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Time-dependent massless Dirac fermions in graphene

Using the Lewis-Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent magnetic field. The eigenvalue equations for the two spinor components of the Lewis-Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians.

preprint2015arXivOpen access
Boubakeur KhantoulAndreas Fring
cond-mat.mes-hallquant-ph
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Boubakeur KhantoulAndreas Fring

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