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

Evidence of striped electronic phases in a structurally modulated superlattice

The electronic properties of crystals can be manipulated by superimposing spatially periodic electric, magnetic or structural modulations. Long-wavelength modulations incommensurate with the atomic lattice are particularly interesting1, exemplified by recent advances in two-dimensional (2D) moiré materials2,3. Bulk van der Waals (vdW) superlattices4-8 hosting 2D interfaces between minimally disordered layers represent scalable bulk analogues of artificial vdW heterostructures and present a complementary venue to explore incommensurately modulated 2D states. Here we report the bulk vdW superlattice SrTa2S5 realizing an incommensurate one-dimensional (1D) structural modulation of 2D transition metal dichalcogenide (TMD) H-TaS2 layers. High-quality electronic transport in the H-TaS2 layers, evidenced by quantum oscillations, is made anisotropic by the modulation and exhibits commensurability oscillations paralleling lithographically modulated 2D systems9-11. We also find unconventional, clean-limit superconductivity in SrTa2S5 with a pronounced suppression of interlayer relative to intralayer coherence. The in-plane magnetic field dependence of interlayer critical current, together with electron diffraction from the structural modulation, suggests superconductivity12-14 in SrTa2S5 is spatially modulated and mismatched between adjacent TMD layers. With phenomenology suggestive of pair-density wave superconductivity15-17, SrTa2S5 may present a pathway for microscopic evaluation of this unconventional order18-21. More broadly, SrTa2S5 establishes bulk vdW superlattices as versatile platforms to address long-standing predictions surrounding modulated electronic phases in the form of nanoscale vdW devices12,13 to macroscopic crystals22,23.

Magnetic parity violation and parity-time-reversal-symmetric magnets

Parity-time-reversal symmetry (PTsymmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T), is a fundamental concept of physics and characterizes the functionality of materials as well asPandTsymmetries. In particular, thePT-symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leavesPTsymmetry intact, the simultaneous violation ofPandTsymmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagneticP-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

Link between supercurrent diode and anomalous Josephson effect revealed by gate-controlled interferometry

In Josephson diodes the asymmetry between positive and negative current branch of the current-phase relation leads to a polarity-dependent critical current and Josephson inductance. The supercurrent nonreciprocity can be described as a consequence of the anomalous Josephson effect -a φ0-shift of the current-phase relation- in multichannel ballistic junctions with strong spin-orbit interaction. In this work, we simultaneously investigate φ0-shift and supercurrent diode efficiency on the same Josephson junction by means of a superconducting quantum interferometer. By electrostatic gating, we reveal a direct link between φ0-shift and diode effect. Our findings show that spin-orbit interaction in combination with a Zeeman field plays an important role in determining the magnetochiral anisotropy and the supercurrent diode effect.

Physical properties of newly synthesized noncentrosymmetric TaIr2B2 and NbIr2B2 superconductors: an extensive comparison of GGA and LDA functional investigations

In recent years, noncentrosymmetric (NCS) structural compounds have received much attention from the scientific community in the exploration for the unconventional nature of superconductivity with exciting physical properties. This study uses the comprehensive generalized gradient approximation (GGA) and local density approximation (LDA) to gain insights into the physical properties of two recently synthesized Ir-based NCS superconductors, TaIr2B2 and NbIr2B2. The structural parameters, mechanical performance, electronic structure, Debye temperature, melting temperature, electronic specific heat, and electron-phonon coupling constant of TaIr2B2 and NbIr2B2 are explored and discussed in detail. Density functional theory (DFT) optimized structural parameters of both NCS phases agree well with experimental observation. Both GGA and LDA calculations show that the compounds are ductile, machinable, mechanically stable, and anisotropic in nature. The elastic moduli and hardness calculations reveal that TaIr2B2 is harder than NbIr2B2. The calculation of the melting temperature reveals that TaIr2B2 is more suitable for high temperature technology applications compared to NbIr2B2. Both GGA and LDA functionals reveal that the optical functions are very similar. Both compounds display a significant amount of reflectivity spectra over a wide range of photon energies. The GGA functional reveals a somewhat higher density of states value compared to that of LDA. The present calculated values of the electron-phonon coupling constant of both compounds are consistent with values previously reported from experimental studies.

