Magnetotransport properties of 8-Pmmn borophene: effects of Hall field and strain

The polymorph of ${\rm 8-Pmmn}$ borophene is an anisotropic Dirac material with tilted Dirac cones at two valleys. The tilting of the Dirac cones at two valleys are in opposite direction, which manifests itself via valley dependent Landau levels in presence of an in-plane electric field (Hall field). The sensitivity of the Landau levels on valley index causes valley polarized magnetotransport properties in presence of a Hall field, which is in contrast to the monolayer graphene with isotropic non-tilted Dirac cones. The longitudinal conductivity and Hall conductivity are evaluated by using linear response theory in low temperature regime. An analytical approximate form of longitudinal conductivity is also obtained to reveal how the tilting of the Dirac cones affects the frequency of longitudinal conductivity oscillation (Shubnikov-de Hass oscillation). On the other hand, Hall conductivity exhibits graphene-like plateau excepts the appearance of valley dependent steps which is purely attributed to the Hall field induced lifting valley degeneracy in Landau levels. Another noticeable point is that if the real magnetic field is replaced by the strain induced pseudo magnetic field then the electric field looses its ability to cause valley polarized transport.