Abstract
Real magnetic and lattice deformation gauge fields have been investigated in honeycomb lattice of graphene. The coexistence of these two gauges will induce a gap difference between two valley points (K and K′) of system. This gap difference allows us to study the possible topological valley Hall current and valley polarization in the graphene sheet. In the absence of magnetic field, 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 field. In the context of Berry curvature within the linear response regime the valley polarization (both magnetic free polarization, Π0, and field dependent response function, χα) in different values of gauge fields of lattice deformation has been obtained.
Highlights
Valleytronics, the valley version of spintronics is based on quantum valley number which carries the information by valley degree of freedom[1]
Further challenges for generating pseudomagnetic fields in graphene and other two dimensional materials not restricted to locally strained graphene nanobubbles
By means of this setup, we demonstrated that the valley polarized current can be achieved in strained graphene in the presence of magnetic field which can be expressed in terms of Berry curvature
Summary
Both strain and magnetic field could be realized as experimental tuning parameters[31,32,33,34]. TM potential depends on electrons position in real spac e, the Hamiltonian of magnetic field, as indicated in Eq (3), contains momentum transfer contributions and cannot be represented in block diagonal form of independent k subspaces. Within the first order perturbation approach, in which the momentum transferring terms cannot contribute, it can be shown that the previous results could be considered reliable at the qualitative level[18]. Unlike the first order correction, momentum transferring terms contribute in the higher orders of the perturbation and generally used block diagonalization approach cannot give rise to an exact answer. First order perturbation accounts for the zero momentum transfer contribution of the magnetic field It can be shown that in strained graphene this valley gap difference depends on both magnetic field and applied strain.
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