Fermi Surface Spin Texture and Topological Superconductivity in Spin-Orbit Free Noncollinear Antiferromagnets

We explore the relationship among the magnetic ordering in real space, the resulting spin texture on the Fermi surface, and the related superconducting gap structure in noncollinear antiferromagnetic metals without spin-orbit coupling. Via a perturbative approach, we show that noncollinear magnetic ordering in a metal can generate momentum-dependent spin texture on its Fermi surface, even in the absence of spin-orbit coupling, if the metal has more than three sublattices in its magnetic unit cell. Thus, our theory naturally extends the idea of altermagnetism to noncollinear spin structures. When superconductivity is developed in a magnetic metal, as the gap-opening condition is strongly constrained by the spin texture, the nodal structure of the superconducting state is also enforced by the magnetism-induced spin texture. Taking the noncollinear antiferromagnet on the kagome lattice as a representative example, we demonstrate how the Fermi surface spin texture induced by noncollinear antiferromagnetism naturally leads to odd-parity spin-triplet superconductivity with nontrivial topological properties.

Evidence for a finite-momentum Cooper pair in tricolor d-wave superconducting superlattices

Fermionic superfluidity with a nontrivial Cooper-pairing, beyond the conventional Bardeen-Cooper-Schrieffer state, is a captivating field of study in quantum many-body systems. In particular, the search for superconducting states with finite-momentum pairs has long been a challenge, but establishing its existence has long suffered from the lack of an appropriate probe to reveal its momentum. Recently, it has been proposed that the nonreciprocal electron transport is the most powerful probe for the finite-momentum pairs, because it directly couples to the supercurrents. Here we reveal such a pairing state by the non-reciprocal transport on tricolor superlattices with strong spin-orbit coupling combined with broken inversion-symmetry consisting of atomically thin d-wave superconductor CeCoIn5. We find that while the second-harmonic resistance exhibits a distinct dip anomaly at the low-temperature (T)/high-magnetic field (H) corner in the HT-plane for H applied to the antinodal direction of the d-wave gap, such an anomaly is absent for H along the nodal direction. By carefully isolating extrinsic effects due to vortex dynamics, we reveal the presence of a non-reciprocal response originating from intrinsic superconducting properties characterized by finite-momentum pairs. We attribute the high-field state to the helical superconducting state, wherein the phase of the order parameter is spontaneously spatially modulated.

Engineering Symmetry Breaking in Twisted MoS2-MoSe2 Heterostructures for Optimal Thermoelectric Performance

Engineering symmetry breaking in thermoelectric materials holds promise for achieving an optimal thermoelectric efficiency. van der Waals (vdW) layered transition metal dichalcogenides (TMDCs) provide critical opportunities for manipulating the intrinsic symmetry through in-plane symmetry breaking interlayer twists and out-of-plane symmetry breaking heterostructures. Herein, the symmetry-dependent thermoelectric properties of MoS2 and MoSe2 obtained via first-principles calculations are reported, yielding an advanced ZT of 2.96 at 700 K. The underlying mechanisms reveal that the in-plane symmetry breaking results in a lowest thermal conductivity of 1.96 W·m-1·K-1. Additionally, the electric properties can be significantly modulated through band flattening and bandgap alteration, stemming directly from the modified interlayer electronic coupling strength owing to spatial repulsion effects. In addition, out-of-plane symmetry breaking induces band splitting, leading to a decrease in the degeneracy and complex band structures. Consequently, the power factor experiences a notable enhancement from ∼1.32 to 1.71 × 10-2 W·m-1·K-2, which is attributed to the intricate spatial configuration of charge densities and the resulting intensified intralayer electronic coupling. Upon simultaneous implementation of in-plane and out-of-plane symmetry breaking, the TMDCs exhibit an indirect bandgap to direct bandgap transition compared to the pristine structure. This work demonstrates an avenue for optimizing thermoelectric performance of TMDCs through the implementation of symmetry breaking.

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.

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.

Reentrance of interface superconductivity in a high-Tc cuprate heterostructure

Increasing the carrier density in a Mott insulator by chemical doping gives rise to a generic superconducting dome in high temperature superconductors. An intriguing question is whether a second superconducting dome may exist at higher dopings. Here we heavily overdope La2-xSrxCuO4 (0.45 ≤ x ≤ 1.0) and discover an unprecedented reentrance of interface superconductivity in La2-xSrxCuO4 /La2CuO4 heterostructures. As x increases, the superconductivity is weakened and completely fades away at x = 0.8; but it revives at higher doping and fully recovers at x = 1.0. This is shown to be correlated with the suppression of the interfacial charge transfer around x = 0.8 and the weak-to-strong localization crossover in the La2-xSrxCuO4 layer. We further construct a theoretical model to account for the sophisticated relation between charge localization and interfacial charge transfer. Our work advances both the search for and control of new superconducting heterostructures.

