Evidence for time-reversal symmetry breaking in the noncentrosymmetric superconductor LaNiC2

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.

Evidence of multi-band superconductivity in non-centrosymmetric full Heusler alloy LuPd2Sn

In this work, evidence of multi-band superconductivity and presence of mixed parity states in full Heusler alloy LuPd₂Sn is investigated using the x-ray diffraction, temperature and field dependent resistivity, temperature dependent magnetization, and heat capacity measurements. Our studies reveal that LuPd₂Sn is a type II superconductor and undergoes superconducting transition below 2.5 K. Above 2.5 K, the temperature and field dependence of resistivity indicate to the presence of multiple bands and inter-band phonon assisted scattering. The upper critical field,H_C2(T) exhibits linear behaviour and deviates from Werthamer, Helfand and Hohenberg model over the measured temperature range. Additionally, the Kadowaki-Woods ratio plot supports the unconventional superconductivity in this alloy. Moreover, a significant deviation from the s-wave behaviour is noted, which is studied using phases fluctuation analysis. It indicates the presence of spin triplet along with spin singlet component arising due to antisymmetric spin orbit coupling.

Nonequilibrium Green's function approach to multi-band Cooper-pair transport: linear magnetoresistance effect due to nonunitary superconductivity

Many-body transport has emerged as an efficient tool for understanding interaction effects in quantum materials with a multi-band electronic structure. This paper proposes a formula for the two-particle transmission coefficient for Cooper-pair transport between multi-band normal and superconducting materials. The approach employs a tight-binding nonequilibrium Green's function technique, allowing a direct calculation of the two-particle current, without invoking the paradigm of Andreev reflection. As an application of the theory, we demonstrate a low-field linear magnetoresistance effect for superconductors with an induced nonunitary order parameter. These results uncover an unexplored route for detecting unconventional nonunitary superconductivity in quantum materials of current theoretical and experimental interest.

Unconventional superconductivity in topological Kramers nodal-line semimetals

Crystalline symmetry is a defining factor of the electronic band topology in solids, where many-body interactions often induce a spontaneous breaking of symmetry. Superconductors lacking an inversion center are among the best systems to study such effects or even to achieve topological superconductivity. Here, we demonstrate that TRuSi materials (with T a transition metal) belong to this class. Their bulk normal states behave as three-dimensional Kramers nodal-line semimetals, characterized by large antisymmetric spin-orbit couplings and by hourglass-like dispersions. Our muon-spin spectroscopy measurements show that certain TRuSi compounds spontaneously break the time-reversal symmetry at the superconducting transition, while unexpectedly showing a fully gapped superconductivity. Their unconventional behavior is consistent with a unitary (s + ip) pairing, reflecting a mixture of spin singlets and spin triplets. By combining an intrinsic time-reversal symmetry-breaking superconductivity with nontrivial electronic bands, TRuSi compounds provide an ideal platform for investigating the rich interplay between unconventional superconductivity and the exotic properties of Kramers nodal-line/hourglass fermions.

Mo3ReRuC: A Noncentrosymmetric Superconductor Formed in the MoReRu-Mo2C System

A quaternary compound with the composition Mo₃ReRuC is obtained in a previously unexplored MoReRu-Mo₂C system. According to X-ray structural analysis, Mo₃ReRuC crystallizes in the noncentrosymmetric space group P4₁32 [cubic β-Mn-type structure, a = 6.8107(1) Å]. Below 7.7 K, Mo₃ReRuC becomes a bulk type-II superconductor with an upper critical field close to the Pauli paramagnetic limit. The specific heat data give a large normalized jump ΔC_p/γT_c = 2.3 at T_c, which points to a strongly coupled superconducting state. First-principles calculations show that its electronic states at the Fermi level are mainly contributed by Mo, Re, and Ru atoms and strongly increased by the spin-orbit coupling. Our finding suggests that the intermediate phase between alloys and carbides may be a good place to look for β-Mn-type noncentrosymmetric superconductors.

