Beyond Triplet: Unconventional Superconductivity in a Spin-3/2 Topological Semimetal
Hyunsoo Kim, Kefeng Wang, Yasuyuki Nakajima, Rongwei Hu, Steven Ziemak, Paul Syers, Limin Wang, Halyna Hodovanets, Jonathan D. Denlinger, Philip M. R. Brydon, D… 展开作者
Hyunsoo Kim, Kefeng Wang, Yasuyuki Nakajima, Rongwei Hu, Steven Ziemak, Paul Syers, Limin Wang, Halyna Hodovanets, Jonathan D. Denlinger, Philip M. R. Brydon, Daniel F. Agterberg, Makariy A. Tanatar, Ruslan Prozorov, Johnpierre Paglione
In all known fermionic superfluids, Cooper pairs are composed of spin-1/2 quasi-particles that pair to form either spin-singlet or spin-triplet bound states. The "spin" of a Bloch electron, however, is fixed by the symmetries of the crystal and the atomic orbitals from which it is derived, and in some cases can behave as if it were a spin-3/2 particle. The superconducting state of such a system allows pairing beyond spin-triplet, with higher spin quasi-particles combining to form quintet or septet pairs. Here, we report evidence of unconventional superconductivity emerging from a spin-3/2 quasiparticle electronic structure in the half-Heusler semimetal YPtBi, a low-carrier density noncentrosymmetric cubic material with a high symmetry that preserves the $p$-like $j=3/2$ manifold in the Bi-based $Γ_8$ band in the presence of strong spin-orbit coupling. With a striking linear temperature dependence of the London penetration depth, the existence of line nodes in the superconducting order parameter $Δ$ is directly explained by a mixed-parity Cooper pairing model with high total angular momentum, consistent with a high-spin fermionic superfluid state. We propose a $\mathbf{k\cdot p}$ model of the $j=3/2$ fermions to explain how a dominant $J$=3 septet pairing state is the simplest solution that naturally produces nodes in the mixed even-odd parity gap. Together with the underlying topologically non-trivial band structure, the unconventional pairing in this system represents a truly novel form of superfluidity that has strong potential for leading the development of a new generation of topological superconductors.
YPtBi, a topological semimetal with very low carrier density, was recently found to be superconducting below $T_\mathrm{c} = 0.77$\,K. In the conventional theory, the nearly vanishing density of states around the Fermi level would imply a vanishing electron-phonon coupling and would therefore not allow for superconductivity. Based on relativistic density functional theory calculations of the electron-phonon coupling in YPtBi it is found that carrier concentrations of more than $10^{21}$\,cm$^{-3}$ are required to explain the observed critical temperature with the conventional pairing mechanism…
Weyl fermion is a massless Dirac fermion with definite chirality, which has been long pursued since 1929. Though it has not been observed as a fundamental particle in nature, Weyl fermion can be realized as low-energy excitation around Weyl point in Weyl semimetal, which possesses Weyl fermion cones in the bulk and nontrivial Fermi arc states on the surface. As a firstly discovered Weyl semimetal, TaAs crystal possesses 12 pairs of Weyl points in the momentum space, which are topologically protected against small perturbations. Here, we report for the first time the tip induced superconductivi…
Stimulated by the success of graphene and its emerging Dirac physics, the quest for versatile and tunable electronic properties in atomically thin systems has led to the discovery of various chemical classes of 2D compounds. In particular, honeycomb lattices of group-IV elements, such as silicene and germanene, have been found experimentally. Whether it is a necessity of synthesis or a desired feature for application purposes, most 2D materials demand a supporting substrate. In this work, we highlight the constructive impact of substrates to enable the realization of exotic electronic quantum …
Recently, we presented a paper about the tip-induced superconducting phase on TaAs single crystal (arXiv:1607.00513). A conductance plateau with double conductance peaks at finite bias, sharp double dips and a zero bias conductance peak were observed in the point contact spectra (PCS). These three features in one PCS suggest the possibility of p-wave like superconductivity and Majorana zero modes in the surface. Soon after our paper posted on arXiv, Gayen el al. (arXiv:1607.01405) questioned the underlying mechanism of our observations based on their experimental measurements in conventional s…
