Time-Reversal Invariant Superconductivity of Sr${}_2$RuO${}_4$ Revealed by Josephson Effects

Abstract

Sr${}_2$RuO${}_4$ is one of the most promising candidates of a topological superconductor with broken time-reversal symmetry, because a number of experiments have revealed evidences for a spin-triplet chiral $p$-wave superconductivity. In order to clarify the time-reversal symmetry of Sr${}_2$RuO${}_4$, we introduce a novel test that examines the invariance of the Josephson critical current under the inversion of both the current and magnetic fields, in contrast to the detection of a spontaneous magnetic field employed in past experiments. Analyses of the transport properties of the planar and corner Josephson junctions formed between Sr${}_2$RuO${}_4$ and Nb reveal the time-reversal invariant superconductivity, most probably helical $p$-wave, of Sr${}_2$RuO${}_4$. This state corresponds to a yet-to-be confirmed $topologicalcrystallinesuperconductivity$ that can host two Majorana edge modes at the surface protected by crystalline mirror symmetry.

10 pages 6 figures