High Conductance 2D Transport around the Hall Mobility Peak in Electrolyte-Gated Rubrene Crystals

We report the observation of the Hall effect at hole densities up to $6\times {10}^{13}{\mathrm{cm}}^{-2}$ ($0.3\text{holes}/\text{molecule}$) on the surface of electrolyte-gated rubrene crystals. The perplexing peak in the conductance as a function of gate voltage is confirmed to result from a maximum in mobility, which reaches $4{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at $2.5\times {10}^{13}{\mathrm{cm}}^{-2}$. Measurements to liquid helium temperatures reveal that this peak is markedly asymmetric, with bandlike and hopping-type transport occurring on the low density side, while unconventional, likely electrostatic-disorder-affected transport dominates the high density side. Most significantly, near the mobility peak the temperature coefficient of the resistance remains positive to as low as 120 K, the low temperature resistance becomes weakly temperature dependent, and the conductance reaches within a factor of 2 of $e^2/h$, revealing conduction unprecedentedly close to a two-dimensional metallic state.

Figure 1

(a) Cross-sectional device structure of a rubrene EDLT. (b) Optical micrograph of a rubrene EDLT in a Hall-bar configuration. (c) Transfer characteristics of Device #1 at 240 K with a sweep rate of $50\mathrm{mV}/\mathrm{s}$: (left axis, squares) $I_D\text{−}{V}_G$ plot on linear-linear scale at $V_D=-0.1\mathrm{V}$ and (right axis, lines) same $I_D\text{−}{V}_G$ plot on log-linear scale. (d) 240 K $V_G$-dependent hole density $p_{\text{gate}}$ (red, left axis) and mobility ${\mu }_{\text{gate}}$ (black, right axis). $p_{\text{gate}}$ is measured from the gate displacement current.

Figure 2

(a) Hall voltage ($V_{\text{Hall}}$) (black circles) and ${\mu }_{0}H$ (red lines) as a function of time at $V_G=-0.5\mathrm{V}$ and a source current of 100 nA. (b) Hall resistance ($R_{\text{Hall}}$) versus field (${\mu }_{0}H$) for $V_G=0.2\mathrm{V}$ (black circles) and $-0.75\mathrm{V}$ (red triangles). $R_{\text{Hall}}$ has been bin averaged and the zero-field value has been subtracted; solid lines are linear fits. (c) Hole density measured from Hall effect ($p_{\text{Hall}}$) and displacement current ($p_{\text{gate}}$), (d) Hall mobility (${\mu }_{\text{Hall}}$) and (e) four-terminal channel sheet resistance ($R$) as a function of $V_G$. All results are measured on Device #1.

Figure 3

(a) ${\mu }_{\text{Hall}}\text{−}{p}_{\text{Hall}}$ relation in Device #2 at 200 K. Each $p_{\text{Hall}}$ is labeled $a$ through $h$. Insets: ${\mu }_{\text{Hall}}(T)$ before the mobility peak ($c$), at the peak ($e$), and after the peak ($g$). (b) Temperature dependence of the sheet resistance $R$ at each $p_{\text{Hall}}$ shown in (a).

Figure 4

(a) ${\log }_{10}(R)$ vs $T^{-1}$ for $p_{\text{Hall}}$ from $a$ to $f$. Inset: low-$T$ activation energy $E_A$ as a function of $p_{\text{Hall}}$. Horizontal dashed line is $k_{B}T$ at the minimum temperature probed. (b) ${\log }_{10}(R)$ vs ${\log }_{10}(T)$ for $p_{\text{Hall}}$ from $g$ to $h$. Inset: sheet conductance $G$ as a function of $T$ for $d$, $e$, and $f$.