Revealing the Hidden Spin-Polarized Bands in a Superconducting Tl Bilayer Crystal

The interplay of spin-orbit coupling and crystal symmetry can generate spin-polarized bands in materials only a few atomic layers thick, potentially leading to unprecedented physical properties. In the case of bilayer materials with global inversion symmetry, locally broken inversion symmetry can generate degenerate spin-polarized bands, in which the spins in each layer are oppositely polarized. Here, we demonstrate that the hidden spins in a Tl bilayer crystal are revealed by growing it on Ag(111) of sizable lattice mismatch, together with the appearance of a remarkable phenomenon unique to centrosymmetric hidden-spin bilayer crystals: a novel band splitting in both spin and space. The key to success in observing this novel splitting is that the interaction at the interface has just the right strength: it does not destroy the original wave functions of the Tl bilayer but is strong enough to induce an energy separation.

Topological Superconductors from a Materials Perspective

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

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.

Microscopic Imaging Homogeneous and Single Phase Superfluid Density in UTe_{2}

Odd-parity superconductor UTe_{2} shows spontaneous time-reversal symmetry breaking and multiple superconducting phases, which imply chiral superconductivity, but only in a subset of samples. Here we microscopically observe a homogeneous superfluid density n_{s} on the surface of UTe_{2} and an enhanced superconducting transition temperature near the edges. We also detect vortex-antivortex pairs even at zero magnetic field, indicating the existence of a hidden internal field. The temperature dependence of n_{s}, determined independent of sample geometry, does not support point nodes along the b axis for a quasi-2D Fermi surface and provides no evidence for multiple phase transitions in UTe_{2}.

Controlling Dzyaloshinskii-Moriya interaction in a centrosymmetric nonsymmorphic crystal

Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking P4/nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions.

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.

Local inversion-symmetry breaking in a bismuthate high-Tc superconductor

The doped perovskite BaBiO₃ exhibits a maximum superconducting transition temperature (T_c) of 34 K and was the first high-T_c oxide to be discovered, yet pivotal questions regarding the nature of both the metallic and superconducting states remain unresolved. Although it is generally thought that superconductivity in the bismuthates is of the conventional s-wave type, the pairing mechanism is still debated, with strong electron-phonon coupling and bismuth valence or bond disproportionation possibly playing a role. Here we use diffuse x-ray scattering and Monte Carlo modeling to study the local structure of Ba_1-xK_xBiO₃ across its insulator-metal boundary. We find no evidence for either long- or short-range disproportionation, which resolves a major conundrum, as disproportionation and the related polaronic effects are likely not relevant for the metallic and superconducting states. Instead, we uncover nanoscale structural correlations that break inversion symmetry, with far-reaching implications for the electronic physics. This unexpected finding furthermore establishes that the bismuthates belong to the broader classes of materials with hidden spin-orbit coupling and a tendency towards inversion-breaking displacements.

Trimorphic TaCrP – A diffraction and 31P solid state NMR spectroscopic study

The metal-rich phosphide TaCrP forms from the elements by step-wise solid state reaction in an alumina crucible (maximum annealing temperature 1180 K). TaCrP is trimorphic. The structural data of the hexagonal ZrNiAl high-temperature phase (space group P 6 ‾ 2 m $P\overline{6}2m$ ) was deduced from a Rietveld refinement. At room temperature TaCrP crystallizes with the TiNiSi type (Pnma, a = 623.86(5), b = 349.12(3), c = 736.78(6) pm, wR = 0.0419, 401 F 2 values, 20 variables) and shows a Peierls type transition below ca. 280 K to the monoclinic low-temperature modification (P121/c1, a = 630.09(3), b = 740.3(4), c = 928.94(4) pm, β = 132.589(5)°, wR = 0.0580, 1378 F 2 values, 57 variables). The latter phase transition is driven by pairwise Cr–Cr bond formation out of an equidistant chain in o-TaCrP. The phase transition was monitored via different analytical tools: differential scanning calorimetry, powder synchrotron X-ray diffraction, magnetic susceptibility measurements and 31P solid state NMR spectroscopy.

Theoretical Study of Dynamical and Electronic Properties of Noncentrosymmetric Superconductor NbReSi

The noncentrosymmetric NbReSi superconductor with Tc≃6.5 K is characterized by the relatively large upper critical magnetic field. Its multigap features were observed experimentally. Recent studies suggested the realization of P6¯2m or Ima2 symmetry. We discuss the dynamical properties of both symmetries (e.g., phonon spectra). In this paper, using the ab initio techniques, we clarify this ambiguity, and conclude that the Ima2 symmetry is unstable, and P6¯2m should be realized. The P6¯2m symmetry is also stable in the presence of external hydrostatic pressure. We show that NbReSi with the P6¯2m symmetry should host phonon surface states for (100) and (110) surfaces. Additionally, we discuss the main electronic properties of the system with the stable symmetry.

