  The low-energy electronic properties of strained graphene are usually
obtained by transforming the bond vectors according to the Cauchy-Born rule. In
this work, we derive a new effective Dirac Hamiltonian by assuming a more
general transformation rule for the bond vectors under uniform strain, which
takes into account the strain-induced relative displacement between the two
sublattices of graphene. Our analytical results show that the consideration of
such relative displacement yields a qualitatively different Fermi velocity with
respect to previous reports. Furthermore, from the derived Hamiltonian, we
analyze effects of this relative displacement on the local density of states
and the optical conductivity, as well as the implications on the scanning
tunneling spectroscopy, including external magnetic field, and optical
transmittance experiments of strained graphene.
