magnetic field far beyond the Pauli limit. We theoretically demonstrate that, twisted bilayer Ising superconductors separated by a ferromagnetic buffer layer can naturally host chiral topological superconductivity with Chern numbers, which can be realized in heterostructures like $\mathrm{NbSe_2/CrCl_3/NbSe_2}$. Under appropriate experimental conditions the topological superconducting ga…
Majorana zero modes are a much sought-after consequence of one-dimensional topological superconductivity. Here, we show that, in turn, zero modes accompanying dynamical instanton events strongly enhance -- in some cases even enable -- superconductivity. We find that the dynamics of a one-dimensional topological triplet superconductor is governed by a $θ$ term in the action. For isotropic triplets, this term enables algebraic charge-$2e$ superconductivity, which is destroyed by fluctuations in nontopological superconductors. For anisotropic triplets, zero modes suppress quantum phase slips and …
We study a minimal Hubbard model for electronically driven superconductivity in a correlated flat mini-band resulting from the superlattice modulation of a twisted graphene multilayer. The valley degree of freedom drastically modifies the nature of thepreferred pairing states, favoring spin triplet $d+id$ order with a valley singlet structure. We identify two candidates in this class, which are both topological superconductors. These states support half-vortices carrying half the usual superconducting flux quantum $hc/(4e)$, and have topologically protected gapless edge states.
We propose an exotic scenario that topological superconductivity can emerge by doping strongly interacting fermionic systems whose spin degrees of freedom form bosonic symmetry protected topological (SPT) state. Specifically, we study a 1-dimensional (1D) example where the spin degrees of freedom form a spin-1 Haldane phase. {Before doping, the charge and spin degrees of freedom are both gapped.} Upon doping, {the charge channel becomes gapless and is described by a $c=1$ compactified bosonic conformal field theory (CFT), while the spin channel remains gapped and still form a bosonic SPT state…
We devise a new proximity junction configuration where an s-wave superconductivity and the superconductivity of Sr2RuO4 interfere with each other. We reproducibly observe in such a Pb/Ru/Sr2RuO4 junction with a single Pb electrode that the critical current Ic drops sharply just below the bulk Tc of Sr2RuO4 and furthermore increases again below a certain temperature below Tc. In order to explain this extraordinary temperature dependence of Ic, we propose a competition effect involving topologically distinct superconducting phases around Ru inclusions. Thus, such a device may be called a "topolo…
It was recently suggested that the topology of magic-angle twisted bilayer graphene's (MATBG) flat bands could provide a novel mechanism for superconductivity distinct from both weakly-coupled BCS theory and the $d$-wave phenomenology of the high-$T_c$ cuprates. In this work, we examine this possibility using a density matrix renormalization group (DMRG) study of a model which captures the essential features of MATBG's symmetry and topology. Using large scale cylinder-DMRG calculations to obtain the ground state and its excitations as a function of the electron doping, we find clear evidence f…
Superconductivity in topological materials has drawn a significant interest of the scientific community as these materials provide a hint of the existence of Majorana fermions conceived from the quantized thermal conductivity, a zero-biased conduction peak and the anomalous Josephson effect. In this review, we make a systematic study of recent advances in the field of topological superconductivity. The article comprises of both bulk systems as well as heterostructures. A brief description of Majorana fermions and their relationship with topological superconductors and heterostructures is also …
We find a mixed chirality $d$-wave superconducting state in the coexistence region between antiferromagnetism and interaction-driven superconductivity in lightly doped honeycomb materials. This state has a topological chiral $d+id$-wave symmetry in one Dirac valley but $d-id$-wave symmetry in the other valley and hosts two counter-propagating edge states, protected in the absence of intervalley scattering. A first-order topological phase transition, with no bulk gap closing, separates the chiral $d$-wave state at small magnetic moments from the mixed chirality $d$-wave phase.