Unconventional Superconductivity in the Chiral Topological Semimetal Ag2Pd3S
Indian Institute of Science Education and Research Bhopal（印度科学教育研究所博帕尔分校）；Indian Institute of Technology, Kanpur（坎普尔印度理工学院）；McMaster University（麦克马斯特大学）；Technion-Israel Institute of Technology（以色列理工学院）
Recently, Wang $et$ $al.$ have reported the observation of "unconventional superconductivity" in the Weyl semimetal TaAs [arXiv:1607.00513]. The authors have written "\textit{A conductance plateau and sharp double dips are observed in the point contact spectra, indicating p-wave like unconventional superconductivity. Furthermore, the zero bias conductance peak in low temperature regime is detected, suggesting potentially the existence of Majorana zero modes. The experimentally observed tunneling spectra can be interpreted with a novel mirror-symmetry protected topological superconductor induce…
Have you been lying awake wondering what symmetries determine whether a superconductor is spin singlet, triplet, or both? We show that if BCS theory is supplied with additional degrees of freedom, spin singlet can coexist with spin triplet superconductivity. In the first part, we didactically guide the reader to the most general superconducting state using symmetry arguments. If both singlet and triplet pairing channels are present, a magnetic field can convert between spin singlet and triplet states. In the second part, we discuss two possible singlet-triplet superconductors: CeRh$_2$As$_2$ a…
We theoretically predict proximity-induced odd-frequency (odd-$ω$) pairing on the surface of a Weyl nodal loop semimetal, characterized by a nodal loop Fermi surface and drumhead-like surface states (DSSs), attached to conventional spin-singlet $s$-wave superconducting leads. Due to the complete spin polarization of the DSS, odd-$ω$ equal-spin triplet pairing is present, and we show that it gives rise to a finite Josephson current. Placing an additional ferromagnet in the junction can also generate odd-$ω$ mixed-spin triplet pairing, but the pairing and current is not affected if the magnetiza…
We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a $4 \times 4$ matrix and six types of $k$-independent pair potentials are allowed by the Fermi-Dirac statistics. We show that the unique spin-orbit coupling leads to characteristic superconducting gap structures and $d$ vectors on the Fermi surface and the electron-electron interaction between intra and interorbitals gives a novel phase diagram of superconductivity. It is found that when the inter…
Cooper pairs in two-dimensional unconventional superconductors with broken inversion symmetry are in a mixture of an even-parity spin-singlet pairing state with an odd-parity spin-triplet pairing state. We study the magnetic properties of the impurity bound states in such superconductors and find striking signatures in their spin polarization which allow to unambiguously discriminate a non-topological superconducting phase from a topological one. Moreover, we show how these properties, which could be measured using spin-polarized scanning tunneling microscopy (STM), also enable to determine th…
Odd-parity, spin-triplet superconductor Sr2RuO4 has been found to feature exotic vortex physics including half-flux quanta trapped in a doubly connected sample and the formation of vortex lattices at low fields. The consequences of these vortex states on the low-temperature magnetoresistive behavior of mesoscopic samples of Sr2RuO4 were investigated in this work using ring device fabricated on mechanically exfoliated single crystals of Sr2RuO4 by photolithography and focused ion beam. With the magnetic field applied perpendicular to the in-plane direction, thin-wall rings of Sr2RuO4 were found…
We have studied a general property of unconventional superconductors with spin-orbit coupling by solving the Bogoliubov-de Gennes equation and found that the two of four eigenfunctions for triplet pairing coincide with those for s-wave pairing when a relation holds between pairing symmetry and spin-orbit coupling, indicative of an intrinsically s-wave like property of triplet superconductors. Applying the result, we have studied the tunneling conductance in normal metal / insulator / unconventional superconductor junctions with a candidate of pairing symmetry of CePt$_3$Si. The effect of Rashb…
