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Helical Level Structure of Dirac Potential Wells

Published

Author(s)

Daniel T. Walkup, Joseph A. Stroscio

Abstract

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

Keywords

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