Stimulated by the recent experiment [F. Ando et al., Nature 584, 373 (2020)], 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 tra
nsition. 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 crossover of the helical superconductivity. The intrinsic SDE unveils the rich phase diagram and functionalities of noncentrosymmetric superconductors.
Recent discovery of superconductivity in CeRh$_2$As$_2$ clarified an unusual $H$-$T$ phase diagram with two superconducting phases [Khim et al. arXiv:2101.09522]. The experimental observation has been interpreted based on the even-odd parity transiti
on characteristic of locally noncentrosymmetric superconductors. Indeed, the inversion symmetry is locally broken at the Ce site, and CeRh$_2$As$_2$ molds a new class of exotic superconductors. The low-temperature and high-field superconducting phase is a candidate for the odd-parity pair-density-wave state, suggesting a possibility of topological superconductivity as spin-triplet superconductors are. In this paper, we first derive the formula expressing the $mathbb{Z}_2$ invariant of glide symmetric and time-reversal symmetry broken superconductors by the number of Fermi surfaces on a glide invariant line. Next, we conduct a first-principles calculation for the electronic structure of CeRh$_2$As$_2$. Combining the results, we show that the field-induced odd-parity superconducting phase of CeRh$_2$As$_2$ is a platform of topological crystalline superconductivity protected by the nonsymmorphic glide symmetry and accompanied by boundary Majorana fermions.
The electronic nematic phase emerging with spontaneous rotation symmetry breaking is a central issue of modern condensed matter physics. In particular, various nematic phases in iron-based superconductors and high-$T_{rm c}$ cuprate superconductors a
re extensively studied recently. Electric quadrupole moments (EQMs) are one of the order parameters characterizing these nematic phases in a unified way, and elucidating EQMs is a key to understanding these nematic phases. However, the quantum-mechanical formulation of the EQMs in crystals is a nontrivial issue because the position operators are non-periodic and unbound. Recently, the EQMs have been formulated by local thermodynamics, and such {it thermodynamic EQMs} may be used to characterize the fourfold rotation symmetry breaking in materials. In this paper, we calculate the thermodynamic EQMs in iron-based superconductors LaFeAsO and FeSe as well as a cuprate superconductor La$_2$CuO$_4$ by a first-principles calculation. We show that owing to the orbital degeneracy the EQMs in iron-based superconductors are mainly determined by the geometric properties of wave functions. This result is in sharp contrast to the cuprate superconductor, in which the EQMs are dominated by distortion of the Fermi surface.
Higher-rank electric/magnetic multipole moments are attracting attention these days as candidate order parameters for exotic material phases. However, quantum-mechanical formulation of those multipole moments is still an ongoing issue. In this paper,
we propose a thermodynamic definition of electric quadrupole moments as a measure of symmetry breaking, following previous studies of orbital magnetic dipole moments and magnetic quadrupole moments. The obtained formulas are illustrated with a model of orbital-ordered nematic phases of iron-based superconductors.
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 a
n 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 $mathbb{Z}_2$ 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 node 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.
