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 Little-Parks effect observed in mesoscopic polycrystalline $α-$BiPd ring devices reveals the presence of half-integer magnetic flux quantization, which provides a decisive evidence for the spin-triplet pairing state. We find mixed half-quantum fluxes and integer-quantum fluxes, consistent with the scenario of singlet-triplet pair mixing.
We show that the nonuniform state (Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state) of the spin triplet superconductivity in noncentrosymmetric systems is stabilized by antisymmetric spin-orbit coupling even if the magnetic field is absent. The transition temperature of the spin triplet superconductivity is reduced by the antisymmetric spin-orbit coupling in general. This pair breaking effect is shown to be similar to the Pauli pair breaking effect due to magnetic field for the spin singlet superconductivity, in which FFLO state is stabilized near the Pauli limit (or Chandrasekhar-Clogston limit)…
One of the key effects which is predicted to arise in superconductors without a centre of inversion is the mixing of singlet and triplet order parameters, which are no longer good quantum numbers on their own due to parity. We have probed the gap structure in the noncentrosymmetric superconductor Ru$_7$B$_3$, through small-angle neutron diffraction from the vortex lattice, in order to search for the proposed mixed order parameter. We find that the measured temperature dependence of the vortex-lattice form factor is well characterised by a model constructed to describe the effects of broken inv…
We study pairing symmetry of noncentrosymmetric superconductors based on the extended Hubbard model on square lattice near half-filling, using the random phase approximation. We show that d+f-wave pairing is favored and the triplet f-wave state is enhanced by Rashba type spin-orbit coupling originating from the broken inversion symmetry. The enhanced triplet superconductivity stems from the increase of the effective interaction for the triplet pairing and the reduction of the spin susceptibility caused by the Rashba type spin-orbit coupling which lead to the increase of the triplet component a…
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 …
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…
We describe the superconducting proximity effect taking place in a contact between a noncentrosymmetric superconductor and a diffusive normal/ferromagnetic metal within the quasiclassical theory of superconductivity. By solving numerically the Usadel equation with boundary conditions valid for arbitrary interface transparency, we show that the analysis of the proximity-modified local density of states in the normal side can be used to obtain information about the exotic superconductivity of noncentrosymmetric materials. We point out the signatures of triplet pairing, the coexistence of triplet…
We analytically study electronic bound states around a single vortex core in a noncentrosymmetric superconductor such as ${\rm CePt_3Si}$ without mirror symmetry about the $ab$ plane. Considering a mixed spin-singlet-triplet Cooper pairing model, we obtain a formula about the local density of states (LDOS) around a vortex core in any directions of magnetic fields. The LDOS under a magnetic field perpendicular to the c axis are quite different from those of typical s-wave or d-wave superconductors. From the ellipticity of the spatial pattern of the LDOS around a vortex core, one can estimate ex…
In non-magnetic bulk materials, inversion symmetry protects the spin degeneracy. If the bulk crystal structure lacks a centre of inversion, however, spin-orbit interactions lift the spin degeneracy, leading to a Rashba metal whose Fermi surfaces exhibit an intricate spin texture. In superconducting Rashba metals a pairing wavefunction constructed from these complex spin structures will generally contain both singlet and triplet character. Here we examine the possible triplet components of the order parameter in noncentrosymmetric BiPd, combining for the first time in a noncentrosymmetric super…
We show that the two-band nature of noncentrosymmetric superconductors leads naturally to an anomalous Josephson current appearing at zero phase difference in a clean noncentrosymmetric superconductor/ferromagnet/noncentrosymmetric superconductor junction. The two-band nature provides two sets of Andreev bound states which carry two supercurrents with different amplitudes. When the magnetization direction of the ferromagnet is suitably chosen, two supercurrents experience opposite phase shifts from the conventional sinusoidal current-phase relation. Then the total Josephson current results in …
We consider bound states at the vortex core of a non-centrosymmetric superconductor. We show that, despite the mixing of singlet and triplet order parameters, zero energy states survive within certain parameter space as in vortices of some chiral p-wave states.
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…
For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We demonstrate that such a model on a qualitative level accounts for experimentally observed features of the temperature dependence of the nuclear spin-lattice relaxation rate 1/T1, namely a peak just below Tc and a line-node gap behavior at low temperatures.
