Proximity-Induced Mixed Odd and Even Frequency Pairings in Monolayer NbSe${}_2$

Abstract

Monolayer superconducting transition metal dichalcogenide NbSe${}_2$ is a candidate for a nodal topological superconductor by magnetic field. Because of the so-called Ising spin-orbit coupling that strongly pins the electron spins to the out-of-plane direction, Cooper pairs in monolayer superconductor NbSe${}_2$ are protected against an applied in-plane magnetic field much larger than the Pauli limit. In monolayer NbSe${}_2$, in addition to the Fermi pockets at the corners of Brillouin zone with opposite crystal momentum similar to other semiconducting transition metal dichalcogenides, there is an extra Fermi pocket around the $\Gamma$ point with much smaller spin splitting, which could lead to an alternative strategy for pairing possibilities that are manipulable by a smaller magnetic field. By considering a monolayer NbSe${}_2$-ferromagnet substrate junction, we explore the modified pairing correlations on the pocket at $\Gamma$ point in hole-doped monolayer NbSe${}_2$. The underlying physics is fascinating as there is a delicate interplay of the induced exchange field and the Ising spin-orbit coupling. We realize a mixed singlet-triplet superconductivity, s+f, due to the Ising spin-orbit coupling. Moreover, our results reveal the admixture state including both odd- and even-frequency components, associated with the ferromagnetic proximity effect. Different frequency symmetries of the induced pairing correlations can be realized by manipulating the magnitude and direction of the induced magnetization.

arXiv comment8 pages, 4 figures

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• Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides
• Van der Waals heterostructures with spin-orbit coupling
• Switch effect and $0$-$\pi$ transition in Ising superconductor Josephson junctions
• Pseudo-spin triplet superconductivity in transition-metal dichalcogenide monolayers and Andreev reflection in the lateral heterostructures of 2$H$-NbSe${}_2$
• Unconventional pairing in Ising superconductors: Application to monolayer NbSe${}_2$
• Three-orbital continuous model for $1H$-type metallic transition-metal dichalcogenide monolayers