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.

Machine Learning-Guided Discovery of Ternary Compounds Containing La, P, and Group 14 Elements

We integrate a deep machine learning (ML) method with first-principles calculations to efficiently search for the energetically favorable ternary compounds. Using La-Si-P as a prototype system, we demonstrate that ML-guided first-principles calculations can efficiently explore crystal structures and their relative energetic stabilities, thus greatly accelerate the pace of material discovery. A number of new La-Si-P ternary compounds with formation energies less than 30 meV/atom above the known ternary convex hull are discovered. Among them, the formation energies of La₅SiP₃ and La₂SiP phases are only 2 and 10 meV/atom, respectively, above the convex hull. These two compounds are dynamically stable with no imaginary phonon modes. Moreover, by replacing Si with heavier-group 14 elements in the eight lowest-energy La-Si-P structures from our ML-guided predictions, a number of low-energy La-X-P phases (X = Ge, Sn, Pb) are predicted.

Nodeless superconductivity in topologically nontrivial materials HfRuP and ZrRuAs

Topologically nontrivial electronic states are recently found in a family of noncentrosymmetric transition metal pnictidesTRuX(T=Zr, Hf;X=P, As), presenting a unique platform for superconductivity to interplay with topological electronic states and asymmetric spin-orbit coupling. Here, we investigate the superconducting order parameter of HfRuP and ZrRuAs by measuring the magnetic penetration depth changeΔλ(T)using a method based on the tunnel-diode oscillator. Both compounds show clear exponential temperature dependence inΔλ(T)at low temperatures, suggesting fully-gapped superconductivity. Moreover, the superfluid densities in both HfRuP and ZrRuAs can be reasonably described by ans-wave superconducting model.

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.

Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate

Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the on-site term is paramount. Recently, the onset of superconductivity at 4.7 K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial to yield triplet pairing, which is f-wave (p-wave) for moderate (higher) hole doping. In light of persisting challenges to tailor triplet pairing in an electronic material, our finding promises to pave unprecedented ways for engineering unconventional triplet superconductivity.

Unconventional superconductivity in UTe2

The novel spin-triplet superconductor candidate UTe₂was discovered only recently at the end of 2018 and already attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe₂is a heavy-fermion paramagnet, but following the discovery of superconductivity, it has been expected to be close to a ferromagnetic instability, showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. This view might be too simplistic. The competition between different types of magnetic interactions and the duality between the local and itinerant character of the 5fUranium electrons, as well as the shift of the U valence appear as key parameters in the rich phase diagrams discovered recently under extreme conditions like low temperature, high magnetic field, and pressure. We discuss macroscopic and microscopic experiments at low temperature to clarify the normal phase properties at ambient pressure for field applied along the three axis of this orthorhombic structure. Special attention will be given to the occurrence of a metamagnetic transition atH_m= 35 T for a magnetic field applied along the hard magnetic axisb. Adding external pressure leads to strong changes in the magnetic and electronic properties with a direct feedback on superconductivity. Attention is paid on the possible evolution of the Fermi surface as a function of magnetic field and pressure. Superconductivity in UTe₂is extremely rich, exhibiting various unconventional behaviors which will be highlighted. It shows an exceptionally huge superconducting upper critical field with a re-entrant behavior under magnetic field and the occurrence of multiple superconducting phases in the temperature-field-pressure phase diagrams. There is evidence for spin-triplet pairing. Experimental indications exist for chiral superconductivity and spontaneous time reversal symmetry breaking in the superconducting state. Different theoretical approaches will be described. Notably we discuss that UTe₂is a possible example for the realization of a fascinating topological superconductor. Exploring superconductivity in UTe₂reemphasizes that U-based heavy fermion compounds give unique examples to study and understand the strong interplay between the normal and superconducting properties in strongly correlated electron systems.

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.

Intrinsic Superconducting Diode Effect

Stimulated by the recent experiment [F. Ando et al., Nature (London) 584, 373 (2020).NATUAS0028-083610.1038/s41586-020-2590-4], we propose an intrinsic mechanism to cause the superconducting diode effect (SDE). SDE refers to the nonreciprocity of the critical current for the metal-superconductor transition. Among various mechanisms for the critical current, the depairing current is known to be intrinsic to each material and has recently been observed in several superconducting systems. We clarify the temperature scaling of the nonreciprocal depairing current near the critical temperature and point out its significant enhancement at low temperatures. It is also found that the nonreciprocal critical current shows sign reversals upon increasing the magnetic field. These behaviors are understood by the nonreciprocity of the Landau critical momentum and the change in the nature of the helical superconductivity. The intrinsic SDE unveils the rich phase diagram and functionalities of noncentrosymmetric superconductors.

