Antisymmetric Spin-orbit Coupling Research Articles

Low-Temperature Chiral Crystal Structure and Superconductivity in (Pt0.2Ir0.8)3Zr5.

We report the observation of superconductivity in (Pt0.2Ir0.8)3Zr5 with a chiral space group (P6122) at low temperatures. The bulk nature of the superconductivity at a transition temperature of 2.2 K was confirmed using specific heat measurements. We revealed that (Pt0.2Ir0.8)3Zr5 obeys the weak-coupling Bardeen-Cooper-Schrieffer model, and the dominant mechanism in the upper critical field is the orbital pair-breaking limit rather than the Pauli-Clogston limit. This indicates that the antisymmetric spin-orbit coupling caused by the chiral crystal structure does not significantly affect the superconductivity of (Pt0.2Ir0.8)3Zr5.

Fully gapped superconductivity and topological aspects of the noncentrosymmetric superconductor TaReSi

We report a study of the noncentrosymmetric TaReSi superconductor by means of the muon-spin rotation and relaxation $(\ensuremath{\mu}\mathrm{SR})$ technique, complemented by electronic band-structure calculations. Its superconductivity, with ${T}_{c}=5.5\phantom{\rule{0.28em}{0ex}}\text{K}$ and upper critical field ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}2}(0)\ensuremath{\sim}3.4\phantom{\rule{0.28em}{0ex}}\text{T}$, was characterized via electrical-resistivity and magnetic-susceptibility measurements. The temperature-dependent superfluid density, obtained from transverse-field $\ensuremath{\mu}\mathrm{SR}$, suggests a fully gapped superconducting state in TaReSi, with an energy gap ${\mathrm{\ensuremath{\Delta}}}_{0}=0.79\phantom{\rule{0.28em}{0ex}}\text{meV}$ and a magnetic penetration depth ${\ensuremath{\lambda}}_{0}=562\phantom{\rule{0.28em}{0ex}}\text{nm}$. The absence of a spontaneous magnetization below ${T}_{c}$, as confirmed by zero-field $\ensuremath{\mu}\mathrm{SR}$, indicates a preserved time-reversal symmetry in the superconducting state. The density of states near the Fermi level is dominated by the Ta- and Re-$5d$ orbitals, which account for the relatively large band splitting due to the antisymmetric spin-orbit coupling. In its normal state, TaReSi behaves as a three-dimensional Kramers nodal-line semimetal, characterized by an hourglass-shaped dispersion protected by glide reflection. By combining nontrivial electronic bands with intrinsic superconductivity, TaReSi is a promising material for investigating the topological aspects of noncentrosymmetric superconductors.

Spin-singlet topological superconductivity in the attractive Rashba-Hubbard model

Fully gapped, spin-singlet superconductors with antisymmetric spin-orbit coupling in a Zeeman magnetic field provide a promising route to realize superconducting states with non-Abelian topological order and therefore fault-tolerant quantum computation. Here we use a quantum Monte Carlo dynamical cluster approximation to study the superconducting properties of a doped two-dimensional attractive Hubbard model with Rashba spin-orbit coupling in a Zeeman magnetic field. We generally find that the Rashba coupling has a beneficial effect towards $s$-wave superconductivity. In the presence of a finite Zeeman field, when superconductivity is suppressed by Pauli pair breaking, the Rashba coupling counteracts the spin imbalance created by the Zeeman field by mixing the spins, and thus restores superconductivity at finite temperatures. We show that this favorable effect of the spin-orbit coupling is traced to a spin-flip driven enhancement of the amplitude for the propagation of a pair of electrons in time-reversed states. Moreover, by inspecting the Fermi surface of the interacting model, we show that for sufficiently large Rashba coupling and Zeeman field, the superconducting state is expected to be topologically nontrivial.

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.

Nodeless superconductivity in the noncentrosymmetric compound ThIrSi

ThIrSi is a noncentrosymmetric superconductor, where the presence of the heavy element Th results in a strong antisymmetric spin-orbit coupling (ASOC). A strong ASOC causes the splitting of the Fermi surface and may lead to unconventional triplet superconductivity or to multiband superconductivity. By combining $\ensuremath{\mu}$SR, NMR, and magnetometry measurements, the authors show here that, despite the strong ASOC, ThIrSi exhibits only nodeless superconductivity, most likely of multiband nature.

