Electronic Transport in Dual-Gated Bilayer Graphene at Large Displacement Fields

We study the electronic transport properties of dual-gated bilayer graphene devices. We focus on the regime of low temperatures and high electric displacement fields, where we observe a clear exponential dependence of the resistance as a function of displacement field and density, accompanied by a strong nonlinear behavior in the transport characteristics. The effective transport gap is typically 2 orders of magnitude smaller than the optical band gaps reported by infrared spectroscopy studies. Detailed temperature dependence measurements shed light on the different transport mechanisms in different temperature regimes.

Figure 1

(a) Optical image of a BLG (outlined by white line). $A$, $B$, $C$, and $D$ are contact electrodes and TG is a $1\mu \mathrm{m}$-wide top gate electrode. The red and black diagrams are setups for two and four probe measurements, respectively. (b) Schematic diagram of the measured device (not drawn to scale). (c) When BLG is subject to a transverse electric field, a potential difference is induced between top and bottom layers. (d) Band structure of freestanding BLG (dashed lines) and band structure of BLG subject to transverse electric field (solid lines).

Figure 2

(a) Differential resistance at zero bias as a function of top and back gate voltages at $T=300\mathrm{mK}$ (log-scale). The black horizontal (dashed) and black diagonal (solid) lines correspond to zero charge densities in non-top-gated and top-gated regions, respectively. (b) Cuts in (a) at different displacement fields $D$ (colored lines) and at $n=0$ (black line). Each cut corresponds to the lines in (a) with the same color. (c) 3D plot of (a). (d) Schematic band structure and $E_F$. As $D$ is varied at fixed $n$, the size of the band gap changes while $E_F$ remains fixed. We can also shift $E_F$ and keep the band gap constant by varying $n$ and keeping $D$ the same. (e) $I\mathrm{\text{−}}{V}_{\mathrm{SD}}$ characteristics at different values of $D$ for $n=0$ at $T=300\mathrm{mK}$. (f) The resistance as a function of carrier density and offset top gate voltages at various $D$’s. The black dashed lines are linear fits in log-scale. (g) The slope $\alpha$ of the linear fits in (f) as a function of $D$. The slope $\alpha$ decreases linearly with decreasing $D$.

Figure 3

(a) Conductivity as a function of inverse temperature from $4.2–100\mathrm{K}$. (b) Conductivity as a function of inverse temperature from 300 mK to 100 K. The black and red curves are the fits to the Eq. (1) with NNH and VRH terms, respectively. (c)–(f) The extracted parameters from the fits plotted as a function of $|D|$.