Superconductivity and topologically nontrivial states in noncentrosymmetric XVSe2 (X = Pb, Sn): a first-principles study

Noncentrosymmetric superconductors are strong candidates for exploring intrinsic topological superconductivity. Here, we predict two new noncentrosymmetric superconductors SnVSe₂ and PbVSe₂ by a systematic first-principles study. These two compounds show good thermal and dynamic stabilities. Moreover, the band topology of both compounds is predicted to be nontrivial via Z₂ calculation and slab models. We also investigate the electron-phonon interactions in SnVSe₂ and PbVSe₂, indicating the T_c of SnVSe₂ and PbVSe₂ without external pressure are predicted to be ∼1.18 K and ∼0.22 K, respectively. Furthermore, the results on pressure engineering in PbVSe₂ imply that the T_c of PbVSe₂ can be tuned to 2.39 K for enhanced contributions from Pb layers under pressure up to 6.4 GPa. This work may provide new platforms for probing spin-triplet paring and may help with designing and developing new metal-intercalated transition metal dichalcogenides.

Antiperovskite Superconductor LaPd3P with Noncentrosymmetric Cubic Structure

Antiperovskites are a promising candidate structure for the exploration of new materials. We discovered an antiperovskite phosphide, LaPd₃P, following our recent synthesis of APd₃P (A = Ca, Sr, Ba). While APd₃P and (Ca,Sr)Pd₃P were found to be tetragonal or orthorhombic systems, LaPd₃P is a new prototype cubic system (a = 9.0317(1) Å) with a noncentrosymmetric space group (I4̅3m). LaPd₃P exhibited superconductivity with a transition temperature (T_c) of 0.28 K. The upper critical field, Debye temperature, and Sommerfeld constant (γ) were determined to be 0.305(8) kOe, 267(1) K, and 6.06(4) mJ mol^-1 K^-2 f.u.^-1, respectively. We performed first-principles electronic band structure calculations for LaPd₃P and compared the theoretical and experimental results. The calculated Sommerfeld constant (2.24 mJ mol^-1 K^-2 f.u.^-1) was much smaller than the experimental value of γ because the Fermi energy (E_F) was located slightly below the density of states (DOS) pseudogap. This difference was explained by the increase in the DOS at E_F due to the approximately 5 atom % La deficiency (hole doping) in the sample. The observed T_c value was much lower than that estimated using the Bardeen-Cooper-Schrieffer equation. To explain the discrepancy, we examined the possibility of an unconventional superconductivity in LaPd₃P arising from the lack of space inversion symmetry.

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.

Signatures of bosonic Landau levels in a finite-momentum superconductor

Charged particles subjected to magnetic fields form Landau levels (LLs). Originally studied in the context of electrons in metals¹, fermionic LLs continue to attract interest as hosts of exotic electronic phenomena^2,3. Bosonic LLs are also expected to realize novel quantum phenomena^4,5, but, apart from recent advances in synthetic systems^6,7, they remain relatively unexplored. Cooper pairs in superconductors-composite bosons formed by electrons-represent a potential condensed-matter platform for bosonic LLs. Under certain conditions, an applied magnetic field is expected to stabilize an unusual superconductor with finite-momentum Cooper pairs^8,9 and exert control over bosonic LLs^10-13. Here we report thermodynamic signatures, observed by torque magnetometry, of bosonic LL transitions in the layered superconductor Ba₆Nb₁₁S₂₈. By applying an in-plane magnetic field, we observe an abrupt, partial suppression of diamagnetism below the upper critical magnetic field, which is suggestive of an emergent phase within the superconducting state. With increasing out-of-plane magnetic field, we observe a series of sharp modulations in the upper critical magnetic field that are indicative of distinct vortex states and with a structure that agrees with predictions for Cooper pair LL transitions in a finite-momentum superconductor^10-14. By applying Onsager's quantization rule¹⁵, we extract the momentum. Furthermore, study of the fermionic LLs shows evidence for a non-zero Berry phase. This suggests opportunities to study bosonic LLs, topological superconductivity, and their interplay via transport¹⁶, scattering¹⁷, scanning probe¹⁸ and exfoliation techniques¹⁹.

