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Abstract
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Real magnetic and lattice deformation gauge felds have been investigated in honeycomb lattice of
graphene. The coexistence of these two gauges will induce a gap diference between two valley points
(K and K′) of system. This gap diference allows us to study the possible topological valley Hall current
and valley polarization in the graphene sheet. In the absence of magnetic feld, the strain alone could
not generate a valley polarization when the Fermi energy coincides exactly with the Dirac points. Since
in this case there is not any imbalance between the population of the valley points. In other words
each of these gauges alone could not induce any topological valley-polarized current in the system at
zero Fermi energy. Meanwhile at non-zero Fermi energies population imbalance can be generated as
a result of the external strain even at zero magnetic feld. In the context of Berry curvature within the
linear response regime the valley polarization (both magnetic free polarization, Π0, and feld dependent
response function, χα) in diferent values of gauge felds of lattice deformation has been obtained.
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