The Th$_{7}$Fe$_{3}$ family of superconductors provides a rich playground for unconventional superconductivity. La$_7$Ni$_3$ is the latest member of this family, which we here investigate by means of thermodynamic and muon spin rotation and relaxation measurements. Our specific heat data provides evidence for two distinct and approximately isotropic superconducting gaps. The larger gap has a value slightly higher than that of weak-coupling BCS theory, indicating the presence of significant correlations. These observations are confirmed by transverse-field muon-rotation measurements. Furthermore, zero-field measurements reveal small internal fields in the superconducting state, which occur close to the onset of superconductivity and indicate that the superconducting order parameter breaks time-reversal symmetry. We discuss two possible microscopic scenarios -- an unconventional $E_{2}(1,i)$ state and an $s+i\,s$ superconductor, which is reached by two consecutive transitions -- and illustrate which interactions will favor these phases. Our results establish La$_{7}$Ni$_{3}$ as the first member of the Th$_{7}$Fe$_{3}$ family displaying both time-reversal-symmetry-breaking and multigap superconductivity.
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 report the first observation of multigap superconductivity in TaRh$_{2}$B$_{2}$. We show TaRh$_{2}$B$_{2}$ is a bulk type-II superconductor with a transition temperature, $T_{\mathrm{c}} = 6.00(5)$ K. We present transverse-field muon spin relaxation data where the superconducting gap can be fit using a two-gap $\left(s+s\right)$-wave model. We also report the zero-field electronic specific heat in the superconducting state that is best described by the same $\left(s+s\right)$ model providing further evidence of multiband behavior in this superconductor. Zero-field muon spin relaxation measu…
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 …
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…
We have investigated the superconducting state of the noncentrosymmetric superconductor Re6Ti (Tc = 6.0 K) using muon-spin rotation/relaxation (muSR) technique. The zero-field muon experiment shows the presence of spontaneous magnetic fields in the superconducting state, indicating time-reversal symmetry breaking (TRSB). However, the low-temperature transverse field muon measurements suggest nodeless s-wave superconductivity. The time reversal symmetry breaking further confirmed in the stoichiometric composition Re24Ti5. These results indicate that the pairing symmetry is not affected by spin-…
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.
The noncentrosymmetric superconductor Re$_6$Zr has attracted much interest due to the observation of broken time-reversal symmetry in the superconducting state. Here we report an investigation of the superconducting gap structure of Re$_6$Zr single crystals by measuring the magnetic penetration depth shift $Δλ(T)$ and electronic specific heat $C_e(T)$. $Δλ(T)$ exhibits an exponential temperature dependence behavior for $T~\ll~T_c$, which indicates a fully-open superconducting gap. Our analysis shows that a single gap $s$-wave model is sufficient to describe both the superfluid density $ρ_s(T)$…
Twin boundaries are generic crystalline defects in noncentrosymmetric crystal structures. We study theoretically twin boundaries in time-reversal symmetric noncentrosymmetric superconductors that admit parity-mixed Cooper pairing. Twin boundaries support spin currents as a consequence of this parity mixing. If the singlet and triplet components of the superconducting order parameter are of comparable magnitude, the superconducting state breaks spontaneously the bulk time-reversal symmetry locally near the twin boundary. By self-consistently evaluating the Bogoliubov-de-Gennes equations and the…
We report a comprehensive study of the centrosymmetric Re$_3$B and noncentrosymmetric Re$_7$B$_3$ superconductors. At a macroscopic level, their bulk superconductivity (SC), with $T_c$ = 5.1 K (Re$_3$B) and 3.3 K (Re$_7$B$_3$), was characterized via electrical-resistivity, magnetization, and heat-capacity measurements, while their microscopic superconducting properties were investigated by means of muon-spin rotation/relaxation ($μ$SR). In both Re$_3$B and Re$_7$B$_3$ the low-$T$ zero-field electronic specific heat and the superfluid density (determined via tranverse-field $μ$SR) suggest a nod…
We report an investigation of the superconducting properties of the hexagonal noncentrosymmetric compound LaPdIn. Electrical resistivity, specific heat and ac susceptibility measurements demonstrate the presence of bulk superconductivity below $T_c$ = 1.6 K. The specific heat, together with the penetration depth measured using transverse-field muon spin rotation and the tunnel diode oscillator based method, are well described by single gap $s$-wave superconductivity, with a gap magnitude of 1.8$k_BT_c$. From zero-field muon spin relaxation results no evidence is found for the spontaneous emerg…
Noncentrosymmetric materials are promising paradigm to explore unconventional superconductivity. In particular, several Re containing noncentrosymmetric materials have attracted considerable attention due to a superconducting state with a broken time reversal symmetry. A comprehensive study on the superconducting ground state of NbReSi was investigated using magnetization, resistivity, and muon spin rotation/relaxation measurements. Zero field muon spectroscopy results showed the absence of any spontaneous magnetic field below the superconducting transition temperature, T$ _{c} $ = 6.29 K, ind…
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.
