Sagnac and Mashhoon effects in graphene

Abstract

We investigate the Sagnac and Mashhoon effects in graphene, taking into account both the pseudospin and intrinsic spin of electrons, within a simplified model of a rotating nanotube or infinitesimally narrow ring. Based on considerations of the relativistic phase of the wave function and employing the effective Larmor theorem, we demonstrate that the Sagnac fringe shift retains a form analogous to that for free electrons, governed by the electron's vacuum mass. In the case of a narrow ring, an additional $π$-phase shift arises due to the Berry phase associated with the honeycomb graphene lattice. The Mashhoon fringe shift retains its conventional form, with its dependence on the Fermi velocity.

Figures (3)

• Figure 1: Schematic of the Sagnac experiment. Waves originating in phase at the source ${\cal S}$ propagate in opposite directions around a rotating loop, producing a measurable phase shift at the detector ${\cal D}$.
• Figure 2: Comoving coordinate system $(x, y)$ in a nanotube of radius $R$ rotating around its symmetry axis with angular velocity $\Omega$ relative to the laboratory frame.
• Figure 3: Illustration of the Berry phase in a graphene ring.Left: Waves propagating counterclockwise ($+$) and clockwise ($-$) around the full ring acquire Berry phases $\phi_\pm = \pm \pi$ between entrance and exit. Right: For waves with entrance and exit separated by an angular distance $\phi_\text{A}$, both propagation directions acquire the same Berry phase: $\phi_\pm = \phi_\text{A} - \pi$.