Pseudodiffusive conductance, quantum-limited shot noise, and Landau-level hierarchy in a biased graphene bilayer

Abstract

We discuss, by means of mode-matching analysis for the Dirac equation, how splittings of the Landau-level (LL) degeneracies associated with spin, valley, and layer degrees of freedom affect the ballistic conductance of graphene bilayer. The results show that for wide samples (W L) the Landauer-Büttiker conductance reaches the maximum G se 2 /(πh) × W/L at the resonance via each LL, with the prefactor varying from s = 8 if all three degeneracies are preserved, to s = 1 if all the degeneracies are split. In the absence of bias between the layers, the degeneracies associated with spin and layer degrees of freedom may be split by manipulating the doping and magnetic field; the conductance at the zeroth LL is twice as large, while the conductance at any other LL equals to the corresponding conductance of graphene monolayer. The presence of bias potential allows one also to split the valley degeneracy. Our results show that the charge transfer at each LL has pseudodiffusive character, with the second and third cumulant quantified by F = 1/3 and R = 1/15 (respectively). In case the electrochemical potential is allowed to slowly fluctuate in a finite vicinity of LL, the resulting charge-transfer characteristics are still quantum limited, with F 0.7 and R 0.5 in the limit of large fluctuations. Analogously, the above values of F and R are predicted to be approached in the limit of high source-drain voltage difference applied. The possible effects of indirect interlayer hopping integrals are also briefly discussed.

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

“…(15) and (16) applies for generic crystallographic orientation of the sample. However, for some particular orientations one obtains different asymptotic behaviors, including a slower power-law convergence to σ with the exponent γ ≈ 0.25 if the current is passed precisely along an armchair direction [20], or the oscillating conductivity with the lower bound of σ (7/3) σ 0 if the current is passed precisely along a zigzag direction [18]. Such issues are absent in the Corbino geometry, allowing one to focus on the universal scaling properties of the material.…”

“…(26) with half-odd integer q 5/2 approximates a local conductance minimum (as A ≈ q) with G BLG ≈ 16g 0 R i /R o ; i.e., twice as large as the MLG disk conductance, see Eq. (20); and four dominant channels characterized by T − q+1…”

“…Our discussion of the magnetotransport characteristics starts from pointing out that the influence of a uniform magnetic field B [45] on analytical results given by Eqs. (20) and (21) can be expressed in a very compact form: Namely, it is sufficient to replace j and m in arguments of hyperbolic cosine by [1,25,26]…”

“…1(b). A BLG strip of width W , contacted by the electrodes at a distance L, in a uniform field B, and with periodic boundary conditions in the transverse direction, was earlier discussed in the W L limit [20], in which the pseudodiffusive charge transport is predicted to appear near LLs. Here we primarily focus on the W πL range (a nanotubelike geometry) which do not seem to have a direct physical analogue, but can be treated in analytical terms and possesses a discrete spectrum of transmission channels closely resembling the situation in the Corbino disk.…”

“…The transport anisotropy appears as the secondary Dirac cones, present for t = 0, break the rotational invariance of the dispersion relation [19]. In principle, the experimental study of σ(L) for clean bilayer samples should be sufficient to determine t [20], also in the presence of small interactioninduced energy gap [21][22][23]. (For instance, the value of σ ≈ 2.5 σ 0 reported by Mayorov et al [24] coincides with the above-mentioned large-L predictions.)…”