We present a general theory of the proximity effect in junctions between diffusive normal metals (DN) and unconventional superconductors in the framework of the quasiclassical Green's function formalism. Various possible symmetry classes in a superconductor are considered which are consistent with the Pauli principle: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity (ETO) state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity (OSO) state. For each of the above four cases symmetry and spectral properties of …
Conventional phonon-electron interaction induces either triplet or one of two (degenerate) singlet pairing states in time reversal and inversion invariant 3D Dirac semi - metal. Investigation of the order parameters and energies of these states at zero temperature in wide range of values of chemical potential $μ$, the effective electron-electron coupling constant $λ$ and Debye energy $T_{D}$ demonstrates that when the exchange interaction is neglected the singlet always prevails, however in significant portions of the $\left( μ,λ,T_{D}\right) $ parameter space the energy difference is very sma…
The search for unconventional superconductivity in Weyl semimetal materials is currently an exciting pursuit, since such superconducting phases could potentially be topologically nontrivial and host exotic Majorana modes. The layered material TaIrTe4 is a newly predicted time-reversal invariant type II Weyl semimetal with minimum number of Weyl points. Here, we report the discovery of surface superconductivity in Weyl semimetal TaIrTe4. Our scanning tunneling microscopy/spectroscopy (STM/S) visualizes Fermi arc surface states of TaIrTe4 that are consistent with the previous angle-resolved phot…
Superconductivity was recently observed in CrAs as the helimagnetic order is suppressed by applying pressure, suggesting possible unconventional superconductivity. To reveal the nature of the superconducting order parameter of CrAs, here we report the angular dependence of the upper critical field under pressure. Upon rotating the field by 360 degrees in the $bc$-plane, six maxima are observed in the upper critical field, where the oscillations have both six-fold and two-fold symmetric components. Our analysis suggests the presence of an unconventional odd-parity spin triplet state.
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…
Unconventional superconductivity with spin-triplet Cooper pairing is reviewed on the basis of the quasi-phenomenological Ginzburg-Landau theory. The superconductivity, in particular, the mixed phase of coexistence of ferromagnetism and unconventional superconductivity is triggered by the spontaneous magnetization. The mixed phase is stable whereas the other superconducting phases that usually exist in unconventional superconductors are either unstable, or, for particular values of the parameters of the theory, some of these phases are metastable at relatively low temperatures in a quite narrow…
The crystal structure of the new superconductor UTe2 has been investigated for the first time at low temperature (LT) of 2.7 K, just closely above the superconducting transition temperature of about 1.7 K by single crystal neutron diffraction, in order to prove, whether the orthorhombic structure of type Immm (Nr. 71 Int. Tabl.) reported for room temperature (RT) persists down to the superconducting phase and can be considered as a parent symmetry for the development of spin triplet superconductivity. Our results show that the RT structure reported previously obtained by single crystal X-Ray d…
We have generalized a quasiclassical model for Weyl semimetals with a tilted band in the presence of an externally applied magnetic field. This model is applicable to ballistic, moderately disordered, and samples containing a high density of nonmagnetic impurities. We employ this formalism and show that a self-biased supercurrent, creating a ϕ0-junction, can flow through a triplet channel in Weyl semimetals. Furthermore, our results demonstrate that multiple supercurrent reversals are accessible through varying junction thickness and parameters characterizing Weyl semimetals. We discuss the in…
We calculate the diamagnetic susceptibility in zero external magnetic field above the phase transition from ferromagnetic phase to phase of coexistence of ferromagnetic order and unconventional superconductivity. For this aim we use generalized Ginzburg-Landau free energy of unconventional ferromagnetic superconductor with spin-triplet electron pairing. A possible application of the result to some intermetallic compounds is briefly discussed.
