Quantum anomaly and anomalous Josephson effect in inversion asymmetric Weyl semimetals

TL;DR

This paper investigates how tilts in the Weyl spectra of inversion-asymmetric Weyl semimetals influence Josephson effects, revealing novel valley and chirality supercurrents, and demonstrates their controllability and quantum anomaly implications.

Contribution

It introduces the concept of tilt-induced valley and chirality Josephson currents in Weyl semimetals, showing their controllability and connection to quantum anomalies, which is a novel mechanism for supercurrent manipulation.

Findings

Tilt causes 0-$$ transition and zero bias supercurrents.

TRS tilt yields pure valley Josephson current.

TRS broken tilt induces pure chirality Josephson current.

Abstract

We study a Josephson junction involving an inversion-asymmetric Weyl semimetal in presence of time-reversal symmetric (TRS) or time-reversal symmetry broken tilt in the Weyl spectra. We reveal that both types of tilts in the Weyl nodes lead to a Josephson $0$-$\pi$ transition and a zero bias valley/chiral supercurrent. Strikingly, the TRS tilt gives rise to a pure valley Josephson current (VJC) and TRS broken tilt induces a pure chirality Josephson current (CJC) in this system. The VJC and CJC are the manifestation of valley symmetry broken and $\mathbb{Z}_2$ symmetry broken by the respective tilt. We obtain the reversal of a pure VJC and pure CJC even in the zero bias condition controllable by the junction length. Our analysis of controllability of valley and chirality dependent transport in an inversion asymmetric Weyl semimetal junction could allow applications in valleytronics and chiralitytronics, respectively. The tilt induced Josephson effect provides an alternative route for supercurrent $0$-$\pi$ transition, different from the conventional ferromagnetism Josephson junctions where the spin polarization is essential. In the long junction and zero temperature limit, VJC and CJC are associated with a quantum anomaly which is manifested through a discontinuous jump in the current in absence of TRS and TRS breaking tilts, respectively.