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We show that the modulation of the hopping amplitudes in the honeycomb lattice of the monolayer graphene uniquely defines a metric which corresponds to the shape of the Dirac cone. The spin connection of this effective metric field can be obtained from the microscopic tight-binding Hamiltonian exactly, completing the analogy between the sublattice pseudospin travelling in the monolayer graphene with ripples and strain fields, and the real spin $1/2$ fermion travelling in a curved space. The effective metric as seen by the sublattice pseudospin is different from the real space metric as defined by the two-dimensional manifold of the graphene monolayer. All relevant terms of the effective gauge field from the microscopic model is calculated exactly for a unimodular effective metric.

Author

Yang, Bo

Published

2014

Language

EN