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

TL;DR

This paper analytically investigates quantum magnetoconductance oscillations in bilayer graphene Corbino disks, revealing how flux, geometry, and interlayer coupling influence conductance patterns and comparing these effects with monolayer graphene and 2DEG systems.

Contribution

It provides an analytical study of magnetoconductance oscillations in bilayer graphene Corbino disks, highlighting the effects of geometry, interlayer coupling, and chiral tunneling, extending prior monolayer analyses.

Findings

Conductance oscillates with magnetic flux, with a period depending on disk geometry.

Maximal oscillations occur at specific radius ratios related to interlayer coupling.

Higher Landau levels show similar behavior in monolayer and bilayer graphene.

Abstract

Quantum transport through an impurity-free Corbino disk in bilayer graphene is investigated analytically, by the mode-matching method for effective Dirac equation, in the presence of uniform magnetic fields. Similarly as in the monolayer case (see Refs. [1,2]), conductance at the Dirac point shows oscillations with the flux piercing the disk area $\Phi_D$ characterized by the period $\Phi_0=2\,(h/e)\ln(R_{\rm o}/R_{\rm i})$, where $R_{\rm o}$ ($R_{\rm i}$) is the outer (inner) disk radius. The oscillations magnitude depends either on the radii ratio or on the physical disk size, with the condition for maximal oscillations reading $R_{\rm o}/R_{\rm i}\simeq\left[\,R_{\rm i}t_{\perp}/(2\hbar{}v_{F})\,\right]^{4/p}$ (for $R_{\rm o}/R_{\rm i}\gg{}1$), where $t_\perp$ is the interlayer hopping integral, $v_F$ is the Fermi velocity in graphene, and $p$ is an {\em even} integer. {\em Odd}-integer values of $p$ correspond to vanishing oscillations for the normal Corbino setup, or to oscillations frequency doubling for the Andreev-Corbino setup. At higher Landau levels (LLs) magnetoconductance behaves almost identically in the monolayer and bilayer cases. A brief comparison with the Corbino disk in 2DEG is also provided in order to illustrate the role of chiral tunneling in graphene.