We consider transport through a Josephson junction consisting of a conventional s-wave superconductor coupled via a double quantum dot to a noncentrosymmetric superconductor with both, singlet and triplet pairing. We calculate the Andreev bound state energies and the associated Josephson current. We demonstrate that the current-phase relation is a sensitive probe of the singlet-triplet ratio in the noncentrosymmetric superconductor. In particular, in the presence of an inhomogeneous magnetic field the system exhibits a $φ$-junction behavior.
For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We calculate the superfluid density tensor in the clean limit on the basis of the quasiclassical theory of superconductivity. We demonstrate that such a pairing model accounts for an experimentally observed feature of the temperature dependence of the London penetration depth in CePt3Si, i.e., line-node-gap behavior at low temperatures.
We numerically study the vortex core structure in a noncentrosymmetric superconductor such as CePt3Si without mirror symmetry about the xy plane. A single vortex along the z axis and a mixed singlet-triplet Cooper pairing model are considered. The spatial profiles of the pair potential, local density of states, supercurrent density, and radially-textured magnetic moment density around the vortex are obtained in the clean limit on the basis of the quasiclassical theory of superconductivity.
We study the Josephson effect in a clean noncentrosymmetric superconductor/half-metal/noncentrosymmetric superconductor junction, which is grown on the surface of a three-dimensional Topological Insulator (TI) in the ballistic limit. We find the signature of anomalous Andreev Bound States (ABS) and band splitting for a spin-active barrier whose barrier magnetic moment is misaligned with the bulk moment. The chiral Majorana mode and 4$π$ periodic ABS are found to exist on the surface of TI for parallel orientation of the moments in the normal incidence condition. But for anti-parallel misalignm…
We discuss the Josephson current between two noncentrosymmetric superconductors. The coexistence of superconducting order parameters between spin-singlet $Δ_{\text{S}}$ and helical p-wave spin-triplet $Δ_{\text{T}}$ enriches a variety of low-temperature behavior of Josephson current depending on their relative amplitudes. We will show that characteristic behaviors of the Josephson current for $Δ_{\text{S}} > Δ_{\text{T}}$ are clearly different from those for $Δ_{\text{S}} < Δ_{\text{T}}$. The topologically protected zero-energy surface bound states are responsible for the clear difference. We …
Noncentrosymmetric superconductors with various types of pairing interactions are systematically examined with particular focus on phenomena that originate from the differences between Fermi surfaces split by a strong spin-orbit coupling. In particular, when the spin-orbit coupling increases and one of the split Fermi surfaces disappears, the phase diagram and the structure of the gap function change drastically. For example, we examine the conditions for the transition from full-gap states to line-node states (FLT), which may explain the differences in the experimental results between the non…
We consider a general Hamiltonian describing coexistence of itinerant ferromagnetism, spin-orbit coupling and mixed spin-singlet/triplet superconducting pairing in the context of mean-field theory. The Hamiltonian is diagonalized and exact eigenvalues are obtained, thus allowing us to write down the coupled gap equations for the different order parameters. Our results may then be applied to any model describing coexistence of any combination of these three phenomena. As a specific application of our results, we consider tunneling between a normal metal and a noncentrosymmetric superconductor w…
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…
When the inversion symmetry is broken, the spin-orbit coupling reduces the transition temperature of some types of spin triplet superconductivity, which is similar to the case that magnetic field reduces the spin singlet superconductivity due to Zeeman splitting. It is well known that Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state of spin singlet superconductivity is realized near the Pauli limit (or Chandrasekhar-Clogston limit) of external magnetic field. In FFLO state the amplitude of the order parameter is not uniform in space. In this paper we study the FFLO state in the spin triplet superc…
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…
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 …
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…
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…
The data of temperature dependent superfluid density $n_s(T)$ in Li$_2$Pd$_3$B and Li$_2$Pt$_3$B [Yuan {\it et al.}, \phrl97, 017006 (2006)] show that a sudden change of the slope of $n_s (T)$ occur at slightly lower than the critical temperature. Motivated by this observation, we microscopically derive the Ginzburg-Landau (GL) equations for noncentrosymmetric superconductors with Rashba type spin orbit interaction. Cooper pairing is assumed to occur between electrons only in the same spin split band and pair scattering is allowed to occur between two spin split bands. The GL theory of such a …