Nonreciprocal or nonlinear responses in symmetry-broken systems are powerful probes of emergent properties in quantum materials, including superconductors, magnets, and topological materials. Recently, vortex matter has been recognized as a key ingredient of giant nonlinear responses in superconductors with broken inversion symmetry. However, nonlinear effects have been probed as excess voltage only under broken time-reversal symmetry. In this study, we report intrinsic rectification and nonlinear anomalous Hall effect under time-reversal symmetry in the noncentrosymmetric trigonal superconduc…
The noncentrosymmetric NbReSi superconductor with $T_{c} \simeq 6.5$ K is characterized by the relatively large upper critical magnetic field. Its multigap features were observed experimentally. Recent studies suggested realization of P$\bar{6}$2m or Ima2 symmetry. We discuss the dynamical properties of both symmetries (e.g., phonon spectra). In this paper, using the ab initio techniques, we clarify this ambiguity, and conclude that the Ima2 symmetry is unstable, and P$\bar{6}$2m should be realized. The P$\bar{6}$2m symmetry is also stable in the presence of external hydrostatic pressure. We s…
We report the discovery of Zr$_3$Ir as a new type of unconventional noncentrosymmetric superconductor (with $T_c = 2.3$ K), here investigated mostly via muon-spin rotation/relaxation ($μ$SR) techniques. Its superconductivity was characterized using magnetic susceptibility, electrical resistivity, and heat capacity measurements. The low-temperature superfluid density, determined via transverse-field $μ$SR and electronic specific heat, suggests a fully-gapped superconducting state. The spontaneous magnetic fields, revealed by zero-field $μ$SR below $T_c$, indicate the breaking of time-reversal s…
We report the magnetic and superconducting properties of locally noncentrosymmetric SrPtAs obtained by muon-spin-rotation/relaxation (muSR) measurements. Zero-field muSR reveals the occurrence of small spontaneous static magnetic fields with the onset of superconductivity. This finding suggests that the superconducting state of SrPtAs breaks time-reversal symmetry. The superfluid density as determined by transverse field muSR is nearly flat approaching T = 0 K proving the absence of extended nodes in the gap function. By symmetry, several superconducting states supporting time-reversal symmetr…
NbRh$_{2}$B$_{2}$ crystallises in a chiral noncentrosymmetric structure and exhibits bulk type-II superconductivity below $7.46(5)$~K. Here we show that the temperature dependence of the upper critical field deviates from the behaviour expected for both Werthamer-Helfand-Hohenberg and the Ginzburg-Landau models and that $μ_{0}H_{\mathrm{c2}}\left(0\right)\approx 18$~T exceeds the Pauli paramagnetic limit, $μ_{0}H_{\mathrm{P}}=13.9$~T. We explore the reasons for this enhancement. Transverse-field muon spectroscopy measurements suggest that the superconducting gap is either $s$-wave or $\left(s+…
A newly discovered family of high-Tc Fe-based superconductors, AeAFe4As4 (Ae = Ca, Sr, Eu and A = K, Rb, Cs), offers further opportunities to understand unconventional superconductivity in these materials. In this Rapid Communication, we report on the superconducting and magnetic properties of CaKFe4As4, studied using muon spectroscopy. Zero-field muon spin relaxation studies carried out on the CaKFe4As4 superconductor do not show any detectable magnetic anomaly at Tc or below, implying that time-reversal symmetry is preserved in the superconducting ground state. The temperature dependence of …
We report measurements of the temperature dependence of the magnetic penetration depth in different quality polycrystalline samples of noncentrosymmetric LaNiC2 down to 0.05 K. This compound has no magnetic phases and breaks time-reversal symmetry. In our highest quality sample we observe a T^2 dependence below 0.4Tc indicative of nodes in the energy gap. We argue that previous results suggesting conventional s-wave behavior may have been affected by magnetic impurities.