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.

Nonunitary superconductivity in complex quantum materials

We revisit the concept of nonunitary superconductivity and generalize it to address complex quantum materials. Starting with a brief review of the notion of nonunitary superconductivity, we discuss its spectral signatures in simple models with only the spin as an internal degree of freedom. In complex materials with multiple internal degrees of freedom, there are many more possibilities for the development of nonunitary order parameters. We provide examples focusing on d-electron systems with two orbitals, applicable to a variety of materials. We discuss the consequences for the superconducting spectra, highlighting that gap openings of band crossings at finite energies can be attributed to a nonunitary order parameter if this is associated with a finite superconducting fitness matrix. We speculate that nonunitary superconductivity in complex quantum materials is in fact very common and can be associated with multiple cases of recently reported time-reversal symmetry breaking superconductors.

Intrinsic Nature of Spontaneous Magnetic Fields in Superconductors with Time-Reversal Symmetry Breaking

We present a systematic investigation of muon-stopping states in superconductors that reportedly exhibit spontaneous magnetic fields below their transition temperatures due to time-reversal symmetry breaking. These materials include elemental rhenium, several intermetallic systems, and Sr_{2}RuO_{4}. We demonstrate that the presence of the muon leads to only a limited and relatively localized perturbation to the local crystal structure, while any small changes to the electronic structure occur several electron volts below the Fermi energy, leading to only minimal changes in the charge density on ions close to the muon. Our results imply that the muon-induced perturbation alone is unlikely to lead to the observed spontaneous fields in these materials, whose origin is more likely intrinsic to the time-reversal symmetry-broken superconducting state.

Spectroscopic evidence of mixed angular momentum symmetry in non-centrosymmetric Ru[Formula: see text]B[Formula: see text]

Superconducting crystals with a lack of inversion symmetry can potentially host unconventional pairing. However, till today, no direct conclusive experimental evidence of such unconventional order parameters in non-centrosymmetric superconductors has been reported. In this paper, through direct measurement of the superconducting energy gap by scanning tunnelling spectroscopy, we report the existence of both s-wave (singlet) and p-wave (triplet) pairing symmetries in non-centrosymmetric Ru[Formula: see text]B[Formula: see text]. Our temperature and magnetic field-dependent studies also indicate that the relative amplitudes of the singlet and triplet components change differently with temperature.

Machine learning approach to muon spectroscopy analysis

In recent years, artificial intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised machine learning (ML) algorithm called principal component analysis (PCA) as a tool to analyse the data from muon spectroscopy experiments. Specifically, we apply the ML technique to detect phase transitions in various materials. The measured quantity in muon spectroscopy is an asymmetry function, which may hold information about the distribution of the intrinsic magnetic field in combination with the dynamics of the sample. Sharp changes of shape of asymmetry functions-measured at different temperatures-might indicate a phase transition. Existing methods of processing the muon spectroscopy data are based on regression analysis, but choosing the right fitting function requires knowledge about the underlying physics of the probed material. Conversely, PCA focuses on small differences in the asymmetry curves and works without any prior assumptions about the studied samples. We discovered that the PCA method works well in detecting phase transitions in muon spectroscopy experiments and can serve as an alternative to current analysis, especially if the physics of the studied material are not entirely known. Additionally, we found out that our ML technique seems to work best with large numbers of measurements, regardless of whether the algorithm takes data only for a single material or whether the analysis is performed simultaneously for many materials with different physical properties.

Bogoliubov-Fermi Surfaces in Noncentrosymmetric Multicomponent Superconductors

We show that when the time reversal symmetry is broken in a multicomponent superconducting condensate without inversion symmetry the resulting Bogoliubov quasiparticles generically exhibit mini-Bogoliubov-Fermi (BF) surfaces, for small superconducting order parameter. The absence of inversion symmetry makes the BF surfaces stable with respect to weak perturbations. With sufficient increase of the order parameter, however, the Bogoliubov-Fermi surface may disappear through a Lifshitz transition, and the spectrum this way become fully gapped. Our demonstration is based on the computation of the effective Hamiltonian for the bands near the normal Fermi surface by the integration over high-energy states. Exceptions to the rule, and experimental consequences are briefly discussed.

