Trigonal warping, pseudodiffusive transport, and finite-system version of the Lifshitz transition in magnetoconductance of bilayer graphene Corbino disks

Abstract

Using the transfer matrix in the angular-momentum space we investigate the impact of trigonal warping on magnetotransport and scaling properties of a ballistic bilayer graphene in the Corbino geometry. Although the conductivity at the charge-neutrality point and zero magnetic field exhibits a one-parameter scaling, the shot-noise characteristics, quantified by the Fano factor $\mathcal{F}$ and the third charge-transfer cumulant $\mathcal{R}$, remain pseudodiffusive. This shows that the pseudodiffusive transport regime in bilayer graphene is not related to the universal value of the conductivity but can be identified by higher charge-transfer cumulants. For Corbino disks with larger radii ratios the conductivity is suppressed by the trigonal warping, mainly because the symmetry reduction amplifies backscattering for normal modes corresponding to angular-momentum eigenvalues $\pm{}2\hbar$. Weak magnetic fields enhance the conductivity, reaching the maximal value near the crossover field $B_L=\frac{4}{3}\sqrt{3}\,({\hbar}/{e})\,t't_\perp\!\left[{t_0^2a(R_{\rm o}-R_{\rm i})}\right]^{-1}$, where $t_0$ ($t_\perp$) is the nearest-neighbor intra- (inter-)layer hopping integral, $t'$ is the skew-interlayer hopping integral, and $R_{\rm o}$ ($R_{\rm i}$) is the outer (inner) disk radius. For magnetic fields $B\gtrsim{}B_L$ we observe quasiperiodic conductance oscillations characterized by the decreasing mean value $\langle\sigma\rangle-\sigma_0\propto{}B_L/B$, where $\sigma_0=(8/\pi)\,e^2/h$. The conductivity, as well as higher charge-transfer cumulants, show beating patterns with an envelope period proportional to $\sqrt{B/B_L}$. This constitutes a qualitative difference between the high-field ($B\gg{}B_L$) magnetotransport in the $t'=0$ case (earlier discussed in Ref. [1]) and in the $t'\neq{}0$ case, providing a finite-system analog of the Lifshitz transition.