Topological Phase Transitions in Multicomponent Superconductors

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.

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.

Supercurrent diode effect and finite-momentum superconductors

Our work shows a fascinating application of finite-momentum superconductivity, the supercurrent diode effect, which is being reported in a growing number of experiments. We show that, under external magnetic field, Cooper pairs can acquire finite momentum so that critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal.

When both inversion and time-reversal symmetries are broken, the critical current of a superconductor can be nonreciprocal. In this work, we show that, in certain classes of two-dimensional superconductors with antisymmetric spin–orbit coupling, Cooper pairs acquire a finite momentum upon the application of an in-plane magnetic field, and, as a result, critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal. This supercurrent diode effect is also manifested in the polarity dependence of in-plane critical fields induced by a supercurrent. These nonreciprocal effects may be found in polar SrTiO₃ film, few-layer MoTe₂ in the T_d phase, and twisted bilayer graphene in which the valley degree of freedom plays a role analogous to spin.

Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

The iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

Despite the discovery of Majorana zero modes (MZM) in iron-based superconductors, sample inhomogeneity may destroy MZMs during braiding. Here, authors observe MZM in impurity-assisted vortices due to tuning of the bulk Dirac fermions in a homogeneous superconductor LiFeAs.

Cavity-Mediated Unconventional Pairing in Ultracold Fermionic Atoms

We investigate long-range pairing interactions between ultracold fermionic atoms confined in an optical lattice which are mediated by the coupling to a cavity. In the absence of other perturbations, we find three degenerate pairing symmetries for a two-dimensional square lattice. By tuning a weak local atomic interaction via a Feshbach resonance or by tuning a weak magnetic field, the superfluid system can be driven from a topologically trivial s wave to topologically ordered, chiral superfluids containing Majorana edge states. Our work points out a novel path towards the creation of exotic superfluid states by exploiting the competition between long-range and short-range interactions.

Time-reversal symmetry-breaking in noncentrosymmetric superconductors

In this paper we examine the appearance of time-reversal symmetry-breaking (TRSB) states in the bulk and at the surface of a noncentrosymmetric superconductor. We utilize a Ginzburg-Landau theory, with coefficients derived from a microscopic model of the superconductor. We show that suppression of the triplet order parameter at the surface stabilizes a TRSB state by locally tuning the system into the bulk TRSB phase. We compare these results with those from centrosymmetric systems, and examine the appearance of a magnetization at the surface.

Evidence for Majorana bound states in an iron-based superconductor

The search for Majorana bound states (MBSs) has been fueled by the prospect of using their non-Abelian statistics for robust quantum computation. Two-dimensional superconducting topological materials have been predicted to host MBSs as zero-energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron-based superconductor FeTe_0.55Se_0.45, we observed a sharp zero-bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temperature, and tunneling barrier is consistent with the tunneling to a nearly pure MBS, separated from nontopological bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temperature.