Nodal noncentrosymmetric superconductors have topologically nontrivial properties manifested by protected zero-energy surface states. Specifically, it was recently found that zero-energy surface flat bands of topological origin appear at their surface. We show that the presence of certain inversion-type lattice symmetries can give rise to additional topological features of the gap nodes, resulting in surface states forming one-dimensional arcs connecting the projections of two nodal rings. In addition, we demonstrate that Majorana surface states can appear at time-reversal-invariant momenta of the surface Brillouin zone, even when the system is not fully gapped in the bulk. Within a continuum theory we derive the topological invariants that protect these different types of zero-energy surface states. We independently derive general conditions for the existence of zero-energy surface bound states using the complementary quasiclassical scattering theory, explicitly taking into account the effects of spin-orbit splitting of the bands. We compute surface bound-state spectra for various crystal point-group symmetries and orbital-angular-momentum pairing states. Finally, we examine the signatures of the arc surface states and of the zero-energy surface flat bands in tunneling-conductance spectra and discuss how topological phase transitions in noncentrosymmetric superconductors could be observed in experiments.
The combination with superconductivity and topological nontrivial band structure provides a promising route towards novel quantum states such as topological superconductivity. Here, we report the first observation of superconductivity (4.1 K) in Ba5In4Bi5 single crystal, a noncentrosymmetric topological semimetal featuring nodal chain loops at the high-symmetry points R and X. The magnetization, resistivity, and specific heat capacity measurements reveal that Ba5In4Bi5 is a moderately coupled type-II Bardeen-Cooper-Schrieffer superconductor. Bulk superconductivity is suggested from the magneti…
The newly discovered noncentrosymmetric superconductor ThCoC$_{2}$ exhibits numerous unconventional behavior in the field dependent heat capacity data. Here we present the first measurement of the gap symmetry of ThCoC$_{2}$ by muon spin rotation/relaxation $(μ$SR) measurements. Temperature dependence of the magnetic penetration depth measured using the transverse field $μ$SR measurement reveal the evidence of nodal pairing symmetry. To understand these findings, we carry out the calculations of superconducting pairing eigenvalue and eigenfunction symmetry due to the spin-fluctuation mechanism…
We report superconducting properties of noncentrosymmetric superconductor LaPtGe which crystallizes in noncentrosymmetric $ α$-ThSi$ _{2} $ structure. The magnetization, resistivity and specific heat measurements confirm that LaPtGe is a type-II bulk superconductor with a transition temperature T$ _{c} $ = 3.05 $ \pm $ 0.05 K. Muon-spin relaxation/rotation measurements confirms that time reversal preserved in the superconducting ground state.
In noncentrosymmetric superconductors (NCSs), the conversion of a charge current into spin magnetization - the so called magnetoelectric effect - is the direct indicator of the unconventional, mixed-parity order parameter. This paper proposes a scheme to detect the magnetoelectric effect by anomalous, equal-spin Andreev tunneling in NCS/ferromagnet contacts. The proposal relies on the ability to generate spin-polarized triplet pairing by passing an electric current through an NCS. Such an induced triplet pairing bears a similarity to the paradigmatic nonunitary pairing in triplet superfluids w…
The noncentrosymmetric superconductor TaOs has been characterized using x-ray diffraction, resistivity, magnetization, and specific heat measurements. Magnetization and specific heat measurements show a bulk superconducting transition at 2.07 K. These measurements suggest that TaOs is a weakly coupled type-II superconductor. The electronic specific heat in the superconducting state can be explained by the single-gap BCS model, suggesting s-wave superconductivity in TaOs.
Electronic structure of the noncentrosymmetric superconductor Mg10Ir19B16
采用Korringa-Kohn-Rostoker方法计算了新型非中心对称超导化合物Mg 10 Ir 19 B16的电子结构。采用刚性松饼丁近似（RMTA）计算了电子部分的电子-声子耦合常数，即McMillan-Hopfield参数。电子-声子耦合常数的大小，分析原子的贡献，进行了讨论。结果表明，Mg_（10）Ir_（19）B_（16）的超导电性可能是由电子-声子相互作用引起的.