DFT-Guided Crystal Structure Redetermination and Lattice Dynamics of the Intermetallic Actinoid Compound UIr

UIr has been discussed as a rare example of a noncentrosymmetric, ferromagnetic superconductor crystallizing in the acentric PdBi structure type (P2₁, mP16). Here we present a new structure model for UIr. By means of single-crystal and powder X-ray diffraction we find UIr to crystallize in the centrosymmetric space group P2₁/c, in line with previous ab initio calculations. The discrepancy with the previous noncentrosymmetric model in space group P2₁ is explained by the occurrence of twinning. The observed twinning hints toward a high-temperature displacive phase transition of UIr to the CrB structure type (Cmcm, oS8): we discuss the lattice dynamics corresponding to this transition by crystallographic symmetry mode analysis and by density functional theory (DFT). We find that spin-orbit coupling is essential to understand this phase transition. We apply our theoretical considerations for a critical judgment of the structure models of UPt and NpIr that have been reported to crystallize isotypically with UIr. We confirm that UPt is isotypic to UIr (P2₁/c), whereas we predict NpIr to crystallize in the CrB structure type. Our report on the centrosymmetric crystal structure of UIr has an effect on all those theoretical models that investigated potentially novel superconducting coupling mechanisms of this compound on the basis of the noncentrosymmetric structure model.

Role of Two-Dimensional Ising Superconductivity in the Nonequilibrium Quasiparticle Spin-to-Charge Conversion Efficiency

Nonequilibrium studies of two-dimensional (2D) superconductors (SCs) with Ising spin-orbit coupling are prerequisite for their successful application to equilibrium spin-triplet Cooper pairs and, potentially, Majorana Fermions. By taking advantage of the recent discoveries of 2D SCs and their compatibility with any other materials, we fabricate here nonlocal magnon devices to examine how such 2D Ising superconductivity affects the conversion efficiency of magnon spin to quasiparticle charge in superconducting flakes of 2H-NbSe₂ transferred onto ferrimagnetic insulating Y₃Fe₅O₁₂. Comparison with a reference device based on a conventionally paired superconductor shows that the Y₃Fe₅O₁₂-induced in-plane (IP) exchange spin-splitting in the NbSe₂ flake is hindered by its inherent out-of-plane (OOP) spin-orbit field, which, in turn, limits the transition-state enhancement of the spin-to-charge conversion efficiency. Our out-of-equilibrium study highlights the significance of symmetry matching between underlying Cooper pairs and exchange-induced spin-splitting for the giant transition-state spin-to-charge conversion and may have implications toward proximity-engineered spin-polarized triplet pairing via tuning the relative strength of IP exchange and OOP spin-orbit fields in ferromagnetic insulator/2D Ising SC bilayers.

Unconventional supercurrent phase in Ising superconductor Josephson junction with atomically thin magnetic insulator

In two-dimensional (2D) NbSe₂ crystal, which lacks inversion symmetry, strong spin-orbit coupling aligns the spins of Cooper pairs to the orbital valleys, forming Ising Cooper pairs (ICPs). The unusual spin texture of ICPs can be further modulated by introducing magnetic exchange. Here, we report unconventional supercurrent phase in van der Waals heterostructure Josephson junctions (JJs) that couples NbSe₂ ICPs across an atomically thin magnetic insulator (MI) Cr₂Ge₂Te₆. By constructing a superconducting quantum interference device (SQUID), we measure the phase of the transferred Cooper pairs in the MI JJ. We demonstrate a doubly degenerate nontrivial JJ phase (ϕ), formed by momentum-conserving tunneling of ICPs across magnetic domains in the barrier. The doubly degenerate ground states in MI JJs provide a two-level quantum system that can be utilized as a new dissipationless component for superconducting quantum devices. Our work boosts the study of various superconducting states with spin-orbit coupling, opening up an avenue to designing new superconducting phase-controlled quantum electronic devices.

Van der Waals structures provide a new platform to explore novel physics of superconductor/ferromagnet interfaces. Here, NbSe₂ Josephson junction with Cr₂Ge₂Te₆ enables non-trivial Josephson phase by spin-dependent interaction, boosting the study of superconducting states with spin-orbit coupling and phase-controlled quantum electronic device.

Field-induced transition within the superconducting state of CeRh2As2

Materials with multiple superconducting phases are rare. Here, we report the discovery of two-phase unconventional superconductivity in CeRh₂As₂ Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 tesla, even though the transition temperature is only 0.26 kelvin. Furthermore, a transition between two different superconducting phases is observed in a c axis magnetic field. Local inversion-symmetry breaking at the cerium sites enables Rashba spin-orbit coupling alternating between the cerium sublayers. The staggered Rashba coupling introduces a layer degree of freedom to which the field-induced transition and high critical field seen in experiment are likely related.