Recent progress on superconductors with time-reversal symmetry breaking

Superconductivity and magnetism are adversarial states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms, including the importance of multiple bands.

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.

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.

Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

It is very important to elucidate the mechanism of superconductivity for achieving room temperature superconductivity. In the first half of this paper, we give a brief review on mechanisms of superconductivity in many-electron systems. We believe that high-temperature superconductivity may occur in a system with interaction of large-energy scale. Empirically, this is true for superconductors that have been found so far. In the second half of this paper, we discuss cuprate high-temperature superconductors. We argue that superconductivity of high temperature cuprates is induced by the strong on-site Coulomb interaction, that is, the origin of high-temperature superconductivity is the strong electron correlation. We show the results on the ground state of electronic models for high temperature cuprates on the basis of the optimization variational Monte Carlo method. A high-temperature superconducting phase will exist in the strongly correlated region.

Time Reversal Symmetry Breaking Superconductors: Sr2RuO4 and Beyond

Recent work done on the time reversal symmetry (TRS) breaking superconductors is reviewed in this paper. The special attention is paid to Sr 2 RuO 4 believed to be spin triplet chiral p-wave superconductor which break TRS and is expected to posses non-trivial topological properties. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However not only Sr 2 RuO 4 but also many other superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation ( μ SR) and the Kerr effect. Both methods effectively measure the appearance of the spontaneous bulk magnetic field below superconducting transition temperature. This compound provides an example of the material whose many band, multi-condensate modeling has enjoyed a number of successes, but the full understanding has not been achieved yet. We discuss in some details the properties of the material. Among them is the Kerr effect and by understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multi-orbital character of states at the Fermi energy.

Evidence of a Nodal Line in the Superconducting Gap Symmetry of Noncentrosymmetric ThCoC_{2}

The newly discovered noncentrosymmetric superconductor ThCoC_{2} exhibits numerous types of 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 and relaxation (μSR) measurements. The temperature dependence of the magnetic penetration depth measured using the transverse field μSR experiment reveals the evidence of a nodal pairing symmetry. To understand this finding, we carry out calculations of the superconducting pairing eigenvalue and eigenfunction (pairing symmetry) due to the spin-fluctuation mechanism by directly implementing the ab initio band structures. We find that the system possesses a single Fermi surface with considerable three dimensionality and a strong nesting along the k_{z} direction. Such nesting promotes a superconducting state with a cosk_{z}-like pairing symmetry with a prominent nodal line on the k_{z}=±π/2 plane. The result agrees well with the experimental data.

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.

Nodeless superconductivity in the cage-type superconductor Sc5Ru6Sn18 with preserved time-reversal symmetry

We report the single-crystal synthesis and detailed investigations of the cage-type superconductor Sc₅Ru₆Sn₁₈, using powder x-ray diffraction (XRD), magnetization, specific-heat and muon-spin relaxation (µSR) measurements. Sc₅Ru₆Sn₁₈ crystallizes in a tetragonal structure (space group I4₁/acd) with lattice parameters a  =  1.387(3) nm and c  =  2.641(5) nm. Both DC and AC magnetization measurements prove the type-II superconductivity in Sc₅Ru₆Sn₁₈ with T _c  ≈  3.5(1) K, a lower critical field [Formula: see text]  =  157(9) Oe and an upper critical field, [Formula: see text]  =  26(1) kOe. The zero-field electronic specific-heat data are well fitted using a single-gap BCS model, with [Formula: see text]  =  0.64(1) meV. The Sommerfeld constant γ varies linearly with the applied magnetic field, indicating s-wave superconductivity in Sc₅Ru₆Sn₁₈. Specific-heat and transverse-field (TF) µSR measurements reveal that Sc₅Ru₆Sn₁₈ is a superconductor with strong electron-phonon coupling, with TF-µSR also suggesting a single-gap s-wave character of the superconductivity. Furthermore, zero-field µSR measurements do not detect spontaneous magnetic fields below T _c, hence implying that time-reversal symmetry is preserved in Sc₅Ru₆Sn₁₈.