By employing a series of experimental techniques, we provide clear evidence that CaPtAs represents a rare example of a noncentrosymmetric superconductor which simultaneously exhibits nodes in the superconducting gap and broken time-reversal symmetry (TRS) in its superconducting state (below $T_c$ $\approx$ 1.5 K). Unlike in fully-gapped superconductors, the magnetic penetration depth $λ(T)$ does not saturate at low temperatures, but instead it shows a $T^2$-dependence, characteristic of gap nodes. Both the superfluid density and the electronic specific heat are best described by a two-gap mode…
The superconducting parameters and upper critical field of the noncentrosymmetric superconductor BiPd have proven contentious. This material is of particular interest because it is a singular example of a $4f$-electron-free noncentrosymmetric superconductor of which crystals may be grown and cleaved, enabling surface-sensitive spectroscopies. Here, using bulk probes augmented by tunnelling data on defects, we establish that the lower of the previously reported upper critical fields corresponds to the bulk transition. The material behaves as a nearly-weak-coupled BCS s-wave superconductor, and …
Noncentrosymmetric superconductors have sparked significant research interests due to their exciting properties, such as the admixture of spin-singlet and spin-triplet Cooper pairs. Here we report $μ$SR and thermodynamic measurements on the noncentrosymmetric superconductor La7Rh3 which indicate a fully established superconducting gap and spontaneous time-reversal-symmetry breaking at the onset of superconductivity. We show that our results pose severe constraints on any microscopic theory of superconductivity in the system. A symmetry analysis identifies ground states compatible with time-rev…
Surfaces of nodal noncentrosymmetric superconductors can host flat bands of Majorana modes, which provide a promising platform for quantum computation if one can find methods for manipulating localized Majorana wave packets. We study the fate of such flat bands when part of the surface is subjected to an exchange field induced by a ferromagnetic insulator. We use exact diagonalization to find the eigenstates and eigenenergies of the Bogoliubov-de Gennes Hamiltonian of a model system, for which an exchange field is applied along a strip on the surface of a slab. We consider different orientatio…
Superconductivity in materials whose crystal structure lacks inversion symmetry is a prime candidate for unconventional superconductivity. A new noncentrosymmetric compound Zr$_{3}$Ir crystallizes in a tetragonal $ α$-V$_{3} $S structure. The magnetization, specific heat and muon spin rotation confirm s-wave superconductivity, having a transition temperature T$_{c}$ = 2.3 K. Muon spin relaxation confirms the preservation of time reversal symmetry in the superconducting ground state.
For a noncentrosymmetric superconductor such as Y$_2$C$_3$, we consider a parity-mixing model composed of spin-singlet s-wave and spin-triplet f-wave pairing components. The $d$-vector in f-wave state is chosen to be parallel to the Dresselhaus asymmetric spin-orbit coupling vector. It is found that, the quasiparticle excitation spectrum exhibits distinct nodal structure as a consequence of parity-mixing. Our calculation predict anomalous noninteger power laws for low-temperature nuclear spin-lattice relaxation rate $T_{1}^{-1}$. We demonstrate particularly that such a model can qualitatively …
We investigate the Josephson transport properties in a Josephson junction consisting of a conventional $s$-wave superconductor coupled to a multi-orbital noncentrosymmetric superconductor marked by an orbitally driven inversion asymmetry and isotropic interorbital spin-triplet pairing. Contrary to the canonical single band noncentrosymmetric superconductor, we demonstrate that the local interorbital spin-triplet pairing is tied to the occurrence of sign-changing spin-singlet pair amplitude on different bands with $d$-wave symmetry. Such multi-band $d^{\pm}$-wave state is a unique superconducti…
Noncentrosymmetric superconductors can lead to a variety of exotic properties in the superconducting state such as line nodes, multigap behavior, and time-reversal symmetry breaking. In this paper, we report the properties of the new noncentrosymmetric superconductor TaOs, using muon spin relaxation and rotation measurements. It is shown using the zero-field muon experiment that TaOs preserve the time-reversal symmetry in the superconducting state. From the transverse field muon measurements, we extract the temperature dependence of $λ(T)$ which is proportional to the superfluid density. This …
The magnetoelectric effect (or Edelstein effect) in noncentrosymmetric superconductors states that a supercurrent can induce spin magnetization. This is an intriguing phenomenon which has potential applications in superconducting spintronic devices. However, the original Edelstein effect only applies to superconductors with polar point group symmetry. In recent years, many new noncentrosymmetric superconductors have been discovered, such as superconductors with chiral lattice symmetry and superconducting transition metal dichalcogenides with various lattice structures. In this Rapid Communicat…
