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We present a symmetry analysis of the trigonal band structure in graphene,elucidating the transformational properties of the underlying basis functionsand the crucial role of time-reversal invariance. Group theory is used toderive an invariant expansion of the Hamiltonian for electron states near the Kpoints of the graphene Brillouin zone. Besides yielding the characteristick-linear dispersion and higher-order corrections to it, this approach enablesthe systematic incorporation of all terms arising from external electric andmagnetic fields, strain, and spin-orbit coupling up to any desired order.Several new contributions are found, in addition to reproducing resultsobtained previously within tight-binding calculations. Physical ramificationsof these new terms are discussed.

Invariant expansion for the trigonal band structure of graphene