Multipole Superconductivity in Nonsymmorphic Sr_{2}IrO_{4}

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.

Effects of the on-site energy on the electronic response of Sr3(Ir1−xMnx)2O7

We investigated the doping and temperature evolutions of the optical response of Sr3(Ir1−xMnx)2O7 single crystals with 0 ≤ x ≤ 0.36 by utilizing infrared spectroscopy. Substitution of 3d transition metal Mn ions into Sr3Ir2O7 is expected to induce an insulator-to-metal transition via the decrease in the magnitude of the spin–orbit coupling and the hole doping. In sharp contrast, our data reveal the resilience of the spin–orbit coupling and the incoherent character of the charge transport. Upon Mn substitution, an incoherent in-gap excitation at about 0.25 eV appeared with the decrease in the strength of the optical transitions between the effective total angular momentum Jeff bands of the Ir ions. The resonance energies of the optical transitions between the Jeff bands which are directly proportional to the magnitude of the spin–orbit coupling hardly varied. In addition to these evolutions of the low-energy response, Mn substitution led to the emergence of a distinct high-energy optical excitation at about 1.2 eV which is larger than the resonance energies of the optical transitions between the Jeff bands. This observation indicates that the Mn 3d states are located away from the Ir 5d states in energy and that the large difference in the on-site energies of the transition metal ions is responsible for the incoherent charge transport and the robustness of the spin–orbit coupling. The effect of Mn substitution was also registered in the temperature dependence of the electronic response. The anomaly in the optical response of the parent compound observed at the antiferromagnetic transition temperature is notably suppressed in the Mn-doped compounds despite the persistence of the long-range antiferromagnetic ordering. The suppression of the spin-charge coupling could be related to charge disproportionation of the Ir ions.

Magnetic topological quantum chemistry

For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids - Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states.

Odd-Parity Spin-Triplet Superconductivity in Centrosymmetric Antiferromagnetic Metals

We propose a route to achieve odd-parity spin-triplet (OPST) superconductivity in metallic collinear antiferromagnets with inversion symmetry. Owing to the existence of hidden antiunitary symmetry, which we call the effective time-reversal symmetry (eTRS), the Fermi surfaces of ordinary antiferromagnetic metals are generally spin degenerate, and spin-singlet pairing is favored. However, by introducing a local inversion symmetry breaking perturbation that also breaks the eTRS, we can lift the degeneracy to obtain spin-polarized Fermi surfaces. In the weak-coupling limit, the spin-polarized Fermi surfaces constrain the electrons to form spin-triplet Cooper pairs with odd parity. Interestingly, all the odd-parity superconducting ground states we obtained host nontrivial band topologies manifested as chiral topological superconductors, second-order topological superconductors, and nodal superconductors. We propose that double perovskite oxides with collinear antiferromagnetic or ferrimagnetic ordering, such as SrLaVMoO_{6}, are promising candidate systems where our theoretical ideas can be applied to.

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.

The Jeff = 1/2 Antiferromagnet Sr2 IrO4 : A Golden Avenue toward New Physics and Functions

Iridates have been providing a fertile ground for studying emergent phases of matter that arise from the delicate interplay of various fundamental interactions with approximate energy scale. Among these highly focused quantum materials, the perovskite Sr₂ IrO₄ , which belongs to the Ruddlesden-Popper series, stands out and has been intensively addressed in the last decade, since it hosts a novel J_eff = 1/2 state that is a profound manifestation of strong spin-orbit coupling. Moreover, the J_eff = 1/2 state represents a rare example of iridates that is better understood both theoretically and experimentally. Here, Sr₂ IrO₄ is taken as an example to review the recent advances of the J_eff = 1/2 state in two aspects: materials fundamentals and functionality potentials. In the fundamentals part, the basic issues for the layered canted antiferromagnetic order of the J_eff = 1/2 magnetic moments in Sr₂ IrO₄ are illustrated, and then the progress of the antiferromagnetic order modulation through diverse routes is highlighted. Subsequently, for the functionality potentials, fascinating properties such as atomic-scale giant magnetoresistance, anisotropic magnetoresistance, and nonvolatile memory, are addressed. To conclude, prospective remarks and an outlook are given.

Insulator-Metal Transition and Topological Superconductivity in UTe_{2} from a First-Principles Calculation

We theoretically study superconductivity in UTe_{2}, which is a recently discovered strong candidate for an odd-parity spin-triplet superconductor. Theoretical studies for this compound faced difficulty because first-principles calculations predict an insulating electronic state, incompatible with superconducting instability. To overcome this problem, we take into account electron correlation effects by a GGA+U method and show the insulator-metal transition by Coulomb interaction. Using Fermi surfaces obtained as a function of U, we clarify topological properties of possible superconducting states. Fermi surface formulas for the three-dimensional winding number and three two-dimensional Z_{2} numbers indicate topological superconductivity at an intermediate U for all the odd-parity pairing symmetry in the Immm space group. Symmetry and topology of superconducting gap nodes are analyzed and the gap structure of UTe_{2} is predicted. Topologically protected low-energy excitations are highlighted, and experiments by bulk and surface probes are proposed to link Fermi surfaces and pairing symmetry. Based on the results, we also discuss multiple superconducting phases under magnetic fields, which were implied by recent experiments.

Electric Toroidal Quadrupoles in the Spin-Orbit-Coupled Metal Cd_{2}Re_{2}O_{7}

We report our theoretical results on the order parameters for the pyrochlore metal Cd_{2}Re_{2}O_{7}, which undergoes enigmatic phase transitions with inversion symmetry breaking. By carefully examining active electronic degrees of freedom based on the lattice symmetry, we propose that two parity-breaking phases at ambient pressure are described by unconventional multipoles, electric toroidal quadrupoles (ETQs) with different components, x^{2}-y^{2} and 3z^{2}-r^{2}, in the pyrochlore tetrahedral unit. We elucidate that the ETQs are activated by bond or spin-current order on Re─Re bonds. Our ETQ scenario provides a key to reconciling the experimental contradictions, by measuring ETQ specific phenomena, such as peculiar spin splittings in the electronic band structure, magnetocurrent effect, and nonreciprocal transport under a magnetic field.