Full counting statistics for transport through a molecular quantum dot magnet

TL;DR

This paper derives an analytical expression for the full counting statistics of charge transport through a molecular quantum dot magnet in the incoherent tunneling regime, considering spin interactions and Coulomb blockade effects.

Contribution

It introduces a novel analytical method to compute the full counting statistics for a quantum dot magnet system with arbitrary spin s, using eigenvalue analysis of a modified master equation.

Findings

Analytical FCS generating function derived for specific spin configurations.

Quartic relations among Clebsch-Gordan coefficients simplify the eigenvalue problem.

Numerical contour plots of charge-current distribution functions provided.

Abstract

Full counting statistics (FCS) for the transport through a molecular quantum dot magnet is studied theoretically in the incoherent tunneling regime. We consider a model describing a single-level quantum dot, magnetically coupled to an additional local spin, the latter representing the total molecular spin s. We also assume that the system is in the strong Coulomb blockade regime, i.e., double occupancy on the dot is forbidden. The master equation approach to FCS introduced in Ref. [12] is applied to derive a generating function yielding the FCS of charge and current. In the master equation approach, Clebsch-Gordan coefficients appear in the transition probabilities, whereas the derivation of generating function reduces to solving the eigenvalue problem of a modified master equation with counting fields. To be more specific, one needs only the eigenstate which collapses smoothly to the zero-eigenvalue stationary state in the limit of vanishing counting fields. We discovered that in our problem with arbitrary spin s, some quartic relations among Clebsch-Gordan coefficients allow us to identify the desired eigenspace without solving the whole problem. Thus we find analytically the FCS generating function in the following two cases: i) both spin sectors lying in the bias window, ii) only one of such spin sectors lying in the bias window. Based on the obtained analytic expressions, we also developed a numerical analysis in order to perform a similar contour-plot of the joint charge-current distribution function, which have recently been introduced in Ref. [13], here in the case of molecular quantum dot magnet problem.