Superconducting properties and μSR study of the noncentrosymmetric superconductor Nb0.5Os0.5

The properties of the noncentrosymmetric superconductor (α-[Formula: see text] structure) Nb_0.5Os_0.5 have been investigated using resistivity, magnetization, specific heat, and muon spin relaxation and rotation (μSR) measurements. These measurements suggest that Nb_0.5Os_0.5 is a weakly coupled ([Formula: see text]) type-II superconductor ([Formula: see text]), having a bulk superconducting transition temperature T _c   =  3.07 K. The specific heat data fits well with the single-gap BCS model indicating nodeless s-wave superconductivity in Nb_0.5Os_0.5. The μSR measurements also confirm [Formula: see text]-wave superconductivity with the preserved time-reversal symmetry.

Evidence of s-wave superconductivity in the noncentrosymmetric La7Ir3

Superconductivity in noncentrosymmetric compounds has attracted sustained interest in the last decades. Here we present a detailed study on the transport, thermodynamic properties and the band structure of the noncentrosymmetric superconductor La 7 Ir 3 (T c  ~ 2.3 K) that was recently proposed to break the time-reversal symmetry. It is found that La7Ir3 displays a moderately large electronic heat capacity (Sommerfeld coefficient γ n  ~ 53.1 mJ/mol K2) and a significantly enhanced Kadowaki-Woods ratio (KWR ~32 μΩ cm mol2 K2 J-2) that is greater than the typical value (~10 μΩ cm mol2 K2 J-2) for strongly correlated electron systems. The upper critical field Hc2 was seen to be nicely described by the single-band Werthamer-Helfand-Hohenberg model down to very low temperatures. The hydrostatic pressure effects on the superconductivity were also investigated. The heat capacity below T c reveals a dominant s-wave gap with the magnitude close to the BCS value. The first-principles calculations yield the electron-phonon coupling constant λ = 0.81 and the logarithmically averaged frequency ω ln  = 78.5 K, resulting in a theoretical T c  = 2.5 K, close to the experimental value. Our calculations suggest that the enhanced electronic heat capacity is more likely due to electron-phonon coupling, rather than the electron-electron correlation effects. Collectively, these results place severe constraints on any theory of exotic superconductivity in this system.

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.

Signatures of the topological s +- superconducting order parameter in the type-II Weyl semimetal T d-MoTe2

In its orthorhombic T_d polymorph, MoTe₂ is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in T_d-MoTe₂. Understanding the superconductivity in T_d-MoTe₂, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in T_d-MoTe₂. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature T_c is observed under pressure. Moreover, the superconducting order parameter in T_d-MoTe₂ is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field μSR experiments. Considering the strong suppression of T_c in MoTe₂ by disorder, we suggest that topologically non-trivial s⁺⁻ state is more likely to be realized in MoTe₂ than the topologically trivial s⁺⁺ state.

Understanding the superconductivity in topological materials is of eminent interest. Here, Guguchia et al. report temperature-dependent magnetic penetration depth in the superconducting state of T_d-MoTe₂ under pressure, suggesting a topologically nontrivial s⁺⁻ order parameter.