Topological semimetals are three dimensional materials with symmetry-protected massless bulk excitations. As a special case, Weyl nodal-line semimetals are realized in materials either having no inversion or broken time-reversal symmetry and feature bulk nodal lines. The 111-family of materials, LaNiSi, LaPtSi and LaPtGe (all lacking inversion symmetry), belong to this class. Here, by combining muon-spin rotation and relaxation with thermodynamic measurements, we find that these materials exhibit a fully-gapped superconducting ground state, while spontaneously breaking time-reversal symmetry a…
A general phenomenological theory is presented for the phase behavior of ferromagnetic superconductors with spin-triplet electron Cooper pairing. The theory describes in details the temperature-pressure phase diagrams of real inter-metallic compounds exhibiting the remarkable phenomenon of coexistence of spontaneous magnetic moment of the itinerant electrons and spin-triplet superconductivity. The quantum phase transitions which may occur in these systems are also described. The theory allows for a classification of these itinerant ferromagnetic superconductors in two types: type I and type II…
The superconducting behavior of the topological semimetal CaSn$_{3}$ was investigated by means of magnetotransport and muon spectroscopy $μ$SR measurements, both providing strong evidence of nematic behavior. Magnetotransport detects an anisotropic upper critical field, characterized by a twofold symmetry about $C_{4}$ axis, thus breaking the rotational symmetry of the underlying cubic lattice. Transverse-field $μ$SR data support such picture, with the muon depolarization rate depending strongly on the magnetic field direction, here applied along the [110] or [001] crystal directions. In the f…
We study the Josephson effect in a triplet superconductor--ferromagnet--singlet superconductor junction. We show that the interaction of tunneling Cooper pairs with the interface magnetization can permit a Josephson current at the lowest order of a tunneling Hamiltonian perturbation theory. Two conditions must be satisfied for this to occur: the magnetization of the ferromagnet has a component parallel to the ${\bf d}$-vector of the triplet superconductor, and the gaps of the superconductors have the same parity with respect to the interface momentum. The resulting charge current displays an u…
Superconductive properties of the two-leg ladder compounds are studied theoretically. The antiferromagnetic fluctuations are considered because of the good nesting of the Fermi surfaces. The attractive interaction which is most likely due to the electron-phonon coupling is also taken into account. Under this circumstance, it is shown that the superconductivity has two sets of spin-triplet pairings. The gaps for both pairings have no node.
We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d-wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg--Landau free energy and apply these concepts to the case of an isotropic band touching point. For vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features…
We study the influence of a magnetic field $H$ on the zero-bias conductance peak (ZBCP) due to zero-energy Andreev bound state (ZES) in normal metal / unconventional superconductor. For p-wave junctions, ZBCP does not split into two by $H$ even for sufficiently low transparent junctions, where ZBCP clearly splits for d-wave. This unique property originates from the fact that for p-wave superconductors, perpendicularly injected quasiparticle form ZES, which contribute most dominantly on the tunneling conductance. In addition, we show that for $p_{x}$+i$p_{y}$-wave superconductor junctions, the …
Unconventional superconductivity is usually associated with symmetry breaking in the system. Here we consider a simple setup consisting of a solid state material with conduction electrons and an applied surface acoustic wave (SAW), that can break time and spatial translation symmetries. We study the symmetries of the possible SAW-induced order parameters, showing that even-frequency spin-triplet odd-parity order parameter can occur. We suggest different methods of how to engineer the symmetries of the order parameters using SAWs and the applications of such setups.
