We experimentally investigate charge transport through a single planar junction between Cd$_3$As$_2$ Dirac semimetal and a normal Au lead. For non-superconducting bulk Cd$_3$As$_2$ samples, we observe non-Ohmic $dV/dI(V)$ curves, which strongly resemble standard Andreev reflection with well-defined superconducting gap. Andreev-like behavior is demonstrated for Cd$_3$As$_2$ samples with different surface and contact preparation techniques. We connect this behavior with surface superconductivity due to the flat-band formation in Cd$_3$As$_2$, which has been predicted theoretically. The conclusion on superconductivity is also supported by the gap suppression by magnetic fields or temperature.
Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest possible application of our theory to recently discovered superconducting …
Superconducting Weyl semimetals present a novel and promising system to harbor new forms of unconventional topological superconductivity. Within the context of time-reversal symmetric Weyl semimetals with $d$-wave superconductivity, we demonstrate that the number of Majorana cones equates to the number of intersections between the $d$-wave nodal lines and the Fermi arcs. We illustrate the importance of nodal line-arc intersections by demonstrating the existence of locally stable surface Majorana cones that the winding number does not predict. The discrepancy between Majorana cones and the wind…
The noncentrosymmetric Half Heusler compound YPtBi exhibits superconductivity below a critical temperature T_c = 0.77 K with a zero-temperature upper critical field H_c2(0) = 1.5 T. Magnetoresistance and Hall measurements support theoretical predictions that this material is a topologically nontrivial semimetal having a surprisingly low positive charge carrier density of 2 x 10^18 cm^-3. Unconventional linear magnetoresistance and beating in Shubnikov-de Haas oscillations point to spin-orbit split Fermi surfaces. The sensitivity of magnetoresistance to surface roughness suggests a possible con…
We experimentally investigate charge transport through a single planar junction between a NiTe$_2$ Dirac semimetal and a normal gold lead. At millikelvin temperatures we observe non-Ohmic $dV/dI(V)$ behavior resembling Andreev reflection at a superconductor -- normal metal interface, while NiTe$_2$ bulk remains non-superconducting. The conclusion on superconductivity is also supported by suppression of the effect by temperature and magnetic field. In analogy with the known results for Cd$_3$As$_2$ Dirac semimetal, we connect this behavior with interfacial superconductivity due to the flat-band…
WTe$_2$ is a material with rich topological properties: it is a 2D topological insulator as a monolayer and a Weyl-semimetal and higher-order topological insulator (HOTI) in the bulk form. Inducing superconductivity in topological materials is a way to obtain topological superconductivity, which lays at the foundation for many proposals of fault tolerant quantum computing. Here, we demonstrate the emergence of superconductivity at the interface between WTe$_2$ and the normal metal palladium. The superconductivity has a critical temperature of about 1.2 K. By studying the superconductivity in p…
The superconducting s-wave state in Weyl semimetals in a strong strain-induced pseudomagnetic field is investigated in a model with local four-fermion interaction. It is found that only the inter-node pairing is possible in the lowest pseudo-Landau level approximation. Unlike the case of the lowest Landau level in a conventional magnetic field, the corresponding gap equation has only a trivial solution. Nevertheless, superconductivity can be induced via the proximity effect with a usual s-wave spin-singlet superconductor. Since a pseudomagnetic field is present necessarily at the surface of a …
The motivation to search for signatures of superconductivity in Weyl semi-metals and other topological phases lies in their potential for hosting exotic phenomena such as nonzero-momentum pairing or the Majorana fermion, a viable candidate for the ultimate realization of a scalable quantum computer. Until now, however, all known reports of superconductivity in Weyl semimetals have arisen through surface contact with a sharp tip, focused ion-beam surface treatment or the application of high pressures. Here, we demonstrate the observation of superconductivity in single crystals, even an as-grown…
We study the superconductivity of spin-polarized electrons in centrosymmetric ferromagnetic metals. Due to the spin-polarization and the Fermi statistics of electrons, the superconducting pairing function naturally has odd parity. According to the parity formula proposed by Fu, Berg, and Sato, odd-parity pairing leads to conventional first-order topological superconductivity when a normal metal has an odd number of Fermi surfaces. Here, we derive generalized parity formulae for the topological invariants characterizing higher-order topology of centrosymmetric superconductors. Based on the form…
Chiral topological semimetals host multifold degenerate band crossing points under the protection of crystalline symmetries. In this paper, we suggest that the recently discovered chiral topological semimetals in space group 198, parts of which are superconducting upon doping, can be new candidates of time reversal invariant topological superconductors. By investigating the Fermi surfaces around the band crossing points that carry nonzero Chern numbers, we clarify how the nontrivial topology of chiral topological semimetals affects their superconducting state and show the existence of topologi…
