Momentum space AC Josephson effect and intervalley coherence in multilayer graphene

Electron transport driven by the phase coherence and interference of quantum many-body wavefunctions is a fascinating phenomenon with potential technological significance. Superconductivity, for example, enables dissipationless transport through macroscopic phase twisting, while charge-density waves show broadband noise and AC-DC interference once their phase is depinned. We identify an analogous phase-coherent dynamics in the intervalley-coherent (IVC) state frequently observed in rhombohedral multilayer graphene. We show that a static magnetic field drives an oscillating intervalley current, which produces an oscillating orbital magnetization and thereby a detectable AC Hall response. This mechanism is similar to the Josephson effect observed in superconductors but now happening in momentum space. In this analogy, the static magnetic field acts as the DC voltage, while the oscillating intervalley current is the AC Josephson current. We provide microscopic calculations of all the phase-number free-energy parameters in rhombohedral trilayer graphene, establishing this effect as an experimental signature of IVC order. The authors propose that when an intervalley coherent (IVC) state is subjected to a static magnetic field, it develops an oscillating orbital magnetization at microwave frequency, an effect analogous to a Josephson oscillation in momentum space. The effect could provide an experimental diagnostic for identifying the IVC state.