Nonequilibrium linked cluster expansion for steady-state quantum transport

Abstract

We generalize the linked cluster expansion of Matsubara Green functions into nonequilibrium situations. This allows us to compute nonequilibrium correlation functions and, consequently, physical observables for interacting quantum systems with intermediate interaction strengths. As a specific example, we study nonlinear dc transport in a resonant tunneling system with electron-phonon interaction. The first-and second-order nonequilibrium cluster approximations are explicitly evaluated. The results are compared with those obtained by the standard nonequilibrium Green functions approach within the Migdal approximation for the self-energy and in the low-density limit also with the known exact solution. For moderately strong electron-phonon interactions the first-order linked cluster approximation is more precise than the Migdal approach. The secondorder approximation appears to be problematic in the presence of the Fermi sea. ͓S0163-1829͑97͒02435-1͔

Resonant inelastic tunneling in molecular junctions

“…7 of Ref. 46. Note that our scheme in zero-order is similar to the NLCE approach of 46 (both approaches utilize a cumulant expansion).…”

“…However these works disregard the Fermi population in the leads as mentioned