Spin Triplet Superconducting State due to Broken Inversion Symmetry in Li(2)Pt(3)B

Probing the superconducting pairing of the La4Be33Pt16alloy via muon-spin spectroscopy

We report a study of the superconducting pairing of the noncentrosymmetric La4Be33Pt16alloy using muon-spin rotation and relaxation (µSR) technique. BelowTc=2.4 K, La4Be33Pt16exhibits bulk superconductivity (SC), here characterized by heat-capacity and magnetic-susceptibility measurements. The temperature dependence of the superfluid densityρsc(T), extracted from the transverse-fieldµSR measurements, reveals a nodeless SC in La4Be33Pt16. The best fit ofρsc(T)using ans-wave model yields a magnetic penetration depthλ0=542 nm and a superconducting gapΔ0=0.37 meV at zero Kelvin. The single-gapped superconducting state is further evidenced by the temperature-dependent electronic specific heatCe(T)/Tand the linear field-dependent electronic specific-heat coefficientγH(H). The zero-fieldµSR spectra collected in the normal- and superconducting states of La4Be33Pt16are almost identical, confirming the absence of an additional field-related relaxation and, thus, of spontaneous magnetic fields belowTc. The nodeless SC combined with a preserved time-reversal symmetry in the superconducting state proves that the spin-singlet pairing is dominant in La4Be33Pt16. This material represents yet another example of a complex system showing only a conventional behavior, in spite of a noncentrosymmetric structure and a sizeable spin-orbit coupling.

Antiferromagnetic Spin Fluctuations and Unconventional Superconductivity in Topological Superconductor Candidate YPtBi Revealed by ^{195}Pt-NMR

We report ^{195}Pt nuclear magnetic resonance (NMR) measurements on topological superconductor candidate YPtBi, which has broken inversion symmetry and topological nontrivial band structures due to the strong spin-orbit coupling. In the normal state, we find that Knight shift K is field- and temperature independent, suggesting that the contribution from the topological bands is very small at low temperatures. However, the spin-lattice relaxation rate 1/T_{1} divided by temperature (T), 1/T_{1}T, increases with decreasing T, implying the existence of antiferromagnetic spin fluctuations. In the superconducting state, no Hebel-Slichter coherence peak is seen below T_{c} and 1/T_{1} follows T^{3} variation, indicating the unconventional superconductivity. The finite spin susceptibility at zero-temperature limit and the anomalous increase of the NMR linewidth below T_{c} point to a mixed state of spin-singlet and spin-triplet (or spin-septet) pairing.

Investigation of the Influence of Pressure on the Physical Properties and Superconducting Transition Temperature of Chiral Noncentrosymmetric TaRh2B2 and NbRh2B2

TaRh₂B₂ and NbRh₂B₂ compounds exhibit noncentrosymmetric superconductivity with a chiral structure. Density functional theory-based ab-initio calculations have been executed to analyze the structural properties, mechanical stability, ductility/brittleness behaviors, Debye temperature, melting temperature, optical response to incident photon energy, electronic characteristics, and superconducting transition temperature of chiral TaRh₂B₂ and NbRh₂B₂ compounds under pressure up to 16 GPa. Both the chiral phases are mechanically stable and exhibit ductile nature under the studied pressure. The maximum value of the Pugh ratio (an indicator of ductile/brittle behaviors) is observed to be 2.55 (for NbRh₂B₂) and 2.52 (for TaRh₂B₂) at 16 GPa. The lowest value of the Pugh ratio is noticed at 0 GPa for both these chiral compounds. The analysis of reflectivity spectra suggests that both the chiral compounds can be used as efficient reflecting materials in the visible energy region. At 0 GPa, the calculated densities of states (DOSs) at the Fermi level are found to be 1.59 and 2.13 states eV^-1 per formula unit for TaRh₂B₂ and NbRh₂B₂, respectively. The DOS values of both the chiral phases do not alter significantly with applied pressure. The shape of the DOS curve of both compounds remains almost invariant with applied pressure. The pressure-induced variation of Debye temperatures of both compounds is observed, which may cause the alternation of the superconducting transition temperature, T_c, with applied pressure. The probable changing of T_c with pressure has been analyzed from the McMillan equation.