Superconducting diode effect and nonreciprocal transition lines

Nonreciprocity in superconductors is attracting much interest owing to its fundamental importance as well as the potential applicability to engineering. In this paper, we generalize the previous theories of the intrinsic superconducting diode effect (SDE) and microscopically elucidate its relationship with the nonreciprocity of the transition lines under supercurrent. We derive a general formula for the intrinsic SDE by using the phenomenological Ginzburg-Landau theory and thereby show that the SDE is determined by the relative angle between the magnetic field and an effective anti-symmetric spin-orbit coupling defined from the Ginzburg-Landau coefficients. The obtained formula offers a convenient criterion to obtain a finite SDE. We also study the SDE and the nonreciprocal phase transitions of the $s$-wave and $d$-wave superconductors by using the mean-field theory. It is established that the sign reversal of the SDE accompanied by the crossover of the helical superconductivity is a general feature irrespective of the system details. We study the phase transition lines in the temperature-magnetic-field phase diagram under the supercurrent, and clarify that the sign reversal of the SDE generally accompanies the crossings of the transition lines under positive and negative current directions. Furthermore, the superconducting phases under the supercurrent even become re-entrant under moderate strength of the electric current, implying the current-induced first-order phase transitions. Our findings establish the electric current as the control parameter and the powerful probe to study the superconducting properties related to the finite-momentum Cooper pairs.

Topological Superconductivity Based on Antisymmetric Spin-Orbit Coupling.

Topological superconductivity (TSC) has drawn much attention for its fundamental interest and application in quantum computation. An outstanding challenge is the lack of intrinsic TSC materials with a p-wave pairing gap, which has led to the development of an effective p-wave theory of coupling s-wave gap with Rashba spin-orbit coupling (RSOC). However, the RSOC-strict mechanism and materials pose still both fundamental and practical limitations. Here, we generalize this theory to antisymmetric SOC (ASOC). Using k·p perturbation theory, we demonstrate that 2D crystals, with point groups of C2, C4, C6, C2v, C4v, C6v, D2, D4, D6, S4, or D2d, can all facilitate the desired ASOC. Remarkably, this enables us to discover 314 TSC candidates by screening 2D material databases, which are further confirmed by first-principles calculations of Majorana boundary modes and the topological invariant of the superconducting gap. Our work fundamentally enriches TSC theory and greatly expands the classes of TSC materials for experimental exploration.

La4TX (T = Ru, Rh, Ir; X = Al, In): A family of noncentrosymmetric superconductors with tunable antisymmetric spin-orbit coupling

We report the discovery of superconductivity in a series of noncentrosymmetric compounds La$_4$$TX$ ($T$ = Ru, Rh, Ir; $X$ = Al, In), which have a cubic crystal structure with space group $F\bar{4}3m$. La$_4$RuAl, La$_4$RhAl, La$_4$IrAl, La$_4$RuIn and La$_4$IrIn exhibit bulk superconducting transitions with critical temperatures $T_c$ of 1.77 K, 3.05 K, 1.54 K, 0.58 K and 0.93 K, respectively. The specific heat of the La$_4$$T$Al compounds are consistent with an $s$-wave model with a fully open superconducting gap. In all cases, the upper critical fields are well described by the Werthamer-Helfand-Hohenberg model, and the values are well below the Pauli limit, indicating that orbital limiting is the dominant pair-breaking mechanism. Density functional theory (DFT) calculations reveal that the degree of band splitting by the antisymmetric spin-orbit coupling (ASOC) shows considerable variation between the different compounds. This indicates that the strength of the ASOC is highly tunable across this series of superconductors, suggesting that these are good candidates for examining the relationship between the ASOC and superconducting properties in 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 fields µ 0H(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 () 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 (/k B T 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.

Pressure-induced superconductivity in the noncentrosymmetric Weyl semimetals LaAlX (X=Si,Ge)

In topological materials, Dirac fermions can split into two Weyl fermions with opposite chiralities due to the breaking of space-inversion symmetry, while in noncentrosymmetric superconductors, novel superconducting electron pairing mechanisms arise because of the antisymmetric spin-orbit coupling. In this work, we report the pressure-introduced superconductivity in a typical noncentrosymmetric Weyl semimetal $\mathrm{LaAl}X$ ($X=\mathrm{Si}$ and Ge). Superconductivity was observed at around 65 GPa without structural phase transition. A typical dome-shape phase diagram is obtained with the maximum ${T}_{\mathrm{c}}$ of 2.5 K (2.1 K) for LaAlSi (LaAlGe). Furthermore, the application of pressure does not destroy the nontrivial band topology of LaAlSi up to 80.4 GPa, making such materials potential candidates for realizing topological superconductivity. Our report of superconductivity in $\mathrm{LaAl}X$ ($X=\mathrm{Si}$ and Ge) will provide critical insight in noncentrosymmetric superconductors and stimulate further study on superconductivity in Weyl semimetals.

