Stripe order and diode effect in two-dimensional Rashba superconductors

In two-dimensional superconductors with a Rashba-type spin-orbit coupling, it is known that an in-plane magnetic field can induce a helical superconducting (SC) state with a phase modulation $e^{i {\bf q}\cdot {\bf r}}$. Here, we theoretically investigate the stability of a stripe order, a weight-biased superposition state composed of $+{\bf q}$ and $-{\bf q}$ modes taking the form of $\Delta_+ e^{i{\bf q}\cdot{\bf r}}+\Delta_- e^{-i{\bf q}\cdot{\bf r}}$ with $|\Delta_+|\neq|\Delta_-|\neq 0$, assuming that the spin-singlet pairing channel is dominant. Based on the Ginzburg-Landau theory, we show that for both s-wave and d-wave pairing symmetries, the stripe order can appear in the high-field and low-temperature region inside the helical phase and that the transition between the helical and stripe phases is of second order. It is noteworthy that for the d-wave pairing, the stability region of the stripe phase shrinks when the in-plane field is rotated from the nodal direction to the anti-nodal direction. It is also found that the nonreciprocity of the critical current, the so-called SC diode effect, emerges not only in the helical phase but also in the stripe phase, with no clear nonreciprocity anomaly at the helical-stripe transition due to its second-order nature.Comment: 11 pages, 8 figure

Little-Parks oscillation and d{\bf d}-vector texture in spin-triplet superconducting rings with bias current

We theoretically investigate the critical bias current $j_c$ for a superconducting (SC) ring in a magnetic field. Based on the Ginzburg-Landau theory, we show that $j_c$ exhibits a Little-Parks (LP) oscillation as a function of the magnetic flux passing through the ring, similarly to the LP oscillation in the SC transition temperature. It is also found that for a spin-triplet SC ring, the ${\bf d}$-vector rotates to yield a larger $j_c$, forming a texture along the circumference of the ring. Experimental implications of our result are discussed.Comment: 6 pages, 3 figure

Antiferromagnetic ordering induced by paramagnetic depairing in unconventional superconductors

Antiferromagnetic (AFM) (or spin-density wave) quantum critical fluctuation enhanced just below H_c2(0) have been often observed in d-wave superconductors with a strong Pauli paramagnetic depairing (PD) including CeCoIn_5. It is shown here that such a tendency of field-induced AFM ordering is a consequence of strong PD and should appear particularly in superconductors with a gap node along the AFM modulation. Two phenomena seen in CeCoIn_5, the anomalous vortex lattice form factor and the AFM order in the Fulde-Ferrell-Larkin-Ovchinnikov state, are explained based on this peculiar PD effect.Comment: 4 pages, 3 figures Title and text were changed. References are added. Resubmitted versio

Signatures of the Helical Phase in the Critical Fields at Twin Boundaries of Non-Centrosymmetric Superconductors

Domains in non-centrosymmetric materials represent regions of different crystal structure and spin-orbit coupling. Twin boundaries separating such domains display unusual properties in non-centrosymmetric superconductors (NCS), where magneto-electric effects influence the local lower and upper critical magnetic fields. As a model system, we investigate NCS with tetragonal crystal structure and Rashba spin-orbit coupling (RSOC), and with twin boundaries parallel to their basal planes. There, we report that there are two types of such twin boundaries which separate domains of opposite RSOC. In a magnetic field parallel to the basal plane, magneto-electric coupling between the spin polarization and supercurrents induces an effective magnetic field at these twin boundaries. We show this leads to unusual effects in such superconductors, and in particular to the modification of the upper and lower critical fields, in ways that depend on the type of twin boundary, as analyzed in detail, both analytically and numerically. Experimental implications of these effects are discussed.Comment: 10 pages, 6 figure

Zero-field miniature skyrmion crystal and chiral domain state in breathing-kagome antiferromagnets

The stability of a miniature skyrmion crystal (SkX) with only a small number of spins in the magnetic unit cell has been theoretically investigated in $J_1$-$J_3$ antiferromagnets on the breathing kagome lattice with a single-ion anisotropy $D$ at zero field. It is found by means of Monte Carlo simulations that due to the breathing bond-alternation, a zero-field triple-${\bf Q}$ miniature SkX can be stabilized not only in the specific case of $D=0$ [K. Aoyama and H. Kawamura, Phys. Rev. B 105, L100407 (2022)] but also in more general situations with easy-axis ($D0$) anisotropies which favor triple-${\bf Q}$ collinear and noncoplanar states, respectively. Since the SkX and anti-SkX each having positive or negative chirality are energetically degenerate, the topological Hall effect of alternative sign is possible at zero field. It is also found that reflecting the chiral degeneracy, the collinear and coplanar phases preempting the SkX phase possess random domain structures consisting of positive- and negative-chirality clusters.Comment: 5 pages, 3 figure

Equal-Spin Pairing State of Superfluid 3^3He in Aerogel

The equal-spin pairing (ESP) state, the so-called A-like phase, of superfluid $^3$He in aerogels is studied theoretically in the Ginzburg-Landau (GL) region by examining thermodynamics, and the resulting equilibrium phase diagram is mapped out. We find that, among the ABM, planar, and robust pairing states, the ABM state with presumably quasi long-ranged superfluid order is the best candidate of the A-like phase with a strange lowering of the polycritical point (PCP) observed experimentally.Comment: 4 pages, 1 figure, one reference added, accepted for publication in Phys. Rev.

Strong Coupling Correction in Superfluid 3^3He in Aerogel

Effects of impurity scatterings on the strong coupling (SC) contribution, stabilizing the ABM (axial) pairing state, to the quartic term of the Ginzburg-Landau (GL) free energy of superfluid $^3$He are theoretically studied to examine recent observations suggestive of an anomalously small SC effect in superfluid $^3$He in aerogels. To study the SC corrections, two approaches are used. One is based on a perturbation in the short-range repulsive interaction, and the other is a phenomenological approach used previously for the bulk liquid by Sauls and Serene [Phys.Rev.B 24, 183 (1981)]. It is found that the impurity scattering favors the BW pairing state and shrinks the region of the ABM pairing state in the T-P phase diagram. In the phenomenological approach, the resulting shrinkage of the ABM region is especially substantial and, if assuming an anisotropy over a large scale in aerogel, leads to justifying the phase diagrams determined experimentally.Comment: 19 pages, 9 figures, Accepted for publication in Phys. Rev.