Hanbury-Brown and Twiss exchange and non-equilibrium-induced correlations in disordered, four-terminal graphene-ribbon conductor

Abstract

We have investigated current-current correlations in a cross-shaped conductor made of graphene. The mean free path of charge carriers is on the order of the ribbon width which leads to a hybrid conductor where there is diffusive transport in the device arms while the central connection region displays near ballistic transport. Our data on auto and cross correlations deviate from the predictions of Landauer-Büttiker theory, and agreement can be obtained only by taking into account contributions from non-thermal electron distributions at the inlets to the semiballistic center, in which the partition noise becomes strongly modified. The experimental results display distinct Hanbury - Brown and Twiss (HBT) exchange correlations, the strength of which is boosted by the non-equilibrium occupation-number fluctuations internal to this hybrid conductor. Our work demonstrates that variation in electron coherence along atomically-thin, two-dimensional conductors has significant implications on their noise and cross correlation properties.

Figure 1

Left: False color scanning electron micrograph of the measured GNR sample; green color marks graphene and blue denotes the silicon oxide substrate. Terminals 1 and 3 were employed for cross correlation while bias was supplied via 2 and 4 in the HBT experiments. The white scale bar corresponds to 100 nm. The overlaid arrows define the straight and bent carrier paths with conductances of $G_p$ and $G_t$ in the central region, respectively, for electrons coming from terminal 1; the same definition of $G_p$ and $G_t$ repeats for electrons coming from each terminal. Right: Schematic illustration of our theoretical model with its most essential features: $G_0$ denotes the average arm conductance, $\widehat{G}$ describes the transport in the semiballistic central region, $f_i^c$ and ${\varphi }_i^c$ mark the non-equilibrium distribution and the local voltage at the contact point between the diffusive arm and the central region, and $f_0(E)$ denotes the Fermi distribution. In the diffusive arm, the distribution function varies as $f_i(x,E)=\left(1-\frac{x}{L}\right)f_0(E-e{V}_i)+\frac{x}{L}{f}_i^c(E)$. For details, see text.

Figure 2

Theoretically calculated HBT effect $\mathrm{\Delta }S/(S_A+S_B)$ as a function of $G_p/G_0$ and $G_t/G_0$. In our analysis we are using the overlaid trace for $\mathrm{\Delta }S/(S_A+S_B)$ on the diagonal at which $G_p=G_t$.

Figure 3

Conductance $G=I/V$ vs. $V_g$ measured at $V_b=30$ mV using the bias configuration C: Ingoing currents $I_2$ and $I_4$ are positive, while $I_1<0$ and $I_3<0$. The inset at $V_g=-30$ V displays negative bend voltage $V_{bend}=V_{\mathrm{1,2}}$, where the bias is fed between terminals 4 and 3 and the voltage is measured across terminals 1 and 2.

Figure 4

Ratio of $S_{13}/S_{11}$ vs. $V_g$ with bias applied via terminal 1 having the other terminals DC grounded. The two data sets, light and dark, relate to $V_b\lessgtr 0$, respectively: their difference is indicative of the small uncertainty in the data. The dashed line indicates the result from our HCL model with $G_p/G_0=3.4$. Our data deviates from the diffusive theory value 1/3 as shown in the dot line. The fluctuations in the data are related to universal noise fluctuations. The inset displays the calculated behavior of $S_{13}/S_{11}$ vs. the ratio $G_p/G_0$ (at $G_p/G_t=1$).

Figure 5

HBT exchange correction $\mathrm{\Delta }S$ vs. $V_g$ obtained from low-bias cross correlation experiments extrapolated to $V_b\to 0$. The solid line indicates our HCL model result $\mathrm{\Delta }S/(S_A+S_B)=-0.175$ using $G_p/G_0=3.4$. The inset displays the linear dependence of $\mathrm{\Delta }S$ on $V_b$ measured at $V_g=-30$ V.