One-dimensional Coulomb problem in Dirac materials

Copyright © 2014 American Physical SocietyWe investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated Coulomb problems, with the wave functions expressed in terms of special functions (namely, Whittaker functions), while the energy spectrum must be determined via solutions to transcendental equations. Most notably, there are critical band gaps below which certain low-lying quantum states are missing in a manifestation of atomic collapse.EPSRC (Engineering and Physical Sciences Research Council)EU FP7 ITN NOTEDEVFP7 IRSES project: CANTORFP7 IRSES project: QOCaNFP7 IRSES project: InterNo