Fluctuation theorem and microreversibility in a quantum coherent conductor

Mesoscopic systems provide us a unique experimental stage to address nonequilibrium quantum statistical physics. By using a simple tunneling model, we describe the electron exchange process via a quantum coherent conductor between two reservoirs, which yields the fluctuation theorem (FT) in mesoscopic transport. We experimentally show that such a treatment is semiquantitatively validated in the current and noise measurement in an Aharonov-Bohm ring. The experimental proof of the microreversibility assumed in the derivation of FT is presented.

Figure 1

(a) Schematic picture of the mesoscopic conductor coupled to the two reservoirs in the nonequilibrium regime. ${\mu }_L$ and ${\mu }_R$ are the chemical potentials of the left and the right reservoirs, respectively. Mesoscopic transport based on the Landauer-Büttiker picture is schematically shown. When a conductor is biased, electrons injected from one of the reservoirs are either transmitted or reflected at the conductor, which yields finite current fluctuation [$\langle (\delta I){}^2\rangle \ne 0$]. (b) The transport can be also viewed as the electron exchange process between the two reservoirs.

Figure 2

(a) Current-voltage characteristic as a function of the bias voltage $V$. While Ohm’s law holds around $V=0$, the current $I$ is not linear at large $V$ and the $I-V$ characteristics can be decomposed into a polynomial of $V$ with coefficients $G_1$, $G_2$, $G_3,\dots$ as in Eq. (1). In this study we address $G_2$. This schematic graph shows the total current $I$, the $G_{1}V$ contribution, and the $1/2!G_2{V}^2$ contribution, in the solid, dashed, and dotted curves, respectively. The case with a negative $G_2$ is shown. (b) Similarly, the current noise spectral density $S$ (shown in the solid curve) can be expressed in a polynomial form of $V$ as in Eq. (2). The Johnson-Nyquist relation tells that $S(V=0)=S_0=4k_B{\mathit{TG}}_1$. This schematic graph shows the case with a negative $S_1$ in the dashed curve. Here we address the coefficient of the term linear in $V$ ($S_1$) and the relation between $S_1$ and $G_2$.

Figure 3

(a) Atomic force microscope (AFM) image of the AB ring fabricated by local oxidation using an AFM[33] on a GaAs/AlGaAs 2DEG with the experimental setup for the two-terminal current and noise measurements. (b) Image plot of the conductance of the ring as a function of $V_g$ and $B$ (in the lower panel). The upper panel shows the magnetoconductance at $V_g=-0.09$ V as indicated by a white line in the lower panel. (c) Conductance as a function of $V_g$ at $B=\pm 25$ mT [indicated by dashed lines in the lower panel of (b)]. (d) Equilibrium noise ($S_0$) as a function of $V_g$ at $B=\pm 25$ mT.

Figure 4

(a) $G_2$ obtained at $B=25$ and $-25$ mT is shown as a function of $V_g$. (b) $S_1$ obtained at $B=25$ and $-25$ mT is shown as a function of $V_g$. (c) The symmetrized components $G_2^S$ and $S_1^S$ are shown in the left and right axes. (d) The symmetrized components $G_2^S$ and $S_1^S$ are shown in the left and right axes. (e) $S_1^S$ is plotted against $2k_{B}T{G}_2^S$. The dotted line is the prediction. (f) $S_1^A$ is plotted against $6k_{B}T{G}_2^A$. The dotted line is the prediction.

Figure 5

(a) Based on the data shown in Fig. 4d $3k_{B}T(S_1^A-2k_B{\mathit{TG}}_2^A)$ and $2k_{B}T{S}_1^A$ are plotted as a function of $V_g$. (b) Similar plot is shown for the data set in Fig. 3 in Ref. 25. (c) $3k_{B}T(S_1^A-2k_B{\mathit{TG}}_2^A)$ vs $2k_{B}T{S}_1^A$ obtained at 125 and 450 mK.