We consider the coexistence of superconductivity(SC) and spin-density wave(SDW). The SC is presumed to be of $d_{x^2-y^2}+id_{xy} (d_1 + i d_2) $ type whereas the SDW order parameter is of $BCS$/$d_{x y} $ symmetry. The Hamiltonian having such a structure is shown to have topological coexistence phases in addition to the conventional one. It is shown that the amplitudes of both the order parameters determine the nature of topological phases. A phase diagram characterizing different topological phases with their Chern numbers are obtained. The experimental realization of such topological phases…
We report superconductivity in the ternary half-Heusler compound LuPtBi, with Tc = 1.0 K and Hc2 = 1.6 T. The crystal structure of LuPtBi lacks inversion symmetry, hence the material is a noncentrosymmetric superconductor. Magnetotransport data show semimetallic behavior in the normal state, which is evidence for the importance of spin-orbit interaction. Theoretical calculations indicate that the strong spin-orbit interaction in LuPtBi should cause strong band inversion, making this material a promising candidate for 3D topological superconductivity.
To pinpoint the microscopic mechanism for superconductivity has proven to be one of the most outstanding challenges in the physics of correlated quantum matter. Thus far, the most direct evidence for an electronic pairing mechanism is the observation of a new symmetry of the order-parameter, as done in the cuprate high-temperature superconductors. Like distinctions based on the symmetry of a locally defined order-parameter, global, topological invariants allow for a sharp discrimination between states of matter that cannot be transformed into each other adiabatically. Here we propose an unconv…
We investigate the robustness of topological superconductors under the perturbing influence of a finite charge current. To this aim, we introduce a modified Kitaev Hamiltonian parametrically dependent on the quasiparticle momentum induced by the current. Using different quantifiers of the topological phase, such as the Majorana polarization and the edge state quantum conditional mutual information, we prove the existence of a finite critical value of the quasiparticle momentum below which edge modes and topological superconductivity survive. We also discuss how a finite current breaks time rev…
Point contact conductance measurements on topological $Bi_2Te_2Se$ and $Bi_2Se_3$ films reveal a signature of superconductivity below 2-3 K. In particular, critical current dips and a robust zero bias conductance peak are observed. The latter suggests the presence of zero energy bound states which could be assigned to Majorana Fermions in an unconventional topological superconductor. We attribute these novel observations to proximity induced local superconductivity in the films by small amounts of superconducting Bi inclusions or segregation to the surface, and provide supportive evidence for …
We study the quasiparticle spectrum of 2D topological $s$-wave superconductors with the Zeeman magnetic field and the Rashba spin-orbit coupling in the presence of spatial inhomogeneity. Solving the real-space Bogoliubov-de Gennes equations, we focus on the excitations within the superconducting gap amplitude, i.e., the appearance of mid-gap states. Two kinds of potential functions, line-type (a chain of impurities) and point-type (a single impurity) ones are examined to take spatial inhomogeneity into account. The line setting shows a link of the mid-gap states with the gapless surface modes …
We derive a Kondo Lattice model with a correlated conduction band from a two-band Hubbard Hamiltonian. This mapping allows us to describe the emergence of a robust pairing mechanism in a model that only contains repulsive interactions. The mechanism is due to topological confinement and results from the interplay between antiferromagnetism and delocalization. By using Density-Matrix-Renormalization-Group (DMRG), we demonstrate that this mechanism leads to dominant superconducting correlations in a 1D-system.
The exploration of topological superconductivity and Majorana zero modes has become a rapidly developing field. Many types of proposals to realize topological superconductors have been presented, and significant advances have been recently made. In this review, we conduct a survey on the experimental progress in possible topological superconductors and induced superconductivity in topological insulators or semimetals as well as artificial structures. The approaches to inducing superconductivity in topological materials mainly include high pressure application, the hard-tip point contact method…
We investigate the superconducting gap function of topological superconductor PbTaSe$_2$. Temperature, magnetic field, and three-dimensional (3D) field-angle dependences of the specific heat prove that the superconductivity of PbTaSe$_2$ is fully-gapped, with two isotropic $s$-wave gaps. The pair-breaking effect is probed by systematically increasing non-magnetic disorders through H$^+$-irradiations. The superconducting transition temperature, $T_{\rm{c}}$, is found to be robust against disorders, which suggests that the pairing should be sign-preserved rather than sign-reversed.