We examine intrinsic interfaces separating crystalline twin domains of opposite spin-orbit coupling in a noncentrosymmetric superconductor such as CePt3Si. At these interfaces, low-energy Andreev bound states occur as a consequence of parity-mixed Cooper pairing, and a superconducting phase which violates time reversal symmetry can be realized. This provides an environment allowing flux lines with fractional flux quanta to be formed at the interface. Their presence could have strong implications on the flux creep behavior in such superconductors.
We analyze the possible interaction-induced superconducting instabilities in noncentrosymmetric systems based on symmetries of the normal state. It is proven that pure electron-phonon coupling will always lead to a fully gapped superconductor that does not break time-reversal symmetry and is topologically trivial. We show that topologically nontrivial behavior can be induced by magnetic doping without gapping out the resulting Kramers pair of Majorana edge modes. In case of superconductivity arising from the particle-hole fluctuations associated with a competing instability, the properties of …
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.
Noncentrosymmetric superconductors with $α$-manganese structure has attracted much attention recently, after the discovery of time-reversal symmetry breaking in all the members of Re$_{6}$X (X = Ti, Hf, Zr) family. Similar to Re$_{6}$X, NbOs$_{2}$ also adopts $α$-$Mn$ structure and found to be superconducting with critical temperature $T_{c}$ $\approx$ 2.7 K. The results of the resistivity, magnetization, specific heat and muon-spin relaxation/rotation measurements show that NbOs$_{2}$ is a weakly coupled type-II superconductor. Interestingly, the zero-field muon experiments indicate that the …
We study the stability of topologically protected zero-energy flat bands at the surface of nodal noncentrosymmetric superconductors, accounting for the alteration of the gap near the surface. Within a selfconsistent mean-field theory, we show that the flat bands survive in a broad temperature range below the bulk transition temperature. There is a second transition at a lower temperature, however, below which the system spontaneously breaks time-reversal symmetry. The surface bands are shifted away from zero energy and become weakly dispersive. Simultaneously, a spin polarization and an equili…
We investigate the nature of the time-reversal breaking pairing state in the hole-doped monolayer MoS$_{2}$ on the basis of the realistic three-orbital attractive Hubbard-like model with the atomic spin-orbit coupling. Due to the multi-band features arising from the Mo $d$ orbitals in the noncentrosymmetric crystal structure, the Lifshitz transition takes place upon hole doping. Across the Lifshitz transition point, the sign of the relative phase between the Cooper-pair components drastically changes, leading to the emergence of the time-reversal breaking phase with complex gap functions. It i…
We study the superconducting instabilities of a single species of two-dimensional Rashba-Dirac fermions, as it pertains to the surface of a three-dimensional time-reversal symmetric topological band insulators. We also discuss the similarities as well as the differences between this problem and that of superconductivity in two-dimensional time-reversal symmetric noncentrosymmetric materials with spin-orbit interactions. The superconducting order parameter has both s-wave and p-wave components, even when the superconducting pair potential only transfers either pure singlets or pure triplets pai…
To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed comparative muon-spin rotation/relaxation ($μ$SR) studies of superconducting noncentrosymmetric Re$_{0.82}$Nb$_{0.18}$ ($T_c = 8.8$ K) and centrosymmetric Re ($T_c = 2.7$ K). In Re$_{0.82}$Nb$_{0.18}$, the low temperature superfluid density and the electronic specific heat evidence a fully-gapped superconducting state, whose enhanced gap magnitude and specific-heat discontinuity suggest a moderately strong electron-phonon coupling. In both Re$_{0.82}$Nb$_{0.18}$ and pure Re, the spontaneous …