The upper critical field in the BiCh2-based superconductors CeOBiS1.7Se0.3 and PrO0.5F0.5BiS2-x Se x (x = 0, 0.3)

We report the upper critical field (B c2) in the BiCh2-based superconductors CeOBiS1.7Se0.3 and PrO0.5F0.5BiS2-x Se x (x = 0, 0.3). Single crystals of CeOBiS1.7Se0.3 and PrO0.5F0.5BiS2-x Se x (x = 0, 0.3) were grown using the flux method. Single-crystal structural analysis revealed that the crystal structure at room temperature is tetragonal (P4/nmm). Through electrical resistivity and magnetization measurements, bulk superconductivity was observed in all samples. For CeOBiS1.7Se0.3, the in-plane B c2 is smaller than the conventional orbital limit and Pauli limit, suggesting that ferromagnetic ordering, which has been observed in a related Ce-containing BiCh2-based compound, affects B c2 and superconductivity. In contrast, high in-plane B c2 was observed for PrO0.5F0.5BiS2-x Se x (x = 0, 0.3). We propose that the in-plane B c2 is enhanced by antisymmetric spin–orbit coupling, which arises from the lack of local inversion symmetry.

Superconductivity in noncentrosymmetric NbReSi investigated by muon spin rotation and relaxation

Noncentrosymmetric materials are promising paradigm to explore unconventional superconductivity. In particular, several Re containing noncentrosymmetric materials have attracted considerable attention due to a superconducting state with a broken time reversal symmetry. A comprehensive study on the superconducting ground state of NbReSi was investigated using magnetization, resistivity, and muon spin rotation/relaxation measurements. Zero field muon spectroscopy results showed the absence of any spontaneous magnetic field below the superconducting transition temperature, T$ _{c} $ = 6.29 K, indicating the preserved time-reversal symmetry. Transverse field muon spin rotation measurements confirms a s-wave nature of the sample with $\Delta(0)/k_{B}T_{c} $ = 1.726. This study urges further investigation on more noncentrosymmetric materials to elucidate the selective appearance of unconventional nature and unveil its dependence on antisymmetric spin-orbit coupling strength.

NbReSi: A noncentrosymetric superconductor with large upper critical field

We report the discovery of superconductivity in noncentrosymmetric NbReSi, which crystallizes in a hexagonal ZrNiAl-type crystal structure with space group $P\bar{6}2m$ (No.~189). Bulk superconductivity, with $T_c$ = 6.5 K was characterized via electrical-resistivity, magnetization, and heat-capacity measurements. The low-temperature electronic specific heat suggests a fully gapped superconducting state in NbReSi, while a large upper critical field of $\mu_0H_\mathrm{c2}(0)$ $\sim$ 12.6 T is obtained, which is comparable to the weak-coupling Pauli limit. The electronic band-structure calculations show that the density of states at the Fermi level are dominated by Re and Nb $d$-orbitals, with a sizeable band splitting induced by the antisymmetric spin-orbit coupling. NbReSi represents another candidate material for revealing the puzzle of time-reversal symmetry breaking observed in some Re-based superconductors and its relation to the lack of inversion symmetry.

Fully gapped superconductivity with preserved time-reversal symmetry in noncentrosymmetric LaPdIn

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 emergence of magnetic fields in the superconducting state, indicating that time-reversal symmetry is preserved. Band structure calculations reveal that there is a relatively weak effect of antisymmetric spin-orbit coupling on the electronic bands near the Fermi level, which is consistent with there being negligible singlet-triplet mixing due to broken inversion symmetry. On the other hand, isostructural LuPdIn and LaPtIn do not exhibit superconductivity down to 0.4 K, which may be due to these systems having a smaller density of states at the Fermi level.

Multigap superconductivity in centrosymmetric and noncentrosymmetric rhenium-boron superconductors

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 ($\mu$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 $\mu$SR) suggest a nodeless SC. Both compounds exhibit some features of multigap SC, as evidenced by temperature-dependent upper critical fields $H_\mathrm{c2}(T)$, as well as by electronic band-structure calculations. The absence of spontaneous magnetic fields below the onset of SC, as determined from zero-field $\mu$SR measurements, indicates a preserved time-reversal symmetry in the superconducting state of both Re$_3$B and Re$_7$B$_3$. Our results suggest that a lack of inversion symmetry and the accompanying antisymmetric spin-orbit coupling effects are not essential for the occurrence of multigap SC in these rhenium-boron compounds.

