Field-induced transition within the superconducting state of CeRh2As2

Connecting High-Field and High-Pressure Superconductivity in UTe_{2}

The existence of multiple superconducting phases induced by either pressure or magnetic field is one of the most striking features of superconductivity of UTe_{2}, among the many unusual superconducting properties of this system. Here we report thermodynamic measurements of the superconducting phase diagram combining pressure and magnetic fields up to 30 T. We show that the high-field superconducting phase at ambient pressure continuously evolves under pressure into the zero-field high-temperature superconducting phase, which occurs above 0.2 GPa.

Multiphase superconductivity in PdBi2

Unconventional superconductivity, where electron pairing does not involve electron-phonon interactions, is often attributed to magnetic correlations in a material. Well known examples include high-Tc cuprates and uranium-based heavy fermion superconductors. Less explored are unconventional superconductors with strong spin-orbit coupling, where interactions between spin-polarised electrons and external magnetic field can result in multiple superconducting phases and field-induced transitions between them, a rare phenomenon in the superconducting state. Here we report a magnetic-field driven phase transition in β-PdBi2, a layered non-magnetic superconductor. Our tunnelling spectroscopy on thin PdBi2 monocrystals incorporated in planar superconductor-insulator-normal metal junctions reveals a marked discontinuity in the superconducting properties with increasing in-plane field, which is consistent with a transition from conventional (s-wave) to nodal pairing. Our theoretical analysis suggests that this phase transition may arise from spin polarisation and spin-momentum locking caused by locally broken inversion symmetry, with p-wave pairing becoming energetically favourable in high fields. Our findings also reconcile earlier predictions of unconventional multigap superconductivity in β-PdBi2 with previous experiments where only a single s-wave gap could be detected.

Quasi-Two-Dimensional Antiferromagnetic Spin Fluctuations in the Spin-Triplet Superconductor Candidate CeRh_{2}As_{2}

The tetragonal heavy-fermion superconductor CeRh_{2}As_{2} (T_{c}=0.3  K) exhibits an exceptionally high critical field of 14 T for B∥c. It undergoes a field-driven first-order phase transition between superconducting states, potentially transitioning from spin-singlet to spin-triplet superconductivity. To further understand these superconducting states and the role of magnetism, we probe spin fluctuations in CeRh_{2}As_{2} using neutron scattering. We find dynamic (π,π) antiferromagnetic (AFM) spin correlations with an anisotropic quasi-two-dimensional correlation volume. Our data place an upper limit of 0.31  μ_{B} on the staggered magnetization of corresponding Néel orders at T=0.08  K. Density functional theory calculations, treating Ce 4f electrons as core states, show that the AFM wave vector connects significant areas of the Fermi surface. Our findings indicate that the dominant excitations in CeRh_{2}As_{2} for ℏω<1.2  meV are magnetic and suggest that superconductivity in CeRh_{2}As_{2} is mediated by AFM spin fluctuations associated with a proximate quantum critical point.

Pressure-Tuned Quantum Criticality in the Locally Noncentrosymmetric Superconductor CeRh_{2}As_{2}

The unconventional superconductor CeRh_{2}As_{2} (critical temperature T_{c}≈0.4  K) displays an exceptionally rare magnetic-field-induced transition between two distinct superconducting (SC) phases, proposed to be states of even and odd parity of the SC order parameter, which are enabled by a locally noncentrosymmetric structure. The superconductivity is preceded by a phase transition of unknown origin at T_{0}=0.5  K. Electronic low-temperature properties of CeRh_{2}As_{2} show pronounced non-Fermi-liquid behavior, indicative of a proximity to a quantum critical point (QCP). The role of quantum fluctuations and normal state orders for the superconductivity in a system with staggered Rashba interaction is currently an open question, pertinent to explaining the occurrence of the two-phase superconductivity. In this work, using measurements of resistivity and specific heat under hydrostatic pressure, we show that the T_{0} order vanishes completely at a modest pressure of P_{0}≈0.5  GPa, revealing a QCP. In line with the quantum criticality picture, the linear temperature dependence of the resistivity at P_{0} evolves into a Fermi-liquid quadratic dependence as quantum critical fluctuations are suppressed by increasing pressure. Furthermore, the domelike behavior of T_{c} around P_{0} implies that the fluctuations of the T_{0} order are involved in the SC pairing mechanism.