Superconducting gap structure in the electron doped BiS2-based superconductor

The influence of electron doping on semimetallic SrFBiS₂ has been investigated by means of resistivity, zero and transverse  -  field (ZF/TF) muon spin relaxation/rotation (μSR) experiments. SrFBiS₂ is semimetallic in its normal state and small amounts of La doping results in bulk superconductivity at 2.8 K, at ambient pressure. The temperature dependence of the superfluid density as determined by TF-μSR can be best modelled by an isotropic s  -  wave type superconducting gap. We have estimated the magnetic penetration depth [Formula: see text] nm, superconducting carrier density [Formula: see text] carriers m^-3 and effective-mass enhancement m ^*  =  1.558 m _e. Additionally, there is no clear sign of the occurrence of spontaneous internal magnetic fields below [Formula: see text], which implies that the superconducting state in this material can not be categorized by the broken time-reversal symmetry which is in agreement with the previous theoretical prediction.

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.

Two-Gap Superconductivity in LaNiGa_{2} with Nonunitary Triplet Pairing and Even Parity Gap Symmetry

The nature of the pairing states of superconducting LaNiC_{2} and LaNiGa_{2} has to date remained a puzzling question. Broken time reversal symmetry has been observed in both compounds and a group theoretical analysis implies a nonunitary triplet pairing state. However, all the allowed nonunitary triplet states have nodal gap functions but most thermodynamic and NMR measurements indicate fully gapped superconductivity in LaNiC_{2}. Here we probe the gap symmetry of LaNiGa_{2} by measuring the London penetration depth, specific heat, and upper critical field. These measurements demonstrate two-gap nodeless superconductivity in LaNiGa_{2}, suggesting that this is a common feature of both compounds. These results allow us to propose a novel triplet superconducting state, where the pairing occurs between electrons of the same spin, but on different orbitals. In this case the superconducting wave function has a triplet spin component but isotropic even parity gap symmetry, yet the overall wave function remains antisymmetric under particle exchange. This model leads to a nodeless two-gap superconducting state which breaks time reversal symmetry, and therefore accounts well for the seemingly contradictory experimental results.

Tuning the ferromagnetic phase in the CDW compound SmNiC2 via chemical alloying

We report a study on tuning the charge density wave (CDW) ferromagnet SmNiC2 to a weakly coupled superconductor by substituting La for Sm. X-ray diffraction measurements show that the doped compounds obey Vegard's law, where La (Lu) alloying expands (shrinks) the lattice due to its larger (smaller) atomic size than Sm. In the series Sm1-xLaxNiC2, CDW transition (TCDW = 148 K) for SmNiC2 is gradually suppressed, while the ferromagnetic (FM) ordering temperature (TC) at 17 K slightly increases up to x = 0.3. For x > 0.3, TC starts to decrease and there is no signature that could be related with the CDW phase. Electrical resistivity, magnetic susceptibility and specific heat measurements point toward the possible presence of a FM quantum critical point (QCP) near x = 0.92, where the TC is extrapolated to zero temperature. Superconductivity in LaNiC2 (Tsc = 2.9 K) is completely suppressed with small amount of Sm inclusion near the proposed FM critical point, indicating a competition between the two ordered phases. The tunable lattice parameters via chemical substitution (La,Lu) and the ensuing change among the ordered phases of ferromagnetism, CDW and superconductivity underscores that SmNiC2 provides a rich avenue to study the rare example of a FM QCP, where the broken symmetries are intricately correlated.

Physical properties and electronic band structure of noncentrosymmetric Th7Co3 superconductor

