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 $\pm 2\hslash$. Weak magnetic fields enhance the conductivity, reaching the maximal value near the crossover field $B_L=\frac{4}{3}\sqrt{3}(\hslash /e)t^{\prime }{t}_{\perp }{\left[t_0^{2}a(R_{\mathrm{o}}-R_{\mathrm{i}})\right]}^{-1}$, where $t_0$ ($t_{\perp }$) is the nearest-neighbor intra- (inter-)layer hopping integral, $t^{\prime }$ is the skew-interlayer hopping integral, and $R_{\mathrm{o}}$ ($R_{\mathrm{i}}$) is the outer (inner) disk radius. For magnetic fields $B\gtrsim B_L$ we observe quasiperiodic conductance oscillations characterized by the decreasing mean value $⟨\sigma ⟩-{\sigma }_0\propto B_L/B$, 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 $t^{\prime }=0$ case (earlier discussed in Ref. [1]) and in the $t^{\prime }\ne 0$ case, providing a finite-system analog of the Lifshitz transition.

Minor revisions; new Ref. [41]. A version accepted for publication in Physical Review B

References in corpus (33)

• Valley filter and valley valve in graphene
• The electronic properties of bilayer graphene
• Quantum-limited shot noise in graphene
• Phenomenology with Massive Neutrinos
• Phase Coherent Transport of Charges in Graphene Quantum Billiard
• Ab Initio Theory of Gate Induced Gaps in Graphene Bilayers
• Topological confinement in bilayer graphene
• Graphene valley filter using a line defect
• Electron fractionalization in two-dimensional graphenelike structures
• Probing the Electronic Structure of Bilayer Graphene by Raman Scattering
• Aharonov-Bohm effect and broken valley-degeneracy in graphene rings
• Transport in Bilayer Graphene: Calculations within a self-consistent Born approximation
• Valley filter in strain engineered graphene
• Bound states and magnetic field-induced valley splitting in gate-tunable graphene quantum dots
• Ballistic transmission through a graphene bilayer
• Kondo Quantum Criticality of Magnetic Adatoms in Graphene
• Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
• Role of the trigonal warping on the minimal conductivity of bilayer graphene
• Localized Spins on Graphene
• Spin-valley filtering in strained graphene structures with artificially induced carrier mass and spin-orbit coupling
• Notes on the minimal longitudinal dc conductivity of perfect bilayer graphene
• Impurity-assisted tunneling in graphene
• Finite difference method for transport properties of massless Dirac fermions
• Conformal mapping and shot noise in graphene
• Finite-difference method for transport of two-dimensional massless Dirac fermions in a ribbon geometry
• Nonequilibrium valley polarization in graphene nanoconstrictions
• Valley-based Cooper Pair Splitting via Topologically Confined Channels in Bilayer Graphene
• Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity
• Anisotropic minimal conductivity of graphene bilayers
• Electric field control of the indirect magnetic coupling through a short graphene nanoribbon
• Minimal conductivity and signatures of quantum criticality in ballistic graphene bilayer
• Magnetoconductance of the Corbino disk in graphene: Chiral tunneling and quantum interference in the bilayer case
• Band structure asymmetry of bilayer graphene revealed by infrared spectroscopy

Cited by in corpus (4)

• Ferrimagnetic and antiferromagnetic phase in bilayer graphene nanoflake controlled with external electric fields
• Lifshitz transition and thermoelectric properties of bilayer graphene
• Mesoscopic valley filter in graphene Corbino disk containing a p-n junction
• Effect of asymmetric Fermi velocity on trigonally warped spectrum of bilayer graphene