Probing tilted Dirac cone in $8-Pmmn$ borophene via magnetic oscillation
We investigate magnetotransport properties of $8-Pmmn$ borophene by using linear response theory in low temperature regime. We solve the single electron Hamiltonian exactly in presence of magnetic field perpendicular to the two-dimensional plane of borophene to obtain Landau levels. Longitudinal conductivity is evaluated numerically as well as analytically and it is found that tilted feature of the Dirac cone manifests itself through the enhancement of Shubnikov-de Hass (SdH) oscillation frequency. Moreover, we observe that quantum Hall conductivity exhibits fractional Hall steps i.e., $\sigma_{xy}=4(e^2/h)(n+1/2)g_t$, where $n=0,1,2,3..$ and $g_t$ is a non-integer number governed by the tilt parameter. A close inspection of SdH oscillation and quantum Hall conductivity can be utilized to probe the tilt parameter of borophene.