Fluctuation theorem in a quantum-dot Aharonov-Bohm interferometer

In the present study, we investigate the full counting statistics in a two-terminal Aharonov-Bohm interferometer embedded with an interacting quantum dot. We introduce a nonequilibrium saddle-point solution for a cumulant-generating function, which satisfies the fluctuation theorem and accounts for the interaction in the mean-field level approximation. The approximation properly leads to the following two consequences. (i) The nonlinear conductance can be an uneven function of the magnetic field for a noncentrosymmetric mesoscopic system. (ii) The nonequilibrium current fluctuations couple with the charge fluctuations via the Coulomb interaction. As a result, nontrivial corrections appear in the nonequilibrium current noise. Nonlinear transport coefficients satisfy universal relations imposed by microscopic reversibility, though the scattering matrix itself is not reversible. When the magnetic field is applied, the skewness in equilibrium can be finite owing to the interaction. The equilibrium skewness is an odd function of the magnetic field and is proportional to the asymmetric component of the nonlinear conductance. The universal relations predicted can be confirmed experimentally.

Figure 1

(Color online) (a) AB phase dependent nonequilibrium charge accumulation. (inset) Quantum-dot AB interferometer. Mirror symmetry along the horizontal axis (dotted line) is absent. (b) Demonstration of the fluctuation theorem [Eq. (3)]. The inset shows probability distributions for positive and negative magnetic fields. Parameters: ${\Gamma }_{\text{L}}/\Gamma =0.25$, ${\Gamma }_{\text{R}}/\Gamma =0.75$, $t_{\text{ref}}=0.25$, ${ϵ}_{\text{D}}=0$, and $U=T=V=\Gamma$.

Figure 2

(Color online) (a) Aharonov-Bohm flux dependent third-order nonlinear transport coefficients and (b) the extension of the Onsager relations. The parameters are the same as those in Fig. 1.