Searching for confined modes in graphene channels: the variable phase method

Details Searching for confined modes in graphene channels: the variable phase method Searching for confined modes in graphene channels: the variable phase method

2011-12-17

arxiv.org/abs/1112.4034v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 3 figures

Scientific paper

Using the variable phase method, we reformulate the Dirac equation governing the charge carriers in graphene into a first-order differential equation from which we can treat confined state problems in electron waveguides. We show that this new method agrees with a known analytic result and go on to investigate the nature of more experimentally realizable electron waveguides, showing that when the Fermi energy is set at the Dirac points truly confined states are supported in pristine graphene. In contrast to exponentially-decaying potentials we discover that the threshold potential strength at which the first confined state appears is vanishingly small for potentials decaying at large distances as a power law, but nonetheless further confined states are formed when the strength and spread of the potential reach a certain threshold.

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