The physical properties of the noncentrosymmetric superconductor Th7Co3 have been investigated by means of ac-magnetic susceptibility, magnetization, specific heat, electrical resistivity, magnetoresistance and Hall effect measurements. From these data it is established that Th7Co3 is a dirty type-II superconductor with [Formula: see text] K, [Formula: see text] and moderate electron-phonon coupling [Formula: see text]. Some evidences for anisotropic superconducting gap are found, including e.g. reduced specific heat jump ([Formula: see text]) at T c, diminished superconducting energy gap ([Formula: see text]) as compared to the BCS values, power law field dependence of the Sommerfeld coefficient at 0.4 K ([Formula: see text]), and a concave curvature of the [Formula: see text] line. The magnitudes of the thermodynamic critical field and the energy gap are consistent with mean-squared anisotropy parameter [Formula: see text]. The electronic specific heat in the superconducting state is reasonably fitted to an oblate spheroidal gap model. Calculations of scalar relativistic and fully relativistic electronic band structures reveal considerable differences in the degenerate structure, resulting from asymmetric spin-orbit coupling (ASOC). A large splitting energy of spin-up spin-down bands at the Fermi level E F, [Formula: see text] meV is observed and a sizeable ratio [Formula: see text] could classify the studied compound into the class of noncentrosymmetric superconductors with strong ASOC. The noncentrosymmetry of the crystal structure and the atomic relativistic effects are both responsible for an importance of ASOC in Th7Co3. The calculated results for the density of states show a Van Hove singularity just below E F and dominant role of the 6d electrons of Th to the superconductivity.

Unconventional Superconductivity in La(7)Ir(3) Revealed by Muon Spin Relaxation: Introducing a New Family of Noncentrosymmetric Superconductor That Breaks Time-Reversal Symmetry

The superconductivity of the noncentrosymmetric compound La(7)Ir(3) is investigated using muon spin rotation and relaxation. Zero-field measurements reveal the presence of spontaneous static or quasistatic magnetic fields below the superconducting transition temperature T(c)=2.25  K-a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic and that the pairing symmetry of the superconducting electrons is predominantly s wave with an enhanced binding strength. The results indicate that the superconductivity in La(7)Ir(3) may be unconventional and paves the way for further studies of this family of materials.

Unconventional superconductivity in Y5Rh6Sn18 probed by muon spin relaxation

Conventional superconductors are robust diamagnets that expel magnetic fields through the Meissner effect. It would therefore be unexpected if a superconducting ground state would support spontaneous magnetics fields. Such broken time-reversal symmetry states have been suggested for the high—temperature superconductors, but their identification remains experimentally controversial. We present magnetization, heat capacity, zero field and transverse field muon spin relaxation experiments on the recently discovered caged type superconductor Y₅Rh₆Sn₁₈ ( T_C= 3.0 K). The electronic heat capacity of Y₅Rh₆Sn₁₈ shows a T³ dependence below T_c indicating an anisotropic superconducting gap with a point node. This result is in sharp contrast to that observed in the isostructural Lu₅Rh₆Sn₁₈ which is a strong coupling s—wave superconductor. The temperature dependence of the deduced superfluid in density Y₅Rh₆Sn₁₈ is consistent with a BCS s—wave gap function, while the zero-field muon spin relaxation measurements strongly evidences unconventional superconductivity through a spontaneous appearance of an internal magnetic field below the superconducting transition temperature, signifying that the superconducting state is categorized by the broken time-reversal symmetry.

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.

π-Conjugation in Gd13Fe10C13 and its oxycarbide: unexpected connections between complex carbides and simple organic molecules

