Geometric phase in Stückelberg interferometry

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 Stückelberg 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.

20 pages, 12 figures

References in corpus (9)

• The electronic properties of graphene
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Detecting Topological Currents in Graphene Superlattices
• Merging of Dirac points in a two-dimensional crystal
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Topologically Protected Zero Modes in Twisted Bilayer Graphene
• Interferometric approach to measuring band topology in 2D optical lattices
• The Quantum Geometric Phase between Orthogonal States