Magnetoconductance of the Corbino disk in graphene: chiral tunneling and quantum interference in the bilayer case

Abstract

Quantum transport through an impurity-free Corbino disk in bilayer graphene is investigated analytically, using the mode-matching method to give an effective Dirac equation, in the presence of uniform magnetic fields. Similarly as in the monolayer case (see Rycerz 2010 Phys. Rev. B 81 121404; Katsnelson 2010 Europhys. Lett. 89 17001), conductance at the Dirac point shows oscillations with the flux piercing the disk area ΦD characterized by the period Φ(0) = 2 (h/e) ln(R(o)/R(i)), where R(o)(R(i)) is the outer (inner) disk radius. The oscillation magnitude depends either on the radii ratio or on the physical disk size, with the condition for maximal oscillations being R(o)/R(i) ≃ [ Rit⊥/(2ℏvF) ](4/p) (for R(o)/R(i) ≫ 1), where t⊥ is the interlayer hopping integral, vF is the Fermi velocity in graphene, and p is an even integer. Odd-integer values of p correspond to vanishing oscillations for the normal Corbino setup, or to oscillation frequency doubling for the Andreev-Corbino setup. At higher Landau levels, magnetoconductance behaves almost identically in the monolayer and bilayer cases. A brief comparison with the Corbino disk in a two-dimensional electron gas is also provided in order to illustrate the role of chiral tunneling in graphene.

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

“…The potential energy U (r) depends only on r = x 2 + y 2 , and the remaining symbols are the same as in Eqs. (1)(2)(3). As mentioned earlier, the available values of t following from different experimental [10,11,31] and computational [32] approaches are far from being consistent.…”

“…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]…”

“…For the conductivity, we have ∆σ MLG 0.1σ MLG if R o /R i 5. For BLG disks, the mode-matching analysis for the t = 0 case [1] unveils an interference between the two transmission channels for each angular momentum eigenvalue, following from the coupling between the layers quantified by t ⊥ . In turn, 8 the oscillations magnitude depends also on the physical system size.…”

“…In the most common Bernal stacking, the leading tightbinding parameters: the intralayer hopping integral between nearest neighbors t 0 = 3.16 eV, and the nearest neighbor interlayer hopping integral t ⊥ = 0.38 eV, are both link to the basic BLG band-structure characteristics, which are the Fermi velocity v F = √ 3 t 0 a 2 ≈ 10 6 m/s (1) and the electron effective mass…”

“…It is worth to stress that anisotropic aspects of quantum transport are still present in such a system as the rotational symmetry is intrinsically broken due to trigonal warping. In effect, the total angular momentum is not conserved, and the standard mode-matching method cannot be applied as in simpler systems studied earlier (namely, the monolayer disk [25,26] and the BLG disk with t = 0 [1]). Here, we overcome this difficulty by developing a numerical transfer-matrix approach in the angular momentum space.…”