Thermoelectric and Magnetothermoelectric Transport Measurements of Graphene

The conductance and thermoelectric power (TEP) of graphene is simultaneously measured using a microfabricated heater and thermometer electrodes. The sign of the TEP changes across the charge neutrality point as the majority carrier density switches from electron to hole. The gate dependent conductance and TEP exhibit a quantitative agreement with the semiclassical Mott relation. In the quantum Hall regime at a high magnetic field, quantized thermopower and Nernst signals are observed and are also in agreement with the generalized Mott relation, except for strong deviations near the charge neutrality point.

Figure 1

(a) Conductivity and (b) TEP of a graphene sample as a function of $V_g$ for $T=300\mathrm{K}$ (square), 150 K (circle), 80 K (up triangle), 40 K (down triangle), and 10 K (diamond). Upper inset: Scanning electron microscopy image of a typical device, the scale bar is $2\mu \mathrm{m}$. Lower inset: TEP values taken at $V_g=-30\mathrm{V}$ (square) and $-5\mathrm{V}$ (circle). Dashed lines are linear fits to the data.

Figure 2

Measured TEP values (thick red lines) and TEP values calculated with the Mott formula (thin black lines) using Eq. (1) as a function of applied gate voltage for $T=200\mathrm{K}$ (a), 40 K (b), and 15 K (c).

Figure 3

(a) Hall conductance, (b) longitudinal TEP $S_{xx}$, and (c) transverse TEP $S_{yx}$ as a function of $V_g$ and $B$ at $T=10\mathrm{K}$. The insets show the electrode configurations for $S_{xx}$ and $S_{yx}$ measurement, respectively. (d) $R_{xx}$, (e) $R_{xy}$, (f) $S_{xx}$, and (g) $S_{yx}$ as a function of $V_g$ at a fixed magnetic field $B=8.8\mathrm{T}$ and $T=4.2\mathrm{K}$. The vertical dotted lines indicate filling factors corresponding to $\nu =\pm 2,\pm 6,\pm 10,\pm 14$. All the data are averaged with respect to positive and negative values of magnetic field in order to remove mixing between longitudinal and transverse components.

Figure 4

(a) Temperature dependence of the $S_{xx}/T$ as a function of $V_g$ at $B=8.8\mathrm{T}$. (b) Measured $S_{xx}$ (thick red line) and the $S_{xx}$ predicted by the generalized Mott relation (thin black line) at $B=8.8\mathrm{T}$ and $T=4.2\mathrm{K}$ showing deviations near the $N=0$ LL. Inset: Corresponding $S_{yx}^{\mathrm{measured}}$ and $S_{yx}^{\mathrm{Mott}}$.