A Weyl semimetal is a topologically non-trivial phase of matter that hosts mass-less Weyl fermions, the particles that remained elusive for more than 80 years since their theoretical discovery. The Weyl semimetals exhibit unique transport and magneto-transport properties and remarkably high surface spin polarization. Here we show that a unique mesoscopic superconducting phase with a critical temperature up to 7 K can be realized by forming metallic point contacts with silver (Ag) on single crystals of TaAs, while neither Ag nor TaAs are superconductors. The Andreev reflection spectra obtained …
We study theoretically the superconductivity in doped Weyl semimetals with an inversion symmetry based on the Bogoliubov-de Gennes equations. In principle, the two superconducting states, i.e., the zero momentum BCS-like pairing and the finite momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing are competing in this kind of systems. Our self-consistent calculation indicates that the BCS-type state may be the ground state. The competition between these two pairing states is studied in detail through normal state Fermi surface and the finite energy spectral functions. Generally, the Fermi s…
The Weyl semimetal MoTe$_2$ offers a rare opportunity to study the interplay between Weyl physics and superconductivity. Recent studies have found that Se substitution can boost the superconductivity up to 1.5K, but suppress the Td structure phase that is essential for the emergence of Weyl state. A microscopic understanding of possible coexistence of enhanced superconductivity and the Td phase has not been established so far. Here, we use scanning tunneling microscopy (STM) to study a optimally doped new superconductor MoTe$_{1.85}$Se$_{0.15}$ with bulk Tc ~ 1.5K. By means of quasiparticle in…
Under what conditions does a superconductor inherit topologically protected nodes from its parent normal state? In the context of Weyl semimetals with broken time-reversal symmetry, the pairing order parameter is classified by monopole harmonics and necessarily nodal [Li and Haldane, Phys. Rev. Lett., 120, 067003 (2018)]. Here, we show that a similar conclusion could also apply to 2D Dirac semimetals, although the conditions for the existence of nodes are more complex, depending on the pairing matrix structure in the valley and sublattice space. We analytically and numerically analyze the Bogo…
We study superconducting states of doped inversion-symmetric Weyl semimetals. Specifically, we consider a lattice model realizing a Weyl semimetal with an inversion symmetry and study the superconducting instability in the presence of a short-ranged attractive interaction. With a phonon-mediated attractive interaction, we find two competing states: a fully gapped finite-momentum (FFLO) pairing state and a nodal even-parity pairing state. We show that, in a BCS-type approximation, the finite-momentum pairing state is energetically favored over the usual even-parity paired state and is robust ag…
Unconventional superconductivity has been predicted to arise in the topologically non-trivial Fermi surface of doped inversion symmetric Weyl semimetals (WSM). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and nodal BCS states are theoretically predicted to be possible superconductor pairing states in inversion symmetric doped WSM. In an effort to resolve preferred pairing state, we theoretically study two separate four terminal quantum transport methods that each exhibit a unique electrical signature in the presence of FFLO and nodal BCS states in doped WSMs. We first introduce a Jos…
The effect of Coulomb interaction in an ensemble of Dirac fermions on the formation of superconducting pairing in monolayer and bilayer doped graphene is studied using the Kohn-Luttinger mechanism disregarding the Van der Waals potential of the substrate and impurities. The electronic structure of graphene is described using the Shubin-Vonsovsky model taking into account the intratomic, interatomic, and interlayer (in the case of bilayer graphene) Coulomb interactions between electrons. The Cooper instability is determined by solving the Bethe-Saltpeter integral equation. The renormalized scat…
We present a new switching mechanism that utilizes the proximity coupling between the surface spin texture of a Weyl semimetal and a superconductor, in a Weyl semimetal/superconductor/Weyl semimetal trilayer heterostructure. We show that the superconductivity in the middle layer can be fully suppressed by the surface spin texture of the Weyl semimetals in the presence of an external magnetic field, but it can be recovered again by only changing the field direction. The restoration of the middle-layer superconductivity indicates a sharp transition to a low-resistance state. This sharp switching…
Topological semimetals: surface transport and spin effects
Institute of Solid State Physics of the Russian Academy of Sciences（俄罗斯科学院固体物理研究所）；V.L. Ginzburg Research Centre for High-Temperature Superconductivity and Quantum Materials, P.N. Lebedev Physical Institute of RAS（俄罗斯科学院列别杰夫物理研究所V.L.金兹堡高温超导与量子材料研究中心）
We uncover the properties of complex tensor (d-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-3/2 fermions at a fourfold linear band crossing point. Although the general theory of d-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-3/2 nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a comple…
We investigate topological Cooper pairing, including gapless Weyl and fully gapped class DIII superconductivity, in a three-dimensional doped Luttinger semimetal. The latter describes effective spin-3/2 carriers near a quadratic band touching and captures the normal-state properties of the 227 pyrochlore iridates and half-Heusler alloys. Electron-electron interactions may favor non-$s$-wave pairing in such systems, including even-parity $d$-wave pairing. We argue that the lowest energy $d$-wave pairings are always of complex (e.g., $d + i d$) type, with nodal Weyl quasiparticles. This implies …
