Lifshitz transition and thermoelectric properties of bilayer graphene

Suszalski, Dominik; Rut, Grzegorz; Rycerz, Adam

doi:10.1103/physrevb.97.125403

Cited by 16 publications

(26 citation statements)

References 72 publications

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“…A logarithmic deviation of the maximal absolute thermopower from the Goldsmid-Sharp relation is identified and rationalized with the help of the step-function model for the transmission-energy dependence. In addition to the earlier findings that the trigonal warping term modifies the density of states [24] and transport properties [13] also for Fermi energies 1 meV, we show here that signatures of trigonal warping may still be visible in thermoelectric characteristics for the band gaps as large as ∆ ∼ 100 meV.…”

Section: Discussionsupporting

confidence: 80%

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Thermoelectric properties of gapped bilayer graphene

Suszalski

Rut²,

Rycerz³

2019

J. Phys.: Condens. Matter

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Unlike in conventional semiconductors, both the chemical potential and the band gap in bilayer graphene (BLG) can be tuned via application of external electric field. Among numerous device implications, this property also designates BLG as a candidate for high-performance thermoelectric material. In this theoretical study we have calculated the Seebeck coefficients for abrupt interface separating weakly-and heavily-doped areas in BLG, and for a more realistic rectangular sample of mesoscopic size, contacted by two electrodes. For a given band gap (∆) and temperature (T ) the maximal Seebeck coefficient is close to the Goldsmid-Sharp value |S| GS max = ∆/(2eT ), the deviations can be approximated by the asymptotic expression |S| GS max −|S|max = (kB/e)× 1 2 ln u + ln 2 − 1 2 + O(u −1 ) , with the electron charge −e, the Boltzmann constant kB, and u = ∆/(2kBT ) 1. Surprisingly, the effects of trigonal warping term in the BLG low-energy Hamiltonian are clearly visible at few-Kelvin temperatures, for all accessible values of ∆ 300 meV. We also show that thermoelectric figure of merit is noticeably enhanced (ZT > 3) when a rigid substrate suppresses out-of-plane vibrations, reducing the contribution from ZA phonons to the thermal conductivity.with f BE (T, ω) = 1/ [ exp ( ω/k B T ) − 1 ] the Bose-Einstein distribution function and T ph (ω) the phononic transmission spectrum. We calculate T ph (ω) by adopting the procedure developed by Alofi and Srivastava [30] to the two systems considered in this work (see Supplementary Information, Sec. IV ).

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Section: Discussionsupporting

confidence: 80%

“…1(b) oscillations of the Fabry-Pérot type are well-pronounces, see Ref. [13]. In contrast, the Seebeck coefficient is almost identical for both systems, see Fig.…”

Section: Numerical Resultssupporting

confidence: 59%

Thermoelectric properties of gapped bilayer graphene

Suszalski

Rut²,

Rycerz³

2019

J. Phys.: Condens. Matter

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“…[13], with a numerical stabilization introduced in Ref. [28]. In brief, at finite-precision arithmetics, the modematching equations may become ill defined for sufficiently large L, as they contain both exponentially growing and exponentially decaying coefficients.…”

Section: A Zero-temperature Charge Transportmentioning

confidence: 99%

“…where m = γ 1 /2v 2 0 and k l = γ 1 v 3 / v 2 0 , leading to a nonzero number of propagating modes (open channels) at zero energy, which can be approximated as [28]…”

Section: A Zero-temperature Charge Transportmentioning

confidence: 99%

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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“…Although the dominant contribution to the thermal conductivity originates from lattice vibrations (phonons), particularly these corresponding to out-of-plane deformations [ 3 , 4 ] allowing graphene to outperform more rigid carbon nanotubes, the electronic contribution to the thermal conductivity (

) was also found to be surprisingly high [ 5 ] in relation to the electrical conductivity (

) close to the charge-neutrality point [ 6 ]. One can show theoretically that the electronic contribution dominates the thermal transport at sub-kelvin temperatures [ 7 ], but direct comparison with the experiment is currently missing. Starting from a few kelvins, up to the temperatures of about

K, it is possible to control the temperatures of electrons and lattice independently [ 5 ], since the electron–phonon coupling is weak, and to obtain the value of

directly.…”

Section: Introductionmentioning

confidence: 99%

Wiedemann–Franz Law for Massless Dirac Fermions with Implications for Graphene

Rycerz

2021

Materials

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In the 2016 experiment by Crossno et al. the electronic contribution to the thermal conductivity of graphene was found to violate the well-known Wiedemann–Franz (WF) law for metals. At liquid nitrogen temperatures, the thermal to electrical conductivity ratio of charge-neutral samples was more than 10 times higher than predicted by the WF law, which was attributed to interactions between particles leading to collective behavior described by hydrodynamics. Here, we show, by adapting the handbook derivation of the WF law to the case of massless Dirac fermions, that significantly enhanced thermal conductivity should appear also in few- or even sub-kelvin temperatures, where the role of interactions can be neglected. The comparison with numerical results obtained within the Landauer–Büttiker formalism for rectangular and disk-shaped (Corbino) devices in ballistic graphene is also provided.

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Lifshitz transition and thermoelectric properties of bilayer graphene

Cited by 16 publications

References 72 publications

Thermoelectric properties of gapped bilayer graphene

Thermoelectric properties of gapped bilayer graphene

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

Wiedemann–Franz Law for Massless Dirac Fermions with Implications for Graphene

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