Spin and charge order in doped spin-orbit coupled Mott insulators

We study a two-dimensional single band Hubbard Hamiltonian with antisymmetric spin-orbit coupling. We argue that this is the minimal model to understand the electronic properties of locally non-centrosymmetric transition-metal (TM) oxides such as Sr$_2$IrO$_4$. Based on exact diagonalizations of small clusters and the random phase approximation, we investigate the correlation effects on charge and magnetic order as a function of doping and of the TM-oxygen-TM bond angle $\theta$. For small doping and $\theta$ $\lesssim$ $15^\circ$ we find dominant commensurate in-plane antiferromagnetic fluctuations while ferromagnetic fluctuations dominate for $\theta$ $\gtrsim$ $25^\circ$. Moderately strong nearest-neighbor Hubbard interactions can also stabilize a charge density wave order. Furthermore, we compare the dispersion of magnetic excitations for the hole-doped case to resonant inelastic X-ray scattering data and find good qualitative agreement.

Optical Hall response in spin-orbit coupled metals: Comparative study of magnetic cluster monopole, quadrupole, and toroidal orders

The optical Hall response is theoretically studied for spin-orbit coupled metals with ferroic orders of cluster-type magnetic multipoles. We find that different magnetic multipoles give rise to distinct spectra in the optical Hall conductivity. In the cases of monopole and quadrupole orders, the optical Hall response appears predominantly in high- and low-energy regions, which correspond to the energy scales of electron correlation and kinetic energy, respectively, while the response is dispersed and rather weak in the case of toroidal order. By decomposing the spectra into different interband contributions, we reveal selection rules stemming from the interplay between the antisymmetric spin-orbit coupling and the underlying multipoles. Our results suggest that the optical Hall measurement is useful to detect and distinguish the cluster-type magnetic multipole orders.

Spin-orbital polarization of Majorana edge states in oxide nanowires

We investigate a paradigmatic case of topological superconductivity in a one-dimensional nanowire with $d-$orbitals and a strong interplay of spin-orbital degrees of freedom due to the competition of orbital Rashba interaction, atomic spin-orbit coupling, and structural distortions. We demonstrate that the resulting electronic structure exhibits an orbital dependent magnetic anisotropy which affects the topological phase diagram and the character of the Majorana bound states (MBSs). The inspection of the electronic component of the MBSs reveals that the spin-orbital polarization generally occurs along the direction of the applied Zeeeman magnetic field, and transverse to the magnetic and orbital Rashba fields. The competition of symmetric and antisymmetric spin-orbit coupling remarkably leads to a misalignment of the spin and orbital moments transverse to the orbital Rashba fields, whose manifestation is essentially orbital dependent. The behavior of the spin-orbital polarization along the applied Zeeman field reflects the presence of multiple Fermi points with inequivalent orbital character in the normal state. Additionally, the response to variation of the electronic parameters related with the degree of spin-orbital entanglement leads to distinctive evolution of the spin-orbital polarization of the MBSs. These findings unveil novel paths to single-out hallmarks relevant for the experimental detection of MBSs.

Identification of spin-triplet superconductivity through a helical-chiral phase transition in Sr2RuO4 thin films

Despite much effort for over the two decades, the paring symmetry of a Sr$_2$RuO$_4$ superconductor has been still unclear. In this Rapid Communication, motivated by the recent rapid progress in fabrication techniques for Sr$_2$RuO$_4$ thin-films, we propose a promising strategy for identifying the spin-triplet superconductivity in the thin-film geometry by employing an antisymmetric spin-orbit coupling potential and a Zeeman potential due to an external magnetic field. We demonstrate that a spin-triplet superconducting thin-film undergoes a phase transition from a helical state to a chiral state by increasing the applied magnetic field. This phase transition is accompanied by a drastic change in the property of surface Andreev bound states. As a consequence, the helical-chiral phase transition, which is unique to the spin-triplet superconductors, can be detected through a sudden change in a tunneling conductance spectrum of a normal-metal/superconductor junction. Importantly, our proposal is constructed by combining fundamental and rigid concepts regarding physics of spin-triplet superconductivity.

Chirality-Induced Spin-Polarized State of a Chiral Crystal CrNb_{3}S_{6}.

Chirality-induced spin transport phenomena are investigated at room temperature without magnetic fields in a monoaxial chiral dichalcogenide CrNb_{3}S_{6}. We found that spin polarization occurs in these chiral bulk crystals under a charge current flowing along the principal c axis. Such phenomena are detected as an inverse spin Hall signal which is induced on the detection electrode that absorbs polarized spin from the chiral crystal. The inverse response is observed when applying the charge current into the detection electrode. The signal sign reverses in the device with the opposite chirality. Furthermore, the spin signals are found over micrometer length scales in a nonlocal configuration. Such a robust generation and protection of the spin-polarized state is discussed based on a one-dimensional model with an antisymmetric spin-orbit coupling.