Superconductivity in non-centrosymmetric ZrNiAl and HfRhSn-type compounds

We report the discovery of superconductivity in non-centrosymmetric compounds HfNiAl, ZrNiAl, ZrNiGa, and HfPtAl by measuring their electrical transport and thermodynamic properties. HfNiAl, ZrNiAl, and ZrNiGa crystallize in the ZrNiAl-type crystal structure, whereas HfPtAl crystallizes in the HfRhSn-type crystal structure. Superconducting transitions for HfNiAl, ZrNiAl, ZrNiGa, and HfPtAl are observed at 1.0 K, 1.0 K, 0.42 K, and 0.58 K, respectively. Using the Werthamer-Helfand-Hohenberg model, the zero-temperature upper critical fieldsµ₀Hc2(0) were estimated to be 0.58 T, 0.24 T, 0.08 T, and 0.34 T for HfNiAl, ZrNiAl, ZrNiGa, and HfPtAl, respectively. The observed jump in electronic heat capacity (ΔCe/γT) across the superconducting transition is 1.3, 1.3, and 1.2 for HfNiAl, ZrNiAl, and HfPtAl, respectively. After the inclusion of the spin-orbit coupling in the band structure calculations, a total of six bands for ZrNiAl, HfPtAl, and ZrNiGa, and eight bands for HfNiAl were found to cross the Fermi level. Spin-orbit coupling induced maximum splitting (ΔEASOC/k_BT_c) of the electronic bands near the Fermi level was found to be 1697, 517, 1138, and 4230 for HfNiAl, ZrNiAl, ZrNiGa, and HfPtAl, respectively. Large variation of the antisymmetric spin-orbit coupling (ASOC) among these compounds provides a great opportunity to study the effects of ASOC on the superconducting pairing states.

s-wave superconductivity in the noncentrosymmetric W3Al2C superconductor: an NMR study

We report on a microscopic study of the noncentrosymmetric superconductor W₃Al₂C (withT_c= 7.6 K), mostly by means of²⁷Al- and¹³C nuclear magnetic resonance (NMR). Since in this material the density of states at the Fermi level is dominated by the tungsten's 5dorbitals, we expect a sizeable spin-orbit coupling (SOC) effect. The normal-state electronic properties of W₃Al₂C resemble those of a standard metal, but with a Korringa product 1/(T₁T) significantly smaller than that of metallic Al, reflecting the marginal role played bys-electrons. In the superconducting state, we observe a reduction of the Knight shift and an exponential decrease of the NMR relaxation rate 1/T₁, typical ofs-wave superconductivity (SC). This is further supported by the observation of a small but distinct coherence peak just belowT_cin the¹³C NMR relaxation-rate, in agreement with the fully-gapped superconducting state inferred from the electronic specific-heat data well belowT_c. The above features are compared to those of members of the same family, in particular, Mo₃Al₂C, often claimed to exhibit unconventional SC. We discuss why, despite the enhanced SOC, W₃Al₂C does not show spin-triplet features in its superconducting state and consider the broader consequences of our results for noncentrosymmetric superconductors in general.

Spin-triplet superconductivity in K2Cr3As3

A spin-triplet superconductor can harbor Majorana bound states that can be used in topological quantum computing. Recently, K₂Cr₃As₃ and its variants with critical temperature T_c as high as 8 kelvin have emerged as a new class of superconductors with ferromagnetic spin fluctuations. Here, we report a discovery in K₂Cr₃As₃ single crystal that the spin susceptibility measured by ⁷⁵As Knight shift below T_c is unchanged with the magnetic field H₀ applied in the ab plane but vanishes toward zero temperature when H₀ is along the c axis, which unambiguously establishes this compound as a spin-triplet superconductor described by a vector order parameter d→ parallel to the c axis. Combining with point nodal gap, we show that K₂Cr₃As₃ is a new platform for the study of topological superconductivity and its possible technical application.