In this work we aim to analyze the effect of a strong antisymmetric spin-orbit coupling (ASOC) on superconductivity of noncentrosymmetric LaPtSi. We study the energy gap structure of polycrystalline LaPtSi by using magnetic penetration depth measurements down to 0.02$T_c$. We observed a dirty s-wave behavior, which provides compelling evidence that the spin-singlet component of the mixed pairing state is highly dominant. This is consistent with previous results in the sense that the mere presence of a strong ASOC does not lead to unconventional behaviors. Our result also downplays LaPtSi as a …
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…
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…
We study theoretically the surface of time-reversal-symmetric, noncentrosymmetric superconductor with mixed singlet and triplet order parameters. A pair of counterpropagating subgap quasiparticle surface bound states with opposite spin projections are obtained in the nontrivial Z$_2$ case where the triplet component is larger than the singlet one, contributing to a spin current. In contrast to the pure p-wave cases, these subgap states do not have a fixed spin projections but depend on the momenta along the surface. In the trivial Z$_2$ case where the singlet order parameter is larger, no subg…
The noncentrosymmetric superconductor Re$_{24}$Ti$_{5}$, a time-reversal symmetry (TRS) breaking candidate with $T_c = 6$\,K, was studied by means of muon-spin rotation/relaxation ($μ$SR) and tunnel-diode oscillator (TDO) techniques. At a macroscopic level, its bulk superconductivity was investigated via electrical resistivity, magnetic susceptibility, and heat capacity measurements. The low-temperature penetration depth, superfluid density and electronic heat capacity all evidence an $s$-wave coupling with an enhanced superconducting gap. The spontaneous magnetic fields revealed by zero-field…
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$…
We present muon spin rotation ($μ$SR) measurements on the noncentrosymmetric superconductor PbTaSe$_2$. From measurements in an applied transverse field between $H_{c1}$ and $H_{c2}$, we extract the superfluid density as a function of temperature in the vortex state. This data can be fit with a fully gapped two-band model, consistent with previous evidence from ARPES, thermal conductivity, and resistivity. Furthermore, zero field measurements show no evidence for a time reversal symmetry breaking field greater than 0.05~G in the superconducting state. This makes exotic fully gapped spin-triple…
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…
Evidence for non-unitary triplet-pairing superconductivity in noncentrosymmetric TaRuSi and comparison with isostructural TaReSi
McMaster University（麦克马斯特大学）；Indian Institute of Science Education and Research Bhopal（印度科学教育研究学院博帕尔分校）；Sungkyunkwan University（成均馆大学）；The University of British Columbia（不列颠哥伦比亚大学）
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 calculate the spectrum of the Andreev boundary modes in a two-dimensional superconductor formed at an interface between two different non-superconducting materials, e.g. insulating oxides. Inversion symmetry is absent in this system, and both the electron band structure and the superconducting pairing are strongly affected by the spin-orbit coupling of the Rashba type. We consider isotropic s-wave pairing states, both with and without time-reversal symmetry breaking, as well as various d-wave states. In all cases, there exist subgap Andreev boundary states, whose properties, in particular, …
