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 F and the third charge-transfer cumulant 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 ±2 . Weak magnetic fields enhance the conductivity, reaching the maximal value near the crossover field BL = 4 3 √ 3 ( /e) t t ⊥ t 2 0 a(Ro −Ri) −1 , where t0 (t ⊥ ) is the nearest-neighbor intra-(inter-) layer hopping integral, t is the skew-interlayer hopping integral, and Ro (Ri) is the outer (inner) disk radius. For magnetic fields B BL we observe quasiperiodic conductance oscillations characterized by the decreasing mean value σ − σ0 ∝ BL/B, where σ0 = (8/π) e 2 /h. The conductivity, as well as higher charge-transfer cumulants, show beating patterns with an envelope period proportional to B/BL. This constitutes a qualitative difference between the high-field (B BL) magnetotransport in the t = 0 case (earlier discussed in Ref. [1]) and in the t = 0 case, providing a finite-system analog of the Lifshitz transition.

Lifshitz transition and thermoelectric properties of bilayer graphene

“…To conclude, we have show that thermoelectric measurements may complement the list of techniques allow-ing one to determine tight-binding parameters of bilayergraphene Hamiltonian. Unlike the well-established techniques [34] (or the other recently-proposed [36,37]), they neither require high-magnetic field measurements nor refer to conductivity scaling with the system size. Instead, the proposed single-device thermoelectric measurements must be performed on large ballistic samples (with the length exceeding 10 µm), such that quantum-size effects define the energy scale much smaller then the Lifshitz energy.…”

Mesoscopic valley filter in graphene Corbino disk containing a p–n junction

“…To solve the scattering problem numerically we simplify here, for the case of amonolayer, the method earlier developed for the Corbino disk in bilayer graphene [45]. If  or  in equation (1) is f-dependent the cylindrical symmetry is broken, however, one still can employ the angular-momentum eigenfunctions to represent ageneral solution as asuperposition…”

“…We have employed afixed-step explicit Runge Kutta method of the 4th order [56]. Both the step-size as well as the number of transmission channels M are adjusted to reach the numerical convergence; in practice, these parameters depend on the system size, as well as on the magnetic field, in an approximately linear manner similarly as in the case of bilayer graphene (see [45]).…”

Mesoscopic valley filter in graphene Corbino disk containing a p-n junction

“…To solve the scatering problem numerically we simplify here, for the case of a monolayer, the method earlier developed for the Corbino disk in bilayer graphene [46].…”