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…
Effects of disorder on superconducting properties of noncentrosymmetric compounds are discussed. Elastic impurity scattering, even for scalar impurities, leads to a strongly anisotropic mixing of the electron states in the bands split by the spin-orbit coupling. We focus on the calculation of the critical temperature, the upper critical field, and the spin susceptibility. It is shown that the impurity effects on the critical temperature are similar to those in multi-band centrosymmetric superconductors, in particular, Anderson's theorem holds for isotropic singlet pairing. In contrast, scalar …
We report measurements of London penetration depth $λ(T)$ for the noncentrosymmetric superconductor BiPd by using a tunnel diode oscillator. Pronounced anisotropic behavior is observed in the low-temperature penetration depth; the in-plane penetration depth $λ_{ac}(T)$ follows an exponential decrease, but the interplane penetration depth $λ_b(T)$ shows power-law-type behavior. The superfluid density $ρ_s(T)$, converted from the penetration depth $λ(T)$, is best fitted by an anisotropic two-band BCS model. We argue that such a complex order parameter is attributed to the admixture of spin-singl…
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 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…
In noncentrosymmetric superconductors (NCSs), the inversion symmetry (IS) is most commonly broken by an antisymmetric spin-orbit coupling (SOC) removing the spin degeneracy and splitting the Fermi surface (FS) into two branches. A two component condensate is then produced with a doublet pair potential mixing an even singlet and an odd triplet. When the triplet and the singlet strengths are comparable, the pair potential can have rich nodes. The angular line nodes (ALNs) are associated with strong anisotropy and they are widely studied in the literature. When the anisotropy is not strong, they …
We have synthesized polycrystalline samples of the noncentrosymmetric superconductor Mo3Al2C by arc and RF melting, measured its transport, magnetic and thermodynamic properties, and computed its band structure. Experimental results indicate a bulk superconducting transition at Tc ~ 9.2 K, while the density of states at the Fermi surface is found to be dominated by Mo d-orbitals. Using the measured values for the lower critical field Hc1, upper critical field Hc2, and the specific heat C, we estimated the thermodynamic critical field Hc(0), coherence length ξ(0), penetration depth λ(0), and th…
Helical edge states exist in the mixed spin-singlet and spin-triplet phase of a noncentrosymmetric (NCS) superconductor. In this article we have considered a planar ferromagnetic metal/NCS superconductor tunnel junction and have studied the effect of these helical edge states which manifests itself through the charge and spin tunneling conductance across the junction. We have shown the behavior of conductances for the entire range of variation of $γ= Δ_-/Δ_+$ where $Δ_\pm$ are the order parameters in the positive and negative helicity bands of the NCS superconductor.There exists a competition …
The discovery of noncentrosymmetric superconductors, such as CePt$_3$Si, and chiral superconductors, such as Sr$_2$RuO$_4$, calls for experimental methods to identify the presence of spin-triplet pairing. We here demonstrate a method which accomplishes this in an appealingly simple manner: a spin-sensitive proximity effect in a ferromagnet$\mid$triplet superconductor bilayer. It is shown how the orientation of the field can be used to unambiguously distinguish between different spin-triplet states. Moreover, the proximity effect becomes long-ranged in spite of the presence of an exchange field…
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…
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…
Mixing of spin singlet and spin triplet superconducting pairing state is expected in noncentrosymmetric superconductors (NCS) due to the inherent presence of Rashba-type antisymmetric spin-orbit coupling. Unlike low symmetry (tetragonal or monoclinic) NCS, parity is isotropicaly broken in space for cubic NCS and can additionally lead to the coexistence of magnetic and superconducting state under certain conditions. Motivated with such enriched possibility of unconventional superconducting phases in cubic NCS we are reporting successful formation of single crystalline cubic noncentrosymmetric P…
Transition metal boride Ru$_7$B$_3$ was found to be a noncentrosymmetric superconductor with $T_{C}$ equal to 3.3 K. Superconducting and normal state properties of Ru$_7$B$_3$ were determined by a self-consistent analysis through resistivity($ρ_{xx}$ and $ρ_{xy}$), specific heat, lower critical field measurement and electronic band structure calculation. It is found that Ru$_7$B$_3$ belongs to an s-wave dominated single band superconductor with energy gap 0.5 meV and could be categorized into type II superconductor with weak electron-phonon coupling. Unusual 'kink' feature is clearly observed …
