Non-Hermitian trace in solving the problem of carrier motion in graphene in crossed fields
Rumyantsev E. L.1, Germanenko A. V.1
1Ural Federal University after the first President of Russia B.N. Yeltsin, Yekaterinburg, Russia
Email: alexander.germanenko@urfu.ru
The energy spectrum of carriers in graphene in crossed homogeneous electric and magnetic fields is obtained within the framework of an algebraic approach. This consideration is based only on the gradient-invariant commutative properties of kinetic momentum, which eliminates the need to fix a specific functional dependence of the vector-potential. Special attention is paid to the analysis of the non-Hermitian component in an effective Schrodinger-like Hamiltonian, which is used to describe the system. The effects associated with this unusual property are discussed, as well as a technique that allows us to return to the Hermitian description corresponding to the original formulation of the problem. Keywords: graphene, energy spectrum, crossed electric and magnetic fields.
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