Recently, high entropy alloys (HEAs) have emerged as a new platform for discovering superconducting materials and offer avenues to explore exotic superconductivity. The highly disordered nature of HEA suggests regular phonon required for BCS superconductivity may be unlikely to occur. Therefore understanding the microscopic properties of these superconducting HEA is important. We report the first detailed characterization of the superconducting properties of the noncentrosymmetric ($α$-Mn structure) HEA {(HfNb)}$_{0.10}${(MoReRu)}$_{0.90}$, and {(ZrNb)}$_{0.10}${(MoReRu)}$_{0.90}$ by using mag…
The superconducting order parameter of the noncentrosymmetric superconductor LaRhSn is investigated by means of low temperature measurements of the specific heat, muon-spin relaxation/rotation ($μ$SR) and the tunnel-diode oscillator (TDO) based method. The specific heat and magnetic penetration depth [$λ(T)$] show an exponentially activated temperature dependence, demonstrating fully gapped superconductivity in LaRhSn. The temperature dependence of $λ^{-2}(T)$ deduced from the TDO based method and $μ$SR show nearly identical behavior, which can be well described by a single-gap $s$-wave model,…
In two-dimensional electron systems with broken inversion and time-reversal symmetries, a Josephson junction reveals an anomalous response: the supercurrent is nonzero even at zero phase difference between two superconductors. We consider details of this peculiar phenomenon in the planar double-barrier configurations of hybrid circuits, where the noncentrosymmetric normal region is described in terms of the paradigmatic Rashba model of spin-orbit coupling. We analyze this anomalous Josephson effect by means of both the Ginzburg-Landau formalism and the microscopic Green's functions approach in…
The superconducting gap structure of a charge density wave (CDW) superconductor LaPt$_2$Si$_2$ ($T_c$ = 1.6~K) having a quasi two dimensional crystal structure has been investigated using muon spin rotation/relaxation ($μ$SR) measurements carried out in transverse field (TF), zero field (ZF) and longitudinal field (LF) geometries. Rigorous analysis of TF-$μ$SR spectra in the superconducting state corroborates that the temperature dependence of the effective penetration depth, $λ_L$, derived from muon spin depolarization, fits to an isotropic $s+s-$wave model suggesting that the Fermi surface c…
Topological superconductivity is an exotic phenomenon due to the symmetry-protected topological surface state, in which a quantum system has an energy gap in the bulk but supports gapless excitations confined to its boundary. Symmetries including central and time-reversal (TRS), along with their relations with topology, are crucial for topological superconductivity. We report muon spin relaxation/rotation ($μ$SR) experiments on a topological noncentrosymmetric superconductor PbTaSe$_2$ to study its TRS and gap symmetry. Zero-field $μ$SR experiments indicate the absence of internal magnetic fie…
We report a comprehensive study of the noncentrosymmetric superconductor Mo$_3$P. Its bulk superconductivity, with $T_c = 5.5$ K, was characterized via electrical resistivity, magnetization, and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation/relaxation ($μ$SR) and nuclear magnetic resonance (NMR) techniques. In the normal state, NMR relaxation data indicate an almost ideal metallic behavior, confirmed by band-structure calculations, which suggest a relatively high electron density of states, dominated by the Mo $4d$-orbi…
We study theoretically a model for twin boundaries in superconductors with Rashba spin-orbit coupling, which can be relevant to both three-dimensional noncentrosymmetric tetragonal crystals and two-dimensional gated superconductors such as the LaAlO$_3$/SrTiO$_3$ interface. In both cases, the broken inversion symmetry allows for a coexistence of singlet and triplet pairing. Within the framework of a Ginzburg-Landau theory, we identify two $\mathbb{Z}_2$ symmetries that are broken via two consecutive second order phase transitions as the temperature is lowered. We show that a time-reversal symm…