One approach to discovering topological superconductor is establishing superconductivity based on well-identified topological insulators. However, the coexistence of superconductivity and topological state is always arcane. In this paper, we report how pressure tunes the crystal structure, electronic structure, and superconductivity in topological insulator Bi2Te2.1Se0.9. The first pressure-induced structure transition start from 8.4 GPa, followed by the structure sequence of R-3m - C2/m - C2/c - Im-3m up to 37 GPa. Superconductivity starts to present at 2.4 GPa with the Tc around 6.6 K. Moreo…
The intense search for topological superconductivity is inspired by the prospect that it hosts Majorana quasiparticles. We explore in this work the optimal design for producing topological superconductivity by combining a quantum Hall state with an ordinary superconductor. To this end, we consider a microscopic model for a topologically trivial two-dimensional p-wave superconductor exposed to a magnetic field, and find that the interplay of superconductivity and Landau level physics yields a rich phase diagram of states as a function of $μ/t$ and $Δ/t$, where $μ$, $t$ and $Δ$ are the chemical …
Despite intensive searches for topological superconductors, the realization of topological superconductivity remains under debate. Previous proposals for the topological $s$-wave, $p$-wave, and chiral $d$-wave superconductivity have both advantages and disadvantages. In this review, we discuss two-dimensional topological superconductivity based on the non-chiral $d$-wave superconductors. It is shown that the noncentrosymmetric $d$-wave superconductors become topological superconductors under an infinitesimal Zeeman field without fine-tuning of parameters. Floquet engineering for introducing th…
Topological superconductivity is one of most fascinating properties of topological quantum matters that was theoretically proposed and can support Majorana Fermions at the edge state. Superconductivity was previously realized in a Cu-intercalated Bi2Se3 topological compound or a Bi2Te3 topological compound at high pressure. Here we report the discovery of superconductivity in the topological compound Sb2Te3 when pressure was applied. The crystal structure analysis results reveal that superconductivity at a low-pressure range occurs at the ambient phase. The Hall coefficient measurements indica…
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 a…
We show two-dimensional "strong" topological superconductivity in d-wave superconductors (SCs). Although the topological invariant of the bulk wave function cannot be defined in d_{x^2-y^2}-wave and d_{xy}-wave SCs because of nodal excitations, the bulk energy spectrum of d-wave SCs on a substrate is fully gapped in a magnetic field. Then the superconducting state is specified by a nontrivial Chern number, and hence topologically nontrivial properties are robust against disorders and interactions. We discuss high-temperature topological superconductivity in cuprate SCs recently fabricated on a…
We predict that junctions between an antiferromagnetic insulator and a superconductor provide a robust platform to create a one-dimensional topological superconducting state. Its emergence does not require the presence of intrinsic spin-orbit coupling nor non-collinear magnetism, but arises solely from repulsive electronic interactions on interfacial solitonic states. We demonstrate that a topological superconducting state is generated by repulsive interactions at arbitrarily small coupling strength, and that the size of the topological gap rapidly saturates to the one of the parent trivial su…
We propose a new Rashba-free mechanism to realize topological superconductivity with electron-phonon interaction. In the presence of a magnetic field, electron-phonon interaction with small momentum transfer is found to favor spin-triplet Cooper pairing. This process facilitates the formation of chiral topological superconductivity even when Rashba spin-orbital coupling is absent. As a proof of concept, we propose an experimentally feasible heterostructure to systematically study the entangled relationship among forward-phonon scatterings, Rashba spin-orbital couplings, pairing symmetries, and…
We study how a $d$-wave superconductivity is changed when illuminated by circularly-polarised light (CPL) in the repulsive Hubbard model in the strong-coupling regime. We adopt the Floquet formalism for the Gutzwiller-projected effective Hamiltonian with the time-periodic Schrieffer-Wolff transformation. We find that CPL induces a topological superconductivity with a $d+id$ pairing, which arises from the chiral spin coupling and the three-site term generated by the CPL. The latter term remains significant even for low frequencies and low intensities of the CPL. This is clearly reflected in the…
