Screw-Dislocated Level Structure of Graphene Potential Wells

We investigate the linearized graphene Hamiltonian with a radially-symmetric power-law potential in the two-dimensional parameter space of mass and magnetic field. At zero mass the quasibound eigen-resonances, denoted \textbar n,m\textgreater (where n and m are the radial and azimuthal quantum numbers) form distinct ladders for each m, and each such ladder has the property that for massless particles the energies and eigenstates are discontinuous at a critical field B$_{c}$. Turning on a mass bridges this discontinuity, but negative and positive masses connect different eigenstates, producing a screw dislocation in the eigenstate spectrum. We numerically propagate the wavepacket of an \textbar n,m\textgreater eigenstate in a slowly-evolving Hamiltonian whose path encloses B$_{c}$, and verify that a closed adiabatic loop conveys the particle to the \textbar n$+$/-1,m\textgreater state, demonstrating the existence of a screw dislocation in the spectrum. We explain the dislocation in terms of the Berry phase acquired while encircling the critical magnetic field B$_{c}$.