The superconducting properties of CaTSi3 (where T = Pt and Ir) have been investigated using muon spectroscopy. Our muon-spin relaxation results suggest that in both these superconductors time-reversal symmetry is preserved, while muon-spin rotation data show that the temperature dependence of the superfluid density is consistent with an isotropic s-wave gap. The magnetic penetration depths and upper critical fields determined from our transverse-field muon-spin rotation spectra are found to be 448(6) and 170(6) nm, and 3800(500) and 1700(300) G, for CaPtSi3 and CaIrSi3 respectively. The superc…
We find evidence that the newly discovered Fe-based superconductor KCa$_2$Fe$_4$As$_4$F$_2$ ($T_c~=~33.36(7)$~K) displays multigap superconductivity with line nodes. Transverse field muon spin rotation ($μ$SR) measurements show that the temperature dependence of the superfluid density does not have the expected behavior of a fully-gapped superconductor, due to the lack of saturation at low temperatures. Moreover, the data cannot be well fitted using either single band models or a multiband $s$-wave model, yet are well described by two-gap models with line nodes on either one or both of the gap…
We present a relativistic symmetry analysis of the allowed pairing states in the noncentroymmetric superconductor LaNiC$_2$. The case of zero spin-orbit coupling (SOC) is discussed first and then the evolution of the symmetry-allowed superconducting instabilities as SOC is adiabatically turned on is described. In addition to mixing singlet with triplet pairing, SOC splits some triplet pairing states with degenerate order parameter spaces into non-degenerate pairing states with different critical temperatures. We address the breaking of time-reversal symmetry (TRS) detected in recent muon spin …
The noncentrosymmetric superconductor AuBe have been investigated using the magnetization, resistivity, specific heat, and muon-spin relaxation/rotation measurements. AuBe crystallizes in the cubic FeSi-type B20 structure with superconducting transition temperature observed at $T_{c}$ = 3.2 $\pm$ 0.1 K. The low-temperature specific heat data, $C_{el}$(T), indicate a weakly-coupled fully gapped BCS superconductivity with an isotropic energy gap 2$Δ(0)/k_{B}T_{c}$ = 3.76, which is close to the BCS value of 3.52. Interestingly, type-I superconductivity is inferred from the $μ$SR measurements, whi…
The superconducting properties of the recently discovered double Fe$_2$As$_2$ layered high-$T_c$ superconductor RbCa$_2$Fe$_4$As$_4$F$_2$ with $T_c\approx$ 30~K have been investigated using magnetization, heat capacity, transverse-field (TF) and zero-field (ZF) muon-spin rotation/relaxation ($μ$SR) measurements. Our low field magnetization measurements and heat capacity (C$_p$) reveal an onset of bulk superconductivity with $T_{\bf c}\sim$ 30.0(4) K. Furthermore, the heat capacity exhibits a jump at $T_{\bf c}$ of $Δ$C$_p$/$T_{\bf c}$=94.6 (mJ/mole-K$^2$) and no clear effect of applied magneti…
The existence of edge states and zero energy modes in vortex cores is a hallmark of topologically nontrivial phases realized in various condensed matter systems such as the fractional quantum Hall states, p+ip superconductors, and Z_2 insulators (quantum spin Hall state). We examine this scenario for two dimensional noncentrosymmetric superconductors which allow the parity-mixing of Cooper pairs. It is found that even when the s-wave pairing gap is nonzero, provided that the superconducting gap of spin-triplet pairs is larger than that of spin-singlet pairs, gapless edge states and zero energy…
A detailed zero-field and transverse-field muon spin relaxation/rotation ($μ$SR) experiemnts have been carried out on the recently discovered non-centrosymmetric superconductor W$_3$Al$_2$C to speculate about its superconducting ground state. Bulk nature of superconductivity below 7.6 K is confirmed through magnetization measurements. No change in the $μ$SR spectra collected above and below $T_c$ is visible, ruling out the possibility of spontaneous magnetic field below $T_c$. This confirms that time-reversal symmetry is preserved for W$_3$Al$_2$C upon entering in the superconducting ground st…