Superconductivity and topological quantum states are two frontier fields of research in modern condensed matter physics. The realization of superconductivity in topological materials is highly desired, however, superconductivity in such materials is typically limited to two- or three-dimensional materials and is far from being thoroughly investigated. In this work, we boost the electronic properties of the quasi-one-dimensional topological insulator bismuth iodide \b{eta}-Bi4I4 by applying high pressure. Superconductivity is observed in \b{eta}-Bi4I4 for pressures where the temperature depende…
We present a theory of the high-spin generalization of topological insulators and their doped superconducting states. The higher-spin topological insulators involve a pair of $J=3/2$ bands with opposite parity, and are characterized by their band inversion. The low-energy effective theory reveals that the topological insulators host four different phases characterized by mirror Chern numbers, at which boundaries two different patterns of bulk Dirac points appear. For the carrier-doped case, it is shown that the system may host unique unconventional superconductivity because of its high-spin na…
We show that the topologically protected flat band emerging on a surface of a nodal fermionic system promotes the surface superconductivity due to an infinitely large density of states associated with the flat band. The critical temperature depends linearly on the pairing interaction and can be thus considerably higher than the exponentially small bulk critical temperature. We discuss an example of surface superconductivity in multilayered graphene with rhombohedral stacking.
We compute the angular dependence of the order parameter and tunneling amplitude in a model exhibiting topological superconductivity and sketch its derivation as a model of a doped Mott insulator. We show that ground states differing by an odd number of particles are orthogonal and the order parameter is in the d-representation, although the gap in the electronic spectrum has no nodes. We also develop an operator algebra, that allowes one to compute off-diagonal correlation functions.
We propose a possible way to realize topological superconductivity with application of laser light to superconducting cuprate thin films. Applying Floquet theory to a model of $d$-wave superconductors with Rashba spin-orbit coupling, we derive an effective model and discuss its topological nature. Interplay of the Rashba spin-orbit coupling and the laser light effect induces the synthetic magnetic fields, thus making the system gapped. Then the system acquires the topologically non-trivial nature which is characterized by Chern numbers. The effective magnetic fields do not create the vortices …
High temperature superconductivity in one unit cell (1 UC) FeSe on SrTiO3 heterostructure has become a research frontier in condensed matter physics and material science. The superconducting transition temperature (Tc) of ultrathin FeSe film is significantly enhanced compared to its bulk counterpart and possibly approaches the liquid nitrogen region according to in situ spectroscopic measurements. Particularly, the Fermi surface topology of 1 UC FeSe consists of no hole pockets at Brillouin zone center, which poses a great challenge to the well accepted s+- wave pairing nesting the sign differ…
The coexistence of superconductivity and topology holds the potential to realize exotic quantum states of matter. Here we report that superconductivity induced by high pressure in three thallium-based materials, covering the phase transition from a normal insulator (TlBiS2) to a topological insulator (TlBiSe2) through a Dirac semimetal (TlBiSeS). By increasing the pressure up to 60 GPa, we observe superconductivity phase diagrams with maximal Tc values at 6.0-8.1 K. Our density-functional theory calculations reveal topological surface states in superconductivity phases for all three compounds.…
We show that Floquet chiral topological superconductivity arises naturally in Josephson junctions made of magnetic topological insulator-superconductor sandwich structures. The Josephson phase modulation associated with an applied bias voltage across the junction drives the system into the anomalous Floquet chiral topological superconductor hosting chiral Majorana edge modes in the quasienergy spectrum, with the bulk Floquet bands carrying zero Chern numbers. The bias voltage acts as a tuning parameter enabling novel dynamical topological quantum phase transitions driving the system into a myr…