Recent studies have shown that there are two types of topological quadrupolar semimetals. One is the quadrupolar bulk semimetal, which is a conventional semimetal with gapless nodes in the bulk spectrum. The other type is named the quadrupolar surface semimetal, possessing a gapped bulk but gapless nodes on the surface spectrum. There have been many experiments on the implementation of quadrupolar bulk semimetals. However, the quadrupolar surface semimetal has never been realized. Here we report on the experimental realization of the quadrupolar surface semimetal in the circuit system. To high…
The Luttinger model of a quadratic-node semimetal for electrons with the $j=\frac32$ angular momentum under cubic symmetry is the parent, highest-symmetry low-energy model for a variety of topological and strongly correlated materials, such as HgTe, $α$-Sn, and iridate compounds. Previously, we have theoretically demonstrated that the Luttinger semimetal exhibits surface states. In the present work, we theoretically study the evolution of these surface states under symmetry-lowering perturbations: compressive strain and bulk-inversion asymmetry (BIA). This system is quite special in that each …
Riemann surfaces are geometric constructions in complex analysis that may represent multi-valued holomorphic functions using multiple sheets of the complex plane. We show that the energy dispersion of surface states in topological semimetals can be represented by Riemann surfaces generated by holomorphic functions in the two-dimensional momentum space, whose constant height contours correspond to Fermi arcs. This correspondence is demonstrated in the recently discovered Weyl semimetals and leads us to predict new types of topological semimetals, whose surface states are represented by double- …
We theoretically investigate surface plasmon polaritons propagating in the thin-film Weyl semimetals. We show how the properties of surface plasmon polaritons are affected by hybridization between plasmons localized at the two metal-dielectric interfaces. Generally, this hybridization results in new mixed plasmon modes, which are called short-range surface plasmons and long-range surface plasmons, respectively. We calculate dispersion curves of these mixed modes for three principle configurations of the axion vector describing axial anomaly in Weyl semimetals. We show that the partial lack of …
We experimentally compare two types of interface structures with magnetic and non-magnetic Weyl semimetals. They are the junctions between a gold normal layer and magnetic Weyl semimetal Ti$_2$MnAl, and a ferromagnetic nickel layer and non-magnetic Weyl semimetal WTe$_2$, respectively. Due to the ferromagnetic side of the junction, we investigate spin-polarized transport through the Weyl semimetal surface. For both structures, we demonstrate similar current-voltage characteristics, with hysteresis at low currents and sharp peaks in differential resistance at high ones. Despite this behavior re…
The Fermi arcs of topological surface states in the three-dimensional multi-Weyl semimetals on surfaces by a continuum model are investigated systematically. We calculated analytically the energy spectra and wave function for bulk quadratic- and cubic-Weyl semimetal with a single Weyl point. The Fermi arcs of topological surface states in Weyl semimetals with single- and double-pair Weyl points are investigated systematically. The evolution of the Fermi arcs of surface states variating with the boundary parameter is investigated and the topological Lifshitz phase transition of the Fermi arc co…
Bulk-surface correspondence in Weyl semimetals assures the formation of topological "Fermi-arc" surface bands whose existence is guaranteed by bulk Weyl nodes. By investigating three distinct surface terminations of the ferromagnetic semimetal Co3Sn2S2 we verify spectroscopically its classification as a time reversal symmetry broken Weyl semimetal. We show that the distinct surface potentials imposed by three different terminations modify the Fermi-arc contour and Weyl node connectivity. On the Sn surface we identify intra-Brillouin zone Weyl node connectivity of Fermi-arcs, while on Co termin…
Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no coexisting trivial Fermi surfaces in the bulk, similar to graphene, could feature deep physics such as exotic transport phenomena induced by the chiral anomaly. Here, we show that HgTe and half-Heusler compounds, under a broad range of in-plane compressive strain, could be materials in nature realizing ideal Weyl semimetals with four pairs of Weyl nodes and topological surface Fermi arcs. Generically, we find that the HgTe-class materials with nontrivial band inversion and noncentrosymmetry provide a promising arena to…
Weyl semimetals are a new member of the topological materials family, featuring a pair of singly degenerate Weyl cones with linear dispersion around the nodes in the bulk, and Fermi arcs on the surface. Depending on whether the system conserves or violates Lorentz symmetry, Weyl semimetals can be categorized into two classes. Photoemission spectroscopy measurements have confirmed the TaAs-class and WTe2-class of Weyl semimetals as type-I and type-II respectively. This review article aims to elucidate and elaborate on the basic concepts of Weyl semimetals and quasiparticle interference experime…