Low-temperature thermal conductivity measurements were performed on single crystal of PbTaSe$_2$, a noncentrosymmetric superconductor with topological bulk nodal lines in the electronic band structure. It is found that the residual linear term $κ_0/T$ is negligible in zero magnetic field. Furthermore, the field dependence of $κ_0/T$ exhibits a clear "$S$"-shape curve. These results suggest that PbTaSe$_2$ has multiple nodeless superconducting gaps. Therefore, the spin-triplet state with gap nodes does not play an important role in this noncentrosymmetric superconductor with strong spin-orbital…
We investigate the order parameter of noncentrosymmetric superconductors Li$_2$Pd$_3$B and Li$_2$Pt$_3$B via the behavior of the penetration depth $λ(T)$. The low-temperature penetration depth shows BCS-like behavior in Li$_2$Pd$_3$B, while in Li$_2$Pt$_3$B it follows a linear temperature dependence. We propose that broken inversion symmetry and the accompanying antisymmetric spin-orbit coupling, which admix spin-singlet and spin-triplet pairing, are responsible for this behavior. The triplet contribution is weak in Li$_2$Pd$_3$B, leading to a wholly open but anisotropic gap. The significantly…
We report the measurements of the $^{29}$Si Knight shift $^{29}K$ on the noncentrosymmetric heavy-fermion compound CePt$_{3}$Si in which antiferromagnetism (AFM) with $T_{\rm N}=2.2$ K coexists with superconductivity (SC) with $T_{c}=0.75$ K. Its spin part $^{29}K_{\rm s}$, which is deduced to be $K_{\rm s}^{c}\ge 0.11$ and 0.16% at respective magnetic fields $H=2.0061$ and 0.8671 T, does not decrease across the superconducting transition temperature $T_{c}$ for the field along the c-axis. The temperature dependence of nuclear spin-lattice relaxation of $^{195}$Pt below $T_{c}$ has been accoun…
Layered three-dimensional centrosymmetric crystals can exhibit characteristics of noncentrosymmetric materials. This happens when each individual layer alone lacks inversion, but, when combined, inversion symmetry is restored; hence the designation: locally noncentrosymmertic superconductors (LNCSs). In LNCSs, the effects of impurities and subdominant magnetic field induced pairing channels remain unexplored. Using a minimal model, we examine all pairing channels and show that there is always a subdominant superconducting instability that is favored at high magnetic fields, which can substanti…
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…
Recent discovery of superconductivity in CeRh$_2$As$_2$ clarified an unusual $H$-$T$ phase diagram with two superconducting phases [Khim et al. arXiv:2101.09522]. The experimental observation has been interpreted based on the even-odd parity transition characteristic of locally noncentrosymmetric superconductors. Indeed, the inversion symmetry is locally broken at the Ce site, and CeRh$_2$As$_2$ molds a new class of exotic superconductors. The low-temperature and high-field superconducting phase is a candidate for the odd-parity pair-density-wave state, suggesting a possibility of topological …
Motivated by the recent discovery of superconductivity on the heterointerface $LaAlO_{3}/SrTiO_{3}$, we theoretically investigate its local electronic structures near an impurity considering the influence of Rashba-type spin-orbit interaction (RSOI) originated in the lack of inversion symmetry. We find that local density of states near an impurity exhibits the in-gap resonance peaks due to the quasiparticle scattering on the Fermi surface with the reversal sign of the pairing gap caused by the mixed singlet and RSOI-induced triplet superconducting state. We also analyze the evolutions of densi…
We report on a microscopic study of the noncentrosymmetric superconductor W$_3$Al$_2$C (with $T_c$ = 7.6 K), mostly by means of $^{27}$Al- and $^{13}$C nuclear magnetic resonance (NMR). Since in this material the density of states at the Fermi level is dominated by the tungsten's 5$d$ orbitals, we expect a sizeable spin-orbit coupling (SOC) effect. The normal-state electronic properties of W$_3$Al$_2$C resemble those of a standard metal, but with a Korringa product $1/(T_{1}T)$ significantly smaller than that of metallic Al, reflecting the marginal role played by $s$-electrons. In the supercon…
We systematically investigate the normal and superconducting properties of non-centrosymmetric Re$_{6}$Zr using magnetization, heat capacity, and electrical resistivity measurements. Resistivity measurements indicate Re$_{6}$Zr has poor metallic behavior and is dominated by disorder. Re$_6$Zr undergoes a superconducting transition at $T_{\mathrm{c}} = \left(6.75\pm0.05\right)$ K. Magnetization measurements give a lower critical field, $μ_{0}H_{\mathrm{c1}} = \left(10.3 \pm 0.1\right)$ mT. The Werthamer-Helfand-Hohenberg model is used to approximate the upper critical field $μ_{0}H_{\mathrm{c2}…