The unique nonreciprocal responses of superconductors, which stem from the Cooper pairs' quantum condensation, have been attracting attention. Recently, theories of the second-order nonlinear response in noncentrosymmetric superconductors were formulated based on the Bogoliubov-de Gennes theory. In this paper, we study the mechanism and condition for second-order optical responses of time-reversal symmetric superconductors. The numerical results show the characteristic photocurrent and second harmonic generation in the superconducting state. However, the superconductivity-induced nonlinear opt…
The properties of the noncentrosymmetric superconductor ($α$-$\textit{Mn}$ structure) Nb$_{0.5}$Os$_{0.5}$ is investigated using resistivity, magnetization, specific heat, and muon spin relaxation and rotation ($μ$SR) measurements. These measurements suggest that Nb$_{0.5}$Os$_{0.5}$ is a weakly coupled ($λ_{e-ph}$ $\sim$ 0.53) type-II superconductor ($κ_{GL}$ $\approx$ 61) having a bulk superconducting transition temperature $T_c$ = 3.07 K. The specific heat data in the superconductive regime fits well with the single-gap BCS model indicating nodeless s-wave superconductivity in Nb$_{0.5}$Os$…
The discovery of the multiple $H$-$T$ phase diagram of CeRh$_2$As$_2$ offers a new route to designing topological superconductors. Although weak-coupling theories explain the experimental phase diagram qualitatively, a quantitative discrepancy between them has discouraged conclusive interpretation. In this Letter, we thoroughly study the effect of Coulomb interaction and the phase diagrams of locally noncentrosymmetric superconductors. We reveal even-odd parity transition and the enhancement of the parity transition field in strongly correlated superconductors, and an issue of CeRh$_2$As$_2$ i…
Noncentrosymmetric superconductors with broken inversion symmetry $P$ offer rich physical phenomena such as the upper critical magnetic field $H_{c2}$ beyond the Pauli limit and magnetoelectric effect. The relativistic spin-orbit interaction (SOI) plays an essential role in these novel phenomena, which lifts the Kramers degeneracy at each $\mathbf{k}$-point, and leads to the mixing of the spin singlet-even parity and spin triplet odd-parity parings. On the other hand, the time-reversal symmetry $T$ relates the two states at $\mathbf{k}$ and $-\mathbf{k}$ points with the opposite spins, and the…
We report the measurements of de Haas-van Alphen (dHvA) oscillations in the noncentrosymmetric superconductor BiPd. Several pieces of a complex multi-sheet Fermi surface are identified, including a small pocket (frequency 40 T) which is three dimensional and anisotropic. From the temperature dependence of the amplitude of the oscillations, the cyclotron effective mass is ($0.18$ $\pm$ 0.1) $m_e$. Further analysis showed a non-trivial $π$-Berry phase is associated with the 40 T pocket, which strongly supports the presence of topological states in bulk BiPd and may result in topological supercon…
The discovery of new families of unconventional superconductors is important both experimentally and theoretically, especially if it challenges current models and thinking. By using muon spin relaxation in zero-field, time-reversal symmetry breaking has been observed in Re6Hf. Moreover, the temperature dependence of the superfluid density exhibits s-wave superconductivity with an enhanced electron-phonon coupling. This, coupled with the results from isostructural Re6Zr, shows that the Re6X family are indeed a new and important group of unconventional superconductors.
A prime category of superconducting materials in which to look for spin-triplet pairing and topological superconductivity are superconductors without inversion symmetry. It is predicted that the breaking of parity symmetry gives rise to an admixture of spin-singlet / spin-triplet pairing states; a triplet pairing component, being substantial, seems all but guaranteed. However, the experimental confirmation of pair mixing in any particular material remains elusive. In this work, we perform phase-sensitive experiment to examine the pairing state of noncentrosymmetric superconductor $α-$BiPd. The…
We present synthesis and $^{75}$As-nuclear quadrupole resonance (NQR) measurements for the noncentrosymmetric superconductor CaPtAs with a superconducting transition temperature $T_c$ of $\sim 1.5$ K. We discovered two different forms of CaPtAs during synthesis; one is a high-temperature tetragonal form that was previously reported, and the other is a low-temperature form consistent with the orthorhombic structure of CaPtP. According to the $^{75}$As-NQR measurement for superconducting tetragonal CaPtAs, the nuclear spin-lattice relaxation rate $1/T_1$ has an obvious coherence peak below $T_c$…
We study the fermionic boundary modes (Andreev bound states) in a time-reversal invariant one-dimensional superconductor. In the presence of a substrate, spatial inversion symmetry is broken and the electronic properties are strongly affected by an antisymmetric spin-orbit coupling. We assume an arbitrary even number of nondegenerate bands crossing the Fermi level. We show that there is only one possible pairing symmetry in one dimension, an analog of s-wave pairing. The zero-energy Andreev bound states are present if the sign of the gap function in an odd number of bands is different from all…
