Symmetry in full counting statistics, fluctuation theorem, and relations among nonlinear transport coefficients in the presence of a magnetic field

We study the full counting statistics of electron transport through multiterminal interacting quantum dots under a finite magnetic field. Microscopic reversibility leads to a symmetry of the cumulant generating function, which generalizes the fluctuation theorem in the context of the quantum transport. Using the symmetry, we derive the Onsager-Casimir relations in the linear transport regime and universal relations among nonlinear transport coefficients. One of the measurable relations is that the nonlinear conductance, the second-order coefficient with respect to the bias voltage, is connected to the third current cumulant in equilibrium, which can be a finite and uneven function of the magnetic field for two-terminal noncentrosymmetric system.

Figure 1

(Color online) The flux dependence of nonlinear transport coefficients (the unit is $t/\hslash$). Parameters: $\epsilon =\mu$, $t/\Gamma =10$, and $t\beta =10$. Equations (32, 34) are satisfied. $L_{11,-}^{10}$ is always zero.