Evidences for local non-centrosymmetricity and strong phonon anomaly in EuCu2As2: a Raman spectroscopy and lattice dynamics study

Phonon modes and their association with the electronic states have been investigated for the metallic EuCu2As2system. In this work, we present the Raman spectra of this pnictide system which clearly shows the presence of seven well defined peaks above 100 cm-1that is consistent with the locally non-centrosymmetricP4/nmmcrystal structure, contrary to that what is expected from the accepted symmorphicI4/mmmstructure. Lattice dynamics calculations using theP4/nmmsymmetry attest that there is a commendable agreement between the calculated phonon spectra at the Γ point and the observed Raman mode frequencies, with the most intense peak at∼232 cm-1being ascribed to the A1gmode. Temperature dependent Raman measurements show that there is a significant deviation from the expected anharmonic behaviour around 165 K for the A1gmode, with anomalies being observed for several other modes as well, although to a lesser extent. Attempts are made to rationalize the observed anomalous behavior related to the hardening of the phonon modes, with parallels being drawn from metal dichalcogenide and allied systems. Similarities in the evolution of the Raman peak frequencies with temperature seem to suggest a strong signature of a subtle electronic density wave instability below 165 K in this compound.

Discovery of Magnetic Phase Transitions in Heavy-Fermion Superconductor CeRh_{2}As_{2}

We report on the specific heat studies performed on a new generation of CeRh_{2}As_{2} single crystals. Superior quality of the samples and dedicated experimental protocol allowed us to observe an antiferromagneticlike behavior in the normal state and to detect the first-order phase transition of magnetic origin within the superconducting state of the compound. Although in the available literature the physical behavior of CeRh_{2}As_{2} is most often described with the use of quadrupole density wave scenario, we propose an alternative explanation using analogies to antiferromagnetic heavy-fermion superconductors CeRhIn_{5} and Ce_{2}RhIn_{8}.

Horizontal flux growth as an efficient preparation method of CeRh2As2 single crystals

We report an efficient method to obtain CeRh2As2 single crystals with the use of a bismuth flux growth method in a horizontal configuration. Based on our numerous attempts, we found this technique to be scalable and repeatable. The crystals thus obtained are characterized by much sharper phase transitions and distinctly higher characteristic temperatures Tc and T0, compared to previous reports. Moreover, based on our specific heat studies of the obtained single crystals, we also indicate a clear connection between both transition temperatures.

Spectroscopic Evidence of Kondo-Induced Quasiquartet in CeRh_{2}As_{2}

CeRh_{2}As_{2} is a new multiphase superconductor with strong suggestions for an additional itinerant multipolar ordered phase. The modeling of the low-temperature properties of this heavy-fermion compound requires a quartet Ce^{3+} crystal-field ground state. Here, we provide the evidence for the formation of such a quartet state using x-ray spectroscopy. Core-level photoelectron and x-ray absorption spectroscopy confirm the presence of Kondo hybridization in CeRh_{2}As_{2}. The temperature dependence of the linear dichroism unambiguously reveals the impact of Kondo physics for coupling the Kramer's doublets into an effective quasiquartet. Nonresonant inelastic x-ray scattering data find that the |Γ_{7}^{-}⟩ state with its lobes along the 110 direction of the tetragonal structure (xy orientation) contributes most to the multiorbital ground state of CeRh_{2}As_{2}.

Unequivocal Identification of Spin-Triplet and Spin-Singlet Superconductors with Upper Critical Field and Flux Quantization

Spin-triplet superconductors play central roles in Majorana physics and quantum computing but are difficult to identify. We show the methods of kink-point upper critical field and flux quantization in superconducting rings can unequivocally identify spin-singlet, spin-triplet in centrosymmetric superconductors, and singlet-triplet admixture in noncentrosymmetric superconductors, as realized in γ-BiPd, β-Bi_{2}Pd, and α-BiPd, respectively. Our findings are essential for identifying triplet superconductors and exploring their quantum properties.

Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors

Majorana excitations are the quasiparticle analog of Majorana fermions in solid materials. Typical examples are the Majorana zero modes (MZMs) and the dispersing Majorana modes. When probed by scanning tunneling spectroscopy, the former manifest as a pronounced conductance peak locating precisely at zero-energy, while the latter behaves as constant or slowly varying density of states. The MZMs obey non-abelian statistics and are believed to be building blocks for topological quantum computing, which is highly immune to the environmental noise. Existing MZM platforms include hybrid structures such as topological insulator, semiconducting nanowire or 1D atomic chains on top of a conventional superconductor, and single materials such as the iron-based superconductors (IBSs) and 4Hb-TaS2. Very recently, ordered and tunable MZM lattice has also been realized in IBS LiFeAs, providing a scalable and applicable platform for future topological quantum computation. In this review, we present an overview of the recent local probe studies on MZMs. Classified by the material platforms, we start with the MZMs in the iron-chalcogenide superconductors where FeTe0.55Se0.45and (Li0.84Fe0.16)OHFeSe will be discussed. We then review the Majorana research in the iron-pnictide superconductors as well as other platforms beyond the IBSs. We further review recent works on ordered and tunable MZM lattice, showing that strain is a feasible tool to tune the topological superconductivity. Finally, we give our summary and perspective on future Majorana research.

Superconducting spin reorientation in spin-triplet multiple superconducting phases of UTe2

Superconducting (SC) state has spin and orbital degrees of freedom, and spin-triplet superconductivity shows multiple SC phases because of the presence of these degrees of freedom. However, the observation of spin-direction rotation occurring inside the SC state (SC spin rotation) has hardly been reported. Uranium ditelluride, a recently found topological superconductor, exhibits various SC phases under pressure: SC state at ambient pressure (SC1), high-temperature SC state above 0.5 gigapascal (SC2), and low-temperature SC state above 0.5 gigapascal (SC3). We performed nuclear magnetic resonance (NMR) and ac susceptibility measurements on a single-crystal uranium ditelluride. The b axis spin susceptibility remains unchanged in SC2, unlike in SC1, and decreases below the SC2-SC3 transition with spin modulation. These unique properties in SC3 arise from the coexistence of two SC order parameters. Our NMR results confirm spin-triplet superconductivity with SC spin parallel to b axis in SC2 and unveil the remaining of spin degrees of freedom in SC uranium ditelluride.

Superconductivity beyond the Conventional Pauli Limit in High-Pressure CeSb_{2}

We report the discovery of superconductivity at a pressure-induced magnetic quantum phase transition in the Kondo lattice system CeSb_{2}, sustained up to magnetic fields that exceed the conventional Pauli limit eightfold. Like CeRh_{2}As_{2}, CeSb_{2} is locally noncentrosymmetric around the Ce site, but the evolution of critical fields and normal state properties as CeSb_{2} is tuned through the quantum phase transition motivates a fundamentally different explanation for its resilience to applied field.

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.

Parity Transition of Spin-Singlet Superconductivity Using Sublattice Degrees of Freedom

Recently, a superconducting (SC) transition from low-field (LF) to high-field (HF) SC states was reported in CeRh_{2}As_{2}, indicating the existence of multiple SC states. It has been theoretically noted that the existence of two Ce sites in the unit cell, the so-called sublattice degrees of freedom owing to the local inversion symmetry breaking at the Ce sites, can lead to the appearance of multiple SC phases even under an interaction inducing spin-singlet superconductivity. CeRh_{2}As_{2} is considered as the first example of multiple SC phases owing to this sublattice degree of freedom. However, microscopic information about the SC states has not yet been reported. In this study, we measured the SC spin susceptibility at two crystallographically inequivalent As sites using nuclear magnetic resonance for various magnetic fields. Our experimental results strongly indicate a spin-singlet state in both SC phases. In addition, the antiferromagnetic phase, which appears within the SC phase, only coexists with the LF SC phase; there is no sign of magnetic ordering in the HF SC phase. The present Letter reveals unique SC properties originating from the locally noncentrosymmetric characteristics.

Triplet Pairing Mechanisms from Hund's-Kondo Models: Applications to UTe_{2} and CeRh_{2}As_{2}

Observing that several U and Ce based candidate triplet superconductors share a common structural motif, with pairs of magnetic atoms separated by an inversion center, we hypothesize a triplet pairing mechanism based on an interplay of Hund's and Kondo interactions that is unique to this structure. In the presence of Hund's interactions, valence fluctuations generate a triplet superexchange between electrons and local moments. The offset from the center of symmetry allows spin-triplet pairs formed by the resulting Kondo effect to delocalize onto the Fermi surface, precipitating superconductivity. We demonstrate this mechanism within a minimal two-channel Kondo lattice model and present support for this pairing mechanism from existing experiments.