The exceptionally low-symmetry crystal structures of the time-reversal symmetry breaking superconductors LaNiC$_2$ and LaNiGa$_2$ lead to an internally-antisymmetric non-unitary triplet (INT) state as the only possibility compatible with experiments. We argue that this state has a distinct signature: a double-peak structure in the Density of States (DOS) which resolves in the spin channel in a particular way. We construct a detailed model of LaNiGa$_2$ capturing its electronic band structure and magnetic properties ab initio. The pairing mechanism is described via a single adjustable parameter…
The coupling of a superconductor to a different material often results in a system with unconventional superconducting properties. A conventional superconductor is a perfect diamagnet expelling magnetic fields out of its volume, a phenomenon known as Meissner effect. Here, we show that the simple adsorption of a monolayer of chiral molecules, which are non-magnetic in solution, onto the surface of a conventional superconductor can markedly change its diamagnetic Meissner response. By measuring the internal magnetic field profile in superconducting Nb thin films under an applied transverse fiel…
The spin-orbital polarization of superconducting excitations in momentum space is shown to provide distinctive marks of unconventional pairing in the presence of inversion symmetry breaking.Taking the prototypical example of an electronic system with atomic spin-orbit and orbital-Rashba couplings, we provide a general description of the spin-orbital textures and their most striking changeover moving from the normal to the superconducting state. We find that the variation of the spin-texture is strongly imprinted by the combination of the misalignment of spin-triplet d-vector with the inversion…
Recent results for the coexistence of ferromagnetism and unconventional superconductivity with spin-triplet Cooper pairing are reviewed on the basis of the quasi-phenomenological Ginzburg-Landau theory. New results are reported. The results are discussed in view of applications to metallic compounds as UGe2, URhGe, ZrZn2.
Two-dimensional transition metal dichalcogenides entwine interaction, spin-orbit coupling, and topology. Hole-doped systems lack spin degeneracy: states are indexed with spin and valley specificity. This unique structure offers new possibilities for correlated phases and phenomena. We realize an unconventional superconducting pairing phase which is an equal mixture of a spin singlet and the $m = 0$ spin triplet. It is stable against large in-plane magnetic fields, and its topology allows quasiparticle excitations of net nonzero Berry curvature via pair-breaking circularly polarized light.
Lately, the three-dimensional (3D) Dirac semimetal, which possesses 3D linear dispersion in electronic structure as a bulk analogue of graphene, has generated widespread interests in both material science and condensed matter physics. Very recently, crystalline Cd3As2 has been proposed and proved to be one of 3D Dirac semimetals which can survive in atmosphere. Here, by controlled point contact (PC) measurement, we observe the exotic superconductivity around point contact region on the surface of Cd3As2 crystal. The observation of zero bias conductance peak (ZBCP) and double conductance peaks …
Ferromagnetic spin valves offer the key building blocks to integrate giant- and tunneling-magnetoresistance effects into spintronics devices. Starting from a generalized Blonder-Tinkham-Klapwijk approach, we theoretically investigate the impact of interfacial Rashba and Dresselhaus spin-orbit couplings on the tunneling conductance, and thereby the magnetoresistance characteristics, of ferromagnet/superconductor/ferromagnet spin-valve junctions embedding thin superconducting spacers between the either parallel or antiparallel magnetized ferromagnets. We focus on the unique interplay between usu…
Coexisting electronic smectic liquid crystal and superconductivity in a Si square-net semimetal
RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Department of Physics and Center for Theoretical Physics, National Taiwan University（国立台湾大学物理系暨理论物理中心）；Department of Applied Physics, Nagoya University（名古屋大学应用物理系）；Institute of Multidisciplinary Research for Advanced Materials, Tohoku University（东北大学先进材料跨学科研究所）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理分部）
We present direct imaging of magnetic flux structures in the anisotropic, spin-triplet superconductor Sr$_{2}$RuO$_{4}$ using a scanning $μ$SQUID microscope. Individual quantized vortices were seen at low magnetic fields. Coalescing vortices forming flux domains were revealed at intermediate fields. Based on our observations we suggest that a mechanism intrinsic to the material stabilizes the flux domains against the repulsive vortex-vortex interaction. Topological defects like domain walls can provide this, implying proof for unconventional chiral superconductivity.