Interplay between ferroelectricity and metallicity in BaTiO3

We explore the interplay between ferroelectricity and metallicity, which are generally considered to be contra-indicated properties, in the prototypical ferroelectric barium titanate, BaTiO₃. Using first-principles density functional theory, we calculate the effects of electron and hole doping, first by introducing a hypothetical background charge, and second through the introduction of explicit impurities (La, Nb and V for electron doping, and K, Al and Sc for hole doping). We find that, apart from a surprising increase in polarization at small hole concentrations, both charge-carrier types decrease the tendency towards ferroelectricity, with the strength of the polarization suppression, which is different for electrons and holes, determined by the detailed structure of the conduction and valence bands. Doping with impurity atoms increases the complexity and allows us to identify three factors that influence the ferroelectricity: structural effects arising largely from the size of the impurity ion, electronic effects from the introduction of charge carriers, and changes in unit-cell volume and shape. A competing balance between these contributions can result in an increase or decrease in ferroelectricity with doping.

Reversible engineering of spin-orbit splitting in monolayer MoS2via laser irradiation under controlled gas atmospheres

Monolayer transition metal dichalcogenides, manifesting strong spin-orbit coupling combined with broken inversion symmetry, lead to coupling of spin and valley degrees of freedom. These unique features make them highly interesting for potential spintronic and valleytronic applications. However, engineering spin-orbit coupling at room temperature as demanded after device fabrication is still a great challenge for their practical applications. Here we reversibly engineer the spin-orbit coupling of monolayer MoS2 by laser irradiation under controlled gas environments, where the spin-orbit splitting has been effectively regulated within 140 meV to 200 meV. Furthermore, the photoluminescence intensity of the B exciton can be reversibly manipulated over 2 orders of magnitude. We attribute the engineering of spin-orbit splitting to the reduction of binding energy combined with band renormalization, originating from the enhanced absorption coefficient of monolayer MoS2 under inert gases and subsequently the significantly boosted carrier concentrations. Reflectance contrast spectra during the engineering stages provide unambiguous proof to support our interpretation. Our approach offers a new avenue to actively control the spin-orbit splitting in transition metal dichalcogenide materials at room temperature and paves the way for designing innovative spintronic devices.

Growth, electronic structure and superconductivity of ultrathin epitaxial CoSi2films

We report growth, electronic structure and superconductivity of ultrathin epitaxial CoSi₂films on Si (111). At low coverages, preferred islands with 2, 5 and 6 monolayers height develop, which agrees well with the surface energy calculation. We observe clear quantum well states as a result of electronic confinement and their dispersion agrees well with density functional theory calculations, indicating weak correlation effect despite strong contributions from Co 3delectrons.Ex situtransport measurements show that superconductivity persists down to at least 10 monolayers, with reducedT_cbut largely enhanced upper critical field. Our study opens up the opportunity to study the interplay between quantum confinement, interfacial symmetry breaking and superconductivity in an epitaxial silicide film, which is technologically relevant in microelectronics.

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.

Discovery of Real-Space Topological Ferroelectricity in Metallic Transition Metal Phosphides

Ferroelectric metals-with coexisting ferroelectricity and structural asymmetry-challenge traditional perceptions because free electrons screen electrostatic forces between ions, the driving force of breaking the spatial inversion symmetry. Despite ferroelectric metals having been unveiled one after another, topologically switchable polar objects with metallicity have never been identified so far. Here, the discovery of real-space topological ferroelectricity in metallic and non-centrosymmetric Ni₂ P is reported. Protected by the rotation-inversion symmetry operation, it is found that the balanced polarity of alternately stacked polyhedra couples intimately with elemental valence states, which are verified using quantitative electron energy-loss spectroscopy. First-principles calculations reveal that an applied in-plane compressive strain creates a tunable bilinear double-well potential and reverses the polyhedral polarity on a unit-cell scale. The dual roles of nickel cations, including polar displacement inside polyhedral cages and a 3D bonding network, facilitate the coexistence of topological polarity with metallicity. In addition, the switchable in-plane polyhedral polarity gives rise to a spin-orbit-coupling-induced spin texture with large momentum-dependent spin splitting. These findings point out a new direction for exploring valence-polarity-spin correlative interactions via topological ferroelectricity in metallic systems with structural asymmetry.