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.

Electronic landscape of the f-electron intermetallics with the ThCr2Si2 structure

Although strongly correlated f-electron systems are well known as reservoirs for quantum phenomena, a persistent challenge is to design specific states. What is often missing are simple ways to determine whether a given compound can be expected to exhibit certain behaviors and what tuning vector(s) would be useful to select the ground state. In this review, we address this question by aggregating information about Ce, Eu, Yb, and U compounds with the ThCr2Si2 structure. We construct electronic/magnetic state maps that are parameterized in terms of unit cell volumes and d-shell filling, which reveals useful trends including that (i) the magnetic and nonmagnetic examples are well separated, and (ii) the crossover regions harbor the examples with exotic states. These insights are used to propose structural/chemical regions of interest in these and related materials, with the goal of accelerating discovery of the next generation of f-electron quantum materials.

Investigating the A n+1B n X3n+1 Homologous Series: A New Platform for Studying Magnetic Praseodymium Based Intermetallics

The recent discovery of the A _n+1B _n X_3n+1 (A = lanthanide, B = transition metal, X = tetrel) homologous series provides a new platform to study the structure-property relationships of highly correlated electron systems. Several members of Ce _n+1Co _n Ge_3n+1 (n = 1, 4, 5, 6, and ∞) show evidence of heavy electron behavior with complex magnetic interactions. While the Ce analogues have been investigated, only n = 1, 2, and ∞ of Pr _n+1Co _n Ge_3n+1 have been synthesized, with n = 1 and 2 showing a nonsinglet magnetic ground state. The Pr analogues can provide a platform for direct comparison of highly correlated behavior. In this perspective, we discuss the impetus for synthesizing the Pr _n+1Co _n Ge_3n+1 members and present the structural characterization of the n = 3 and n = 4 members. We lay the foundation for future investigations of the Pr _n+1Co _n Ge_3n+1 family of compounds and highlight the importance of complementary methods to characterize new quantum materials.

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.

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.

Observation of Antiferromagnetic Order as Odd-Parity Multipoles inside the Superconducting Phase in CeRh_{2}As_{2}

Spatial inversion symmetry in crystal structures is closely related to the superconducting (SC) and magnetic properties of materials. Recently, several theoretical proposals that predict various interesting phenomena caused by the breaking of the local inversion symmetry have been presented. However, experimental validation has not yet progressed owing to the lack of model materials. Here we present evidence for antiferromagnetic (AFM) order in CeRh_{2}As_{2} (SC transition temperature T_{SC}∼0.37  K), wherein the Ce site breaks the local inversion symmetry. The evidence is based on the observation of different extents of broadening of the nuclear quadrupole resonance spectrum at two crystallographically inequivalent As sites. This AFM ordering breaks the inversion symmetry of this system, resulting in the activation of an odd-parity magnetic multipole. Moreover, the onset of antiferromagnetism T_{N} within an SC phase, with T_{N}<T_{SC}, is quite unusual in systems wherein superconductivity coexists or competes with magnetism. Our observations show that CeRh_{2}As_{2} is a promising system to study how the absence of local inversion symmetry induces or influences unconventional magnetic and SC states, as well as their interaction.

Extremely high upper critical field in BiCh2-based (Ch: S and Se) layered superconductor LaO0.5F0.5BiS2-xSex (x = 0.22 and 0.69)

Centrosymmetric compounds with local inversion symmetry breaking have tremendously interesting and intriguing physical properties. In this study, we focus on a BiCh₂-based (Ch: S, Se) layered superconductor, as a system with local inversion asymmetry, because spin polarisation based on the Rashba–Dresselhaus-type spin–orbit coupling has been observed in centrosymmetric BiCh₂-based LaOBiS₂ systems, while the BiCh₂ layer lacks local inversion symmetry. Herein, we report the existence of extremely high in-plane upper critical fields in the BiCh₂-based system LaO_0.5F_0.5BiS_2−xSe_x (x = 0.22 and 0.69). The superconducting states are not completely suppressed by the applied magnetic fields with strengths up to 55 T. Thus, we consider that the in-plane upper critical field is enhanced by the local inversion symmetry breaking and its layered structure. Our study will open a new pathway for the discovery of superconductors that exhibit a high upper critical field by focusing on the local inversion symmetry breaking.

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.