We present the numerical solutions for the I-V characteristics, and describe the motion of fluxons in a frustrated Josephson junction made of an unconventional triplet superconductor and an s-wave superconductor. In the inline geometry, and long length limit the moving integer fluxon interacts with the bound fractional fluxon but is not able to change its position or polarity. We observe different modes of multifluxon propagation. In the small length limit the moving fluxon is a combination of the stable solutions that exist in the static case and additional steps are introduced in the I-V dia…
Unconventional superconducting states of matter are realized in the presence of strong spin orbit coupling. In particular, non degenerate bands can support odd parity superconductivity with rich topological content. Here we study whether this is the case for Weyl semimetals. These are systems whose low energy sector, in the absence of interactions, is described by linearly dispersing chiral fermions in three dimensions. The energy spectrum has nodes at an even number of points in the Brillouin zone. Consequently both intranodal finite momentum pairing and internodal BCS superconductivity are a…
We present a new theoretical formulation of non-equilibrium superconducting phenomena, including singlet and triplet pairing. We start from the general Keldysh-Nambu-Gor'kov Green's functions in the quasiclassical approximation and represent them in terms of 2x2 spin-matrix coherence functions and distribution functions for particle-type and hole-type excitations. The resulting transport equations for the distribution functions may be interpreted as a generalization to the superconducting state of Landau's transport equation for the normal Fermi liquid of conduction electrons. The equations ar…
Following our previous results, which provide evidence for the emergence of a chiral p-wave triplet-pairing component in superconducting Nb upon the adsorption of chiral molecules, we turned to investigate whether such an effect can take place in a proximal superconductor consisting of metal on superconductor bilayer. Note that in such proximity systems, correlated electron-hole (Andreev) pairs exist in the normal metal rather than genuine Cooper pairs. To that end, we used scanning tunneling spectroscopy (STS) on thin Au films grown in-situ on NbN (a conventional s-wave superconductor) before…
The transition metal dichalcogenide PdTe$_2$ was recently shown to be a unique system where a type II Dirac semimetallic phase and a superconducting phase co-exist. This observation has led to wide speculation on the possibility of the emergence of an unconventional topological superconducting phase in PdTe$_2$. Here, through direct measurement of the superconducting energy gap by scanning tunneling spectroscopy (STS), and temperature and magnetic field evolution of the same, we show that the superconducting phase in PdTe$_2$ is conventional in nature. The superconducting energy gap is measure…
Motivated by recent observations of chiral-induced magnetization and spin-selective transport we studied the effect of chiral molecules on conventional BCS superconductors. By applying scanning tunneling spectroscopy, we demonstrate that the singlet-pairing s-wave order parameter of Nb is significantly altered upon adsorption of chiral polyalanine alpha-helix molecules on its surface. The tunneling spectra exhibit zero-bias conductance peaks embedded inside gaps or gap-like features, suggesting the emergence of unconventional triplet-pairing components with either d-wave or p-wave symmetry, as…
Superconducting crystals with lack of inversion symmetry can potentially host unconventional pairing. However, till date, no direct conclusive experimental evidence of such unconventional order parameters in non-centrosymmetric superconductors has been reported. In this paper, through direct measurement of the superconducting energy gap by scanning tunnelling spectroscopy, we report the existence of both $s$-wave (singlet) and $p$-wave (triplet) pairing symmetries in non-centrosymmetric Ru$_7$B$_3$. Our temperature and magnetic field dependent studies also indicate that the relative amplitudes…
The effects of a strain-induced pseudomagnetic field on inter-node spin-triplet superconducting states in Weyl semimetals are studied by using the quasiclassical Eilenberger formalism. It is found that the Cooper pairing with spins parallel to the pseudomagnetic field has the lowest energy among the spin-triplet states and its gap does not depend on the strength of the field. In such a state, both electric and chiral superconducting currents are absent. This is in contrast to the superconducting states with the spins of Cooper pairs normal to the field, which support a nonzero chiral current a…
