Helical Level Structure of Dirac Potential Wells

Published: November 28, 2017


Daniel T. Walkup, Joseph A. Stroscio


In graphene and other massless 2D Dirac materials, Klein tunneling compromises electron confinement, and momentum-space contours can be assigned a Berry phase which is either zero or π. Consequently, in such systems the energy spectrum of circular potential wells exhibits an interesting discontinuity as a function of magnetic field B: for a given angular momentum the ladder of eigen-resonances is split at an energy-dependent critical field B_"c" . Here we show that introducing a mass term Δ in the Hamiltonian bridges this discontinuity, in such a way that states below B_"c" are adiabatically connected to states above B_"c" whose principal quantum number differs by unity depending on the sign of Δ. In the B-Δ plane, the spectrum of these circular resonators resembles a spiral staircase, in which a particle prepared in the ├ |n,m⟩ resonance state can be promoted to the ├ |n±1,m⟩ state by an adiabatic circuit of the Hamiltonian about B_"c" , the sign depending on the direction of the circuit. We explain the phenomenon in terms of the evolving Berry phase of the orbit, which in such a circuit changes adiabatically by 2π.
Citation: Physical Review B
Volume: 96
Issue: 20
Pub Type: Journals


graphene, Berry phase, Dirac
Created November 28, 2017, Updated November 10, 2018