We examine the requirements placed upon the Hamiltonian under the demand of gauge invariance. From these requirements we derive the gauge-invariant form of the tight-binding Hamiltonian with electromagnetic coupling. In our derivation we do not make recourse to a Peierls substitution and hence avoid introducing any ambiguities of path. Our expression transparently reduces to the familiar expression in a complete basis. We apply this Hamiltonian to study resonant magnetotunneling spectroscopy using a simple tight-binding model.
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