Abstract
We study the current-phase relation of a topological ring-shape Josephson junction, where the ring structure is defined by one-dimensional topological interface states constructed in a two-dimensional honeycomb-lattice system. We show that control of the potential difference between the two ring arms can lead to a ${\ensuremath{\varphi}}_{0}$ Josephson junction. The physics origin is the superconducting electron- and holelike quasiparticles possessing a valley-dependent chirality and moving separately in the two ring arms. Our findings provide a purely electric way to consecutively manipulate the Josephson current-phase relation.
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