We study three-dimensional time-reversal-invariant topological superconductivity in noncentrosymmetric materials such as RhSi, CoSi, and AlPt which host coupled multifold nodes energetically split by the spin-orbit coupling at the same time-reversal-invariant momentum (TRIM). The topological superconductivity arises from the $s_{+} \oplus s_{-}$ gap function, which is $\boldsymbol{k}$ independent, but with opposite signs for the two nodes split at the same TRIM. We consider various electron-electron interactions in the tight-binding model for RhSi and find that the topological superconducting …
Using a cryogenic scanning tunneling microscopy, we report the observation of topologically nontrivial superconductivity on a single material of β-Bi2Pd films grown by molecular beam epitaxy. The superconducting gap associated with spinless odd-parity pairing opens on the surface and appears much larger than the bulk one due to the Dirac-fermion enhanced parity mixing of surface pair potential. Majorana zero modes (MZMs), supported by such superconducting states, are identified at magnetic vortices. The superconductivity and MZMs exhibit resistance to nonmagnetic defects, characteristic of tim…
We study the intrinsic fully-gapped odd-parity superconducting order in doped nodal-loop materials with a torus-shaped Fermi surface. We show that the mirror symmetry, which protects the nodal loop in the normal state, also protects the superconducting state as a topological crystalline superconductor. As a result, the surfaces preserving the mirror symmetry host gapless Majorana cones. Moreover, for a Weyl loop system (two-fold degenerate at the nodal loop), the surfaces that break the mirror symmetry (those parallel to the bulk nodal loop) contribute a Chern (winding) number to the quasi-two…
Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting `fractional Josephson currents'. Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity---even when noise spoils parity conservation.
In this paper, we propose a way to realize topological $s$-wave superconductivity with application of circularly polarized laser light in two-dimensional bilayer transition metal dichalcogenides (TMDs). Using Floquet theory, we analyze a tight-binding model of bilayer TMDs with time-periodic electric fields. After deriving an effective Hamiltonian, we investigate topological properties of the $s$-wave superconducting state. The laser light induces valley-dependent layer polarization and makes the system to be a topologically nontrivial superconducting state characterized by the Chern number. W…
Topological superconductivity is an exotic quantum phenomenon with coupled nontrivial topological order and superconductivity together. A direct idea for producing topological superconductors is to create superconductivity based on the well recognized topological insulators. The topological insulating states in highly efficient thermoelectric materials Bi$_2$Te$_3$ and Bi$_2$Se$_3$ and their alloy Bi$_{2}$Te$_{3-x}$Se$_{x}$ have been established from angle-resolved photoemission and transport experiments. Superconductivity was also observed based on these popular topological insulators by the …
Proximity effect induced intriguing superconductivity in van der Waals heterostructure of magnetic topological insulator and conventional superconductor
A promising direction for harnessing the laws of quantum mechanics to perform quantum computation is the topological quantum computation, for which topological superconductivity is one of the physical platforms. Intensive theoretical studies have been carried out and followed by tremendous experimental efforts in the realization of topological superconductivity, though debates remain mainly because of the inadequacy of the convincing detection techniques. Here we report a theoretical finding in a superconductor with surface or edge states, where the critical field is found to obey the unique p…
We performed angle-resolved photoemission spectroscopy studies on a series of FeTe$_{1-x}$Se$_{x}$ monolayer films grown on SrTiO$_{3}$. The superconductivity of the films is robust and rather insensitive to the variations of the band position and effective mass caused by the substitution of Se by Te. However, the band gap between the electron- and hole-like bands at the Brillouin zone center decreases towards band inversion and parity exchange, which drive the system to a nontrivial topological state predicted by theoretical calculations. Our results provide a clear experimental indication th…
Superconductivity on the surface of topological insulators is known to be anisotropic and unconventional in that the symmetry is the mixture of s-wave and nodeless p-wave component. In contrast to Anderson's theorem for the insensitivity of the s-wave superconducting critical temperature to the nonmagnetic (time-reversal symmetric (TRS)) impurities, anisotropic superconductors including nodeless p-wave one are in general fragile even with small concentration of the TRS impurities. By employing the Abrikosov-Gor'kov theory, we clarify that this type of unconventional superconductivity emergent …