Orbital Angular Momentum Induced Spin Polarization of 2D Metallic Bands

The electrons in 2D systems with broken inversion symmetry are spin-polarized due to spin-orbit coupling and provide perfect targets for observing exotic spin-related fundamental phenomena. We observe a Fermi surface with a novel spin texture in the 2D metallic system formed by indium double layers on Si(111) and find that the primary origin of the spin-polarized electronic states of this system is the orbital angular momentum and not the so-called Rashba effect. The present results deepen the understanding of the physics arising from spin-orbit coupling in atomic-layered materials with consequences for spintronic devices and the physics of the superconducting state.

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.

Clean 2D superconductivity in a bulk van der Waals superlattice

Advances in low-dimensional superconductivity are often realized through improvements in material quality. Apart from a small group of organic materials, there is a near absence of clean-limit two-dimensional (2D) superconductors, which presents an impediment to the pursuit of numerous long-standing predictions for exotic superconductivity with fragile pairing symmetries. We developed a bulk superlattice consisting of the transition metal dichalcogenide (TMD) superconductor 2H-niobium disulfide (2H-NbS2) and a commensurate block layer that yields enhanced two-dimensionality, high electronic quality, and clean-limit inorganic 2D superconductivity. The structure of this material may naturally be extended to generate a distinct family of 2D superconductors, topological insulators, and excitonic systems based on TMDs with improved material properties.

Polar Nanodomains in a Ferroelectric Superconductor

The mechanisms by which itinerant carriers compete with polar crystal distortions are a key unresolved issue for polar superconductors, which offer new routes to unconventional Cooper pairing. Strained, doped SrTiO₃ films undergo successive ferroelectric and superconducting transitions, making them ideal candidates to elucidate the nature of this competition. Here, we reveal these interactions using scanning transmission electron microscopy studies of the evolution of polar nanodomains as a function of doping. These nanodomains are a precursor to the ferroelectric phase and a measure of long-range Coulomb interactions. With increasing doping, the magnitude of the polar displacements, the nanodomain size, and the Curie temperature are systematically suppressed. In addition, we show that disorder caused by the dopant atoms themselves presents a second contribution to the destabilization of the ferroelectric state. The results provide evidence for two distinct mechanisms that suppress the polar transition with doping in a ferroelectric superconductor.

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.

In Search of Chiral Molecular Superconductors: κ-[(S,S)-DM-BEDT-TTF]2 ClO4 Revisited

The relationship between chirality and superconductivity is an intriguing question. The two enantiomeric crystalline radical cation salts κ-[(S,S)-DM-BEDT-TTF]₂ ClO₄ and κ-[(R,R)-DM-BEDT-TTF]₂ ClO₄ , showing κ-type arrangement of the organic layers, are investigated in search for superconducting chiral molecular materials following a 1992 report indicating the occurrence of a superconducting transition in the former compound. While the initial interpretation is presently challenged through in-depth temperature and pressure dependent single crystal resistivity measurements combined with band structure calculations, the two chiral conductors show metal like behavior with room temperature conductivities of 10-30 S cm^-1 at ambient pressure and stabilization of the metallic state down to the lowest temperatures under moderate pressures. Moreover, their structural and theoretical investigations reveal an original feature, namely the existence of two different κ layers with 1D and 2D electronic dimensionality, respectively, as a consequence of an interlayer charge transfer. The resistivity drop observed for one sample below 1 K and insensitive to magnetic field, possibly results from mixing in-plane and out-of-plane contributions to the measured resistance and suggests current induced charge order melting. This feature contradicts the occurrence of superconductivity in these chiral molecular conductors and leaves open the discovery of the first chiral molecular superconductors.

Observation of superconducting diode effect

Nonlinear optical and electrical effects associated with a lack of spatial inversion symmetry allow direction-selective propagation and transport of quantum particles, such as photons¹ and electrons^2-9. The most common example of such nonreciprocal phenomena is a semiconductor diode with a p-n junction, with a low resistance in one direction and a high resistance in the other. Although the diode effect forms the basis of numerous electronic components, such as rectifiers, alternating-direct-current converters and photodetectors, it introduces an inevitable energy loss due to the finite resistance. Therefore, a worthwhile goal is to realize a superconducting diode that has zero resistance in only one direction. Here we demonstrate a magnetically controllable superconducting diode in an artificial superlattice [Nb/V/Ta]_n without a centre of inversion. The nonreciprocal resistance versus current curve at the superconducting-to-normal transition was clearly observed by a direct-current measurement, and the difference of the critical current is considered to be related to the magnetochiral anisotropy caused by breaking of the spatial-inversion and time-reversal symmetries^10-13. Owing to the nonreciprocal critical current, the [Nb/V/Ta]_n superlattice exhibits zero resistance in only one direction. This superconducting diode effect enables phase-coherent and direction-selective charge transport, paving the way for the construction of non-dissipative electronic circuits.