Geometric phase in St\"uckelberg interferometry

TL;DR

This paper investigates how geometric phases influence St"uckelberg interference patterns in a two-band Dirac system, revealing the role of chirality, mass sign, and trajectory type in quantum band coupling.

Contribution

It introduces the concept of a geometric phase in St"uckelberg interferometry within Dirac systems, highlighting its dependence on chirality, mass, and trajectory.

Findings

Geometric phase depends on chirality and mass sign of Dirac cones.

Interference patterns encode band coupling through wavefunction structure.

Trajectory type influences the geometric phase contribution.

Abstract

We study the time evolution of a two-dimensional quantum particle exhibiting an energy spectrum, made of two bands, with two Dirac cones, as e.g. in the band structure of a honeycomb lattice. A force is applied such that the particle experiences two Landau-Zener transitions in succession. The adiabatic evolution between the two transitions leads to St\"uckelberg interferences, due to two possible trajectories in energy space. In addition to well-known dynamical and Stokes phases, the interference pattern reveals a geometric phase which depends on the chirality (winding number) and the mass sign associated to each Dirac cone, as well as on the type of trajectory (parallel or diagonal with respect to the two cones) in parameter space. This geometric phase reveals the coupling between the bands encoded in the structure of the wavefunctions.