Carbometalates are a diverse family of solid state structures formed from transition metal (TM)-carbon polyanionic frameworks whose charges are balanced by rare earth (RE) cations. Remarkable structural features, such as transition metal clusters, are often encountered in these phases, and a pressing challenge is to explain how such features emerge from the competing interaction types (RE-TM, TM-TM, TM-C, etc.) in these systems. In this Article, we describe a joint experimental and theoretical investigation of two compounds, Gd13Fe10C13 and its oxycarbide Gd13Fe10C(13-x)O(x) (x ≈ 1), which add a new dimension to the structural chemistry of carbometalates: π-conjugation through both TM-C and TM-TM multiple bonds. The crystal structures of both compounds are built from layers of Fe-centered Gd prisms stacked along c and surrounded by an Fe-C network, and differ chiefly in the stacking sequence of these layers. The phases' identical local structures have two types of Fe environment: trigonal planar FeC3 sites and H-shaped Fe2C4 sites, with unusually short Fe-Fe and Fe-C bonds. (57)Fe Mössbauer spectroscopy and DFT-calibrated Hückel calculations on Gd13Fe10C13 build a picture of covalent Fe-C σ bonds and conjugated π systems for which Lewis structures can be drawn. Using the reversed approximation Molecular Orbital approach, we can draw isolobal analogies between the Fe centers of this compound and molecular TM complexes: 18-electron configurations could be achieved through σ and π bonds with 18 electrons/Fe for the FeC3 site and 18-n (n = 2 for an Fe═Fe double bond) electrons/Fe for the Fe2C4 site. In this way, the vision of a unified bonding scheme of carbometalates and organometallics proffered by earlier studies is realized in a visual manner, directly from the 1-electron wave functions of the Hückel model. The bonding analysis predicts that Gd13Fe10C13 is one electron/formula unit short of an ideal electron count, explaining the tendency of the system toward a small degree of oxygen substitution. Analogies between the π bonding in Gd13Fe10C13 and that of the allyl anion help rationalize the presence of trigonal planar Fe and linear C units in the structure. The isolobal analogy between Gd13Fe10C13 and an 18-electron coordination complex is expected to apply to carbometalates as a whole, and will be extended to other examples in our future work.

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.

Magnetic and transport properties of PrRhSi3

We have investigated the magnetic and transport properties of a noncentrosymmetric compound PrRhSi3 by dc magnetic susceptibility χ(T), isothermal magnetization M(H), thermoremanent magnetization M(t), specific heat Cp(T), electrical resistivity ρ(T,H) and muon spin relaxation (μSR) measurements. At low fields χ(T) shows two anomalies near 15 and 7 K with an irreversibility between ZFC and FC data below 15 K. In contrast, no anomaly is observed in Cp(T) or ρ(T) data. M(H) data at 2 K exhibit very sharp increase below 0.5 T and a weak hysteresis. M(t) exhibits very slow relaxation, typical for a spin-glass system. Even though the absence of any anomaly in Cp(T) is consistent with the spin-glass type behavior, there is no obvious origin of spin-glass behavior in this structurally well ordered compound. The crystal electric field (CEF) analysis of Cp(T) data indicates a CEF-split singlet ground state lying below a doublet at 81(1) K and a quasi-triplet at 152(2) K. The ρ(T) data indicate a metallic behavior, and ρ(H) exhibits a very high positive magnetoresistance, as high as ~300% in 9 T at 2 K. No long range magnetic order or spin-glass behavior was detected in a μSR experiment down to 1.2 K.

Low-field superconducting phase of (TMTSF)2ClO4

The low-field phase of the organic superconductor (TMTSF)(2)ClO(4) is studied by muon-spin rotation. The zero temperature limit of the magnetic penetration depth within the TMTSF layers is obtained to be λ(ab)(0) = 0.86(2) μm. Temperature dependence of the muon-spin relaxation shows no indication of gap nodes on the Fermi surface nor of any spontaneous fields due to time-reversal-symmetry breaking. The weight of evidence suggests that the symmetry of this low-field phase is odd-frequency p-wave singlet, a novel example of odd-frequency pairing in a bulk superconductor.

Nonunitary triplet pairing in the centrosymmetric superconductor LaNiGa2

Muon spin rotation and relaxation experiments on the centrosymmetric intermetallic superconductor LaNiGa2 are reported. The appearance of spontaneous magnetic fields coincides with the onset of superconductivity, implying that the superconducting state breaks time reversal symmetry, similarly to noncentrosymmetric LaNiC2. Only four triplet states are compatible with this observation, all of which are nonunitary triplets. This suggests that LaNiGa2 is the centrosymmetric analogue of LaNiC2. We argue that these materials are representatives of a new family of paramagnetic nonunitary superconductors.