Non-centrosymmetric superconductor Th[Formula: see text]Be[Formula: see text]Pt[Formula: see text] and heavy-fermion U[Formula: see text]Be[Formula: see text]Pt[Formula: see text] cage compounds

Unconventional superconductivity in non-centrosymmetric superconductors has attracted a considerable amount of attention. While several lanthanide-based materials have been reported previously, the number of actinide-based systems remains small. In this work, we present the discovery of a novel cubic complex non-centrosymmetric superconductor [Formula: see text] ([Formula: see text] space group). This intermetallic cage compound displays superconductivity below [Formula: see text] K, as evidenced by specific heat and resistivity data. [Formula: see text] is a type-II superconductor, which has an upper critical field [Formula: see text] T and a moderate Sommerfeld coefficient [Formula: see text] mJ [Formula: see text] [Formula: see text]. A non-zero density of states at the Fermi level is evident from metallic behavior in the normal state, as well as from electronic band structure calculations. The isostructural [Formula: see text] compound is a paramagnet with a moderately enhanced electronic mass, as indicated by the electronic specific heat coefficient [Formula: see text] mJ [Formula: see text] [Formula: see text] and Kadowaki-Woods ratio [Formula: see text] [Formula: see text] [Formula: see text] cm [Formula: see text] [Formula: see text] (mJ)[Formula: see text]. Both [Formula: see text] and [Formula: see text] are crystallographically complex, each hosting 212 atoms per unit cell.

Structural Phase Transitions and Superconductivity Induced in Antiperovskite Phosphide CaPd3P

In this study, we succeeded in synthesizing new antiperovskite phosphides MPd₃P (M = Ca, Sr, Ba) and discovered the appearance of a superconducting phase (0.17 ≤ x ≤ 0.55) in a solid solution (Ca_1-xSr_x)Pd₃P. Three perovskite-related crystal structures were identified in (Ca_1-xSr_x)Pd₃P, and a phase diagram was built on the basis of experimental results. The first phase transition from centrosymmetric (Pnma) to noncentrosymmetric orthorhombic (Aba2) occurred in CaPd₃P near room temperature. The phase transition temperature decreased as Ca²⁺ was replaced with a larger-sized isovalent Sr²⁺. Bulk superconductivity at a critical temperature (T_c) of approximately 3.5 K was observed in a range of x = 0.17-0.55; this was associated with the centrosymmetric orthorhombic phase. Thereafter, a noncentrosymmetric tetragonal phase (I4₁md) remained stable for 0.6 ≤ x ≤ 1.0, and superconductivity was significantly suppressed as samples with x = 0.75 and 1.0 showed T_c values as low as 0.32 K and 57 mK, respectively. For further substitution with a larger-sized isovalent Ba²⁺, namely, (Sr_1-yBa_y)Pd₃P, the tetragonal phase continued throughout the composition range. BaPd₃P no longer showed superconductivity down to 20 mK. Since the inversion symmetry of structure and superconductivity can be precisely controlled in (Ca_1-xSr_x)Pd₃P, this material may offer a unique opportunity to study the relationship between inversion symmetry and superconductivity.

Simultaneous Nodal Superconductivity and Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor CaPtAs

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}≈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 model comprising of a nodeless gap and a gap with nodes, rather than by single-band models. At the same time, zero-field muon-spin relaxation spectra exhibit increased relaxation rates below the onset of superconductivity, implying that TRS is broken in the superconducting state of CaPtAs, hence indicating its unconventional nature. Our observations suggest CaPtAs to be a new remarkable material that links two apparently disparate classes, that of TRS-breaking correlated magnetic superconductors with nodal gaps and the weakly correlated noncentrosymmetric superconductors with broken TRS, normally exhibiting only a fully gapped behavior.

Direction and symmetry transition of the vector order parameter in topological superconductors CuxBi2Se3

Topological superconductors have attracted wide-spreading interests for the bright application perspectives to quantum computing. Cu0.3Bi2Se3 is a rare bulk topological superconductor with an odd-parity wave function, but the details of the vector order parameter d and its pinning mechanism are still unclear. Here, we succeed in growing CuxBi2Se3 single crystals with unprecedented high doping levels. For samples with x  = 0.28, 0.36 and 0.37 with similar carrier density as evidenced by the Knight shift, the in-plane upper critical field Hc2 shows a two-fold symmetry. However, the angle at which the Hc2 becomes minimal is different by 90° among them, which indicates that the d-vector direction is different for each crystal likely due to a different local environment. The carrier density for x  = 0.46 and 0.54 increases substantially compared to x ≤ 0.37. Surprisingly, the in-plane Hc2 anisotropy disappears, indicating that the gap symmetry undergoes a transition from nematic to isotropic (possibly chiral) as carrier increases.

Nodeless s-wave superconductivity in the [Formula: see text]-Mn structure type noncentrosymmetric superconductor TaOs: a [Formula: see text]SR study

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 a 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 [Formula: see text], which is proportional to the superfluid density. This data can be fit with a fully gapped s-wave model for [Formula: see text]  =  2.01 [Formula: see text] 0.02. Furthermore, the value of magnetic penetration depth is found to be 5919 [Formula: see text] 45 [Formula: see text], which is consistent with the value obtained from the bulk measurements.

Superconductivity and the upper critical field in the chiral noncentrosymmetric superconductor NbRh2B2

NbRh₂B₂ crystallises in a chiral noncentrosymmetric structure and exhibits bulk type-II superconductivity below [Formula: see text] 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 [Formula: see text] T exceeds the Pauli paramagnetic limit, [Formula: see text] T. We explore the reasons for this enhancement. Transverse-field muon spectroscopy measurements suggest that the superconducting gap is either s-wave or [Formula: see text]-wave, and the pressure dependence of [Formula: see text] reveals the superconducting gap is primarily s-wave in character. The magnetic penetration depth [Formula: see text] nm. Heat capacity measurements reveal the presence of a multigap [Formula: see text]-wave superconducting order parameter and moderate electron-phonon coupling.

Point contact Andreev reflection studies of a non-centro symmetric superconductor Re6Zr

Re₆Zr, a non-centrosymmetric superconductor is an interesting system as recent experimental evidence suggests that the superconducting state breaks time reversal symmetry. This implies a mixing of spin singlet-triplet states leading to a complex order parameter in this system. Here, we report point contact Andreev Reflection (PCAR) measurements on a single crystal of Re₆Zr (superconducting transition temperature (T_c) = 6.78 K). We observe multiple gap features in the PCAR spectra which depends on the type of tip and contact. Spectral features appear at voltages 1.0 ± 0.1 mV, 0.75 ± 0.05 mV and 0.45 ± 0.1 mV suggesting that there are at least more than one band contributing to superconductivity. However, strong surface inter-band scattering is possibly responsible for the uncertainty in observing them together distinctly in a single contact in the PCAR measurements. Interestingly, the bulk gap (Δ  = 1.95k_BT_c = 1.1 meV) is occasionally observed in PCAR spectra, mostly with ferromagnetic tips. The gap features associated with the other two smaller gaps disappear at the bulk T_c. In addition, no anisotropy in the upper critical field was observed. Our results suggest an unconventional superconducting order in this compound: Multiband singlet states dominated by inter-band pairing which break the time reversal symmetry or singlet mixed with triplet states.

Time-Reversal Symmetry Breaking in Re-Based Superconductors

To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed comparative muon-spin rotation and relaxation (μSR) 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 magnetic fields revealed by zero-field μSR below T_{c} indicate time-reversal symmetry breaking and thus unconventional superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and noncentrosymmetric ReT (T=transition metal), yet its preservation in the isostructural noncentrosymmetric superconductors Mg_{10}Ir_{19}B_{16} and Nb_{0.5}Os_{0.5}, strongly suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting state in Re and ReT. We discuss the superconducting order parameter symmetries that are compatible with the experimental observations.

Proposed Spontaneous Generation of Magnetic Fields by Curved Layers of a Chiral Superconductor

We demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. This geometric Meissner effect provides an unequivocal signature of chiral superconductivity, which could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of zero-energy Majorana modes.

Specific heat, Electrical resistivity and Electronic band structure properties of noncentrosymmetric Th7Fe3 superconductor

Noncentrosymmetric superconductor Th₇Fe₃ has been investigated by means of specific heat, electrical resisitivity measurements and electronic properties calculations. Sudden drop in the resistivity at 2.05 ± 0.15 K and specific heat jump at 1.98 ± 0.02 K are observed, rendering the superconducting transition. A model of two BCS-type gaps appears to describe the zero-magnetic-field specific heat better than those based on the isotropic BCS theory or anisotropic functions. A positive curvature of the upper critical field H _c2(T _c) and nonlinear field dependence of the Sommerfeld coefficient at 0.4 K qualitatively support the two-gap scenario, which predicts H _c2(0) = 13 kOe. The theoretical densities of states and electronic band structures (EBS) around the Fermi energy show a mixture of Th 6d- and Fe 3d-electrons bands, being responsible for the superconductivity. Furthermore, the EBS and Fermi surfaces disclose significantly anisotropic splitting associated with asymmetric spin-orbit coupling (ASOC). The ASOC sets up also multiband structure, which presumably favours a multigap superconductivity. Electron Localization Function reveals the existence of both metallic and covalent bonds, the latter may have different strengths depending on the regions close to the Fe or Th atoms. The superconducting, electronic properties and implications of asymmetric spin-orbit coupling associated with noncentrosymmetric structure are discussed.

Topological superconductors: a review

This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.

Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.

Transport and noise properties of a normal metal-superconductor-normal metal junction with mixed singlet and chiral triplet pairings

We study transport and zero frequency shot noise properties of a normal metal-superconductor-normal metal (NSN) junction, with the superconductor having mixed singlet and chiral triplet pairings. We show that in the subgapped regime when the chiral triplet pairing amplitude dominates over that of the singlet, a resonance phenomena emerges out at zero energy where all the quantum mechanical scattering probabilities acquire a value of 0.25. At the resonance, crossed Andreev reflection mediating through such junction, acquires a zero energy peak. This reflects as a zero energy peak in the conductance as well depending on the doping concentration. We also investigate shot noise for this system and show that shot noise cross-correlation is negative in the subgapped regime when the triplet pairing dominates over the singlet one. The latter is in sharp contrast to the positive shot noise obtained when the singlet pairing is the dominating one.

Topological surface states in nodal superconductors

Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states.

Detection of time-reversal symmetry breaking in the noncentrosymmetric superconductor Re6Zr using muon-spin spectroscopy

We have investigated the superconducting state of the noncentrosymmetric compound Re6Zr using magnetization, heat capacity, and muon-spin relaxation or rotation (μSR) measurements. Re6Zr has a superconducting transition temperature, Tc=6.75±0.05  K. Transverse-field μSR experiments, used to probe the superfluid density, suggest an s-wave character for the superconducting gap. However, zero and longitudinal-field μSR data reveal the presence of spontaneous static magnetic fields below Tc indicating that time-reversal symmetry is broken in the superconducting state and an unconventional pairing mechanism. An analysis of the pairing symmetries identifies the ground states compatible with time-reversal symmetry breaking.

Edge currents as a signature of flatbands in topological superconductors

We study nondegenerate flatbands at the surfaces of noncentrosymmetric topological superconductors by exact diagonalization of Bogoliubov-de Gennes Hamiltonians. We show that these states are strongly spin polarized and acquire a chiral dispersion when placed in contact with a ferromagnetic insulator. This chiral mode carries a large edge current which displays a singular dependence on the exchange-field strength. The contribution of other edge states to the current is comparably weak. We hence propose that the observation of the edge current can serve as a test of the presence of nondegenerate flatbands.

Existence of Majorana fermions and topological order in nodal superconductors with spin-orbit interactions in external magnetic fields

We demonstrate that Majorana fermions exist in edges of systems and in a vortex core even for superconductors with nodal excitations such as the d-wave pairing state under a particular but realistic condition in the case with an antisymmetric spin-orbit interaction and a nonzero magnetic field below the upper critical field. We clarify that the Majorana fermion state is topologically protected in spite of the presence of bulk gapless nodal excitations, because of the existence of a nontrivial topological number. Our finding drastically enlarges target systems where we can explore the Majorana fermion state.

Physical properties of the noncentrosymmetric superconductor Mg10Ir19B16

Specific heat, electrical resistivity, and magnetic susceptibility measurements on a high quality sample of Mg10Ir19B16 provide a self-consistent determination of its superconducting properties. They indicate that Mg10Ir19B16 is a type-II superconductor [T{C}=4.45 K, kappa(0) approximately 20], with an electron-phonon coupling constant lambda{ep}=0.66. An analysis of the T-dependent specific heat shows that superconducting properties are dominated by an s-wave gap (Delta=0.7 meV). Point contact tunneling data provide evidence for multiple superconducting gaps, as expected from strong asymmetric spin-orbit coupling.