Minimal conductivity and signatures of quantum criticality in ballistic graphene bilayer

Rut, Grzegorz; Rycerz, Adam

doi:10.1209/0295-5075/107/47005

Cited by 4 publications

(19 citation statements)

References 40 publications

(63 reference statements)

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“…In order to determine the transmission matrix t for a given electrochemical potential µ we employ the computational scheme similar to the presented in Ref. [36]. However, at finite-precision arithmetics, the modematching equations become ill-defined for sufficiently large L and µ, as they contain both exponentially growing and exponentially decaying coefficients.…”

Section: Resultsmentioning

confidence: 99%

Lifshitz transition and thermoelectric properties of bilayer graphene

2018

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This is a numerical study of thermoelectric properties of ballistic bilayer graphene in the presence of trigonal warping term in the effective Hamiltonian. We find, in the mesoscopic samples of the length L > 10 µm at sub-Kelvin temperatures, that both the Seebeck coefficient and the Lorentz number show anomalies (the additional maximum and minimum, respectively) when the electrochemical potential is close to the Lifshitz energy, which can be attributed to the presence of the van Hove singularity in a bulk density of states. At higher temperatures the anomalies vanish, but measurable quantities characterizing remaining maximum of the Seebeck coefficient still unveil the presence of massless Dirac fermions and make it possible to determine the trigonal warping strength. Behavior of the thermoelectric figure of merit (ZT ) is also discussed.

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Section: Resultsmentioning

confidence: 99%

Lifshitz transition and thermoelectric properties of bilayer graphene

2018

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“…In order to determine the transmission matrix at a given Fermi energy, t = t(E), for a rectangular sample attached to the two heavily-doped regions, we employ the computational scheme similar to the presented in Ref. [13], with a numerical stabilization introduced in Ref. [28].…”

Section: A Zero-temperature Charge Transportmentioning

confidence: 99%

“…None of these effects is present for γ 4 = 0, for which the conductivity follows the scenario earlier described in Refs. [12,13]. (In Appendix A, we present the analytical derivation explaining why σ(L) → 3σ 0 for L → ∞ and arbitarily small γ 3 = 0.)…”

Section: A Zero-temperature Charge Transportmentioning

confidence: 99%

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Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian

2020

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We study the ballistic conductivity of bilayer graphene in the presence of symmetry-breaking terms in effective Hamiltonian for low-energy excitations, such as the trigonal-warping term (γ3), the electron-hole symmetry breaking interlayer hopping (γ4), and the staggered potential (δAB). Earlier, it was shown that for γ3 = 0, in the absence of remaining symmetry-breaking terms (i.e., γ4 = δAB = 0), the conductivity (σ) approaches the value of 3σ0 for the system size L → ∞ (with σ0 = 8e 2 /(πh) being the result in the absence of trigonal warping, γ3 = 0). We demonstrate that γ4 = 0 leads to the divergent conductivity (σ → ∞) if γ3 = 0, or to the vanishing conductivity (σ → 0) if γ3 = 0. For realistic values of the tight-binding model parameters, γ3 = 0.3 eV, γ4 = 0.15 eV (and δAB = 0), the conductivity values are in the range of σ/σ0 ≈ 4 − 5 for 100 nm < L < 1 µm, in agreement with existing experimental results. The staggered potential (δAB = 0) suppresses zero-temperature transport, leading to σ → 0 for L → ∞. Although σ = σ(L) is no longer universal, the Fano factor approaches the pseudodiffusive value (F → 1/3 for L → ∞) in any case with non-vanishing σ (otherwise, F → 1) signaling the transport is ruled by evanescent waves. Temperature effects are briefly discussed in terms of a phenomenological model for staggered potential δAB = δAB(T ) showing that, for 0 < T Tc ≈ 12 K and δAB(0) = 1.5 meV, σ(L) is noticeably affected by T for L 100 nm. arXiv:1912.03235v1 [cond-mat.mes-hall]

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“…In turn, the parametres γ and σ defines the position and the slope coefficient at the attractive fixed point (β(σ ) = 0, β (σ ) > 0) of the renormalization group flow [23]. It was pointed out that generic MLG billiard with (at least) one narrow opening shows a crossover to the socalled quantum-tunneling transport regime [40], in which charge-transfer characteristics are governed by a limited number of quantum channels, with transmission probabilities showing a power-law decay with the system size.…”

Section: A One-parameter Scalingmentioning

confidence: 99%

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

Rut

Rycerz

2016

Phys. Rev. B

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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.

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Minimal conductivity and signatures of quantum criticality in ballistic graphene bilayer

Cited by 4 publications

References 40 publications

Lifshitz transition and thermoelectric properties of bilayer graphene

Lifshitz transition and thermoelectric properties of bilayer graphene

Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian

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

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