Thermopower and Nernst effect in graphene in a magnetic field

Abstract

We report measurements of the thermopower S and Nernst signal Syx in graphene in a magnetic field H. Both quantities show strong quantum oscillations vs. the gate voltage Vg. Our measurements for Landau Levels of index n = 0 are in quantitative agreement with the edge-current model of Girvin and Jonson (GJ). The inferred off-diagonal thermoelectric conductivity αyx comes close to the quantum of Amps per Kelvin. At the Dirac point (n = 0), however, the width of the peak in αyx is very narrow. We discuss features of the thermoelectric response at the Dirac point including the enhanced Nernst signal.In graphene, the linear dispersion of the electronic states near the chemical potential µ is well described by the Dirac Hamiltonian. As shown by Novoselov et al. [1,2,3] and by Zhang et al. [4,5,6] quantization of the electronic states into Landau Levels leads to the integer quantum Hall Effect (QHE). Because of the linear dispersion, the energy E n of the Landau Level (LL) of index n varies as E n = sgn(n) 2e v 2 F B|n|, where B is the magnetic induction, v F the Fermi velocity, e the electron charge, and h is Planck's constant. The quantized Hall conductivity is given bywhere the factor 4 reflects the degeneracy g of each LL (2 each from spin and valley degrees). Detailed investigations of the longitudinal resistance R xx and Hall resistance R xy have been reported by several groups [1,2,3,4,5,6,7]. By contrast, the thermoelectric tensor S ij is less investigated. S ij relates the observed electric field E to an applied temperature gradient −∇T , viz. E = ↔ S ·(−∇T ). On the other hand, the charge current density J produced by −∇T is expressed by the thermolelectric conductivity tensorAlthough J is not measured directly, α ij may be obtained by measurements of both S ij and the resistivity tensor ρ ij = R ij . (By convention, −S xx is the thermopower S; we refer to S yx = E y /|∇T | as the Nernst signal.)A most unusual feature of the thermoelectric response of a QHE system (for n = 0) is that, despite the dominance of the off-diagonal (Hall-like) current response, the thermopower displays a large peak at each LL whereas the Nernst signal is small. In the geometry treated by Girvin and Jonson [9,10] (Fig. 1a), the 2D sample is of finite width alongx, but is infinite alongŷ (with the applied magnetic field H||ẑ). As we approach either edge, the LL energy E n rises very steeply (bold curve). At T = 0, edge currents I y exist at the intersections (open circles) of E n with the chemical potential µ. In a gradient −∇T , the magnitude of I y is larger at the warmer edge than at the cooler edge because of increased occupation of states above µ. The difference |δI y | is a maximum when µ is aligned with E n in the bulk. The corresponding value of α yx is then a universal quantum (k B e/h) ln 2 with units of Amperes per Kelvin (k B is Boltzmann's constant). In turn, δI y produces a quantized Hall voltage V H = (h/e 2 )δI y that drops ||x. Hence, conflating these 2 large off-diagonal effects, the thermopower S becomes very larg...

Strong interfacial exchange field in the graphene/EuS heterostructure

“…This is because, except for the n = 0 LL, ௬௫ crosses zero and changes sign whenever the gate voltage V g is located in between adjacent LLs or in the middle of a Landau level (LL). [10][11][12][13] Our measured clearly has only one peak at each n = ±1 LLs, similar to ௫௫ (Fig. S2-3 …”

First-principles study of the electrical and lattice thermal transport in monolayer and bilayer graphene

“…It was shown that the sign of Seebeck coefficients changes as the majority carrier density shifts from the electron to that of the hole. The gate-dependent Seebeck coefficient and Nernst signal on graphene in a magnetic field was studied by Ong et al [6]. Quantities closely related to σ are mobility (µ F E ) and resistivity (ρ).…”

“…The experimental works carried out by various groups such as Kim et al [4], Geim et al [15], Ong et al [6], Nam arXiv:1703.00224v1 [cond-mat.mtrl-sci] 1 Mar 2017 et al [16] and Wang et al [17] on gate-dependent electron transport properties of MLG and BLG have motivated us to carry out computational studies based on firstprinciples calculations of MLG-doped hexagonal boron nitride (h-BN) and pure BLG under the influence of an electric field, since there is a direct correspondence between gate voltage and chemical potential. It is observed that S is strongly dependent on the amount of doping in the case of MLG.…”

Effects of a piezoelectric substrate on phonon-drag thermopower in monolayer graphene

“…Phonon-drag thermopower has been extensively studied in bulk semiconductors [20], the conventional 2DEG in semiconductor heterostructures [21][22][23] and graphene systems [24], and it is shown to be generally important at low temperatures. Experimental observations in graphene flakes on substrates hundreds of nanometres in lateral size [25][26][27][28] show no signature of S g , which is attributed to the weak el-ph coupling. However, theoretical studies in freely suspended monolayer [29,30] and bilayer [31] graphene of size ~ 10μm considering the electron-acoustic phonon coupling via deformation potential show S g to be important for temperatures T ≤ 10 K. In graphene nano-ribbons, S g is shown to be of order 1 mV/K and sensitive to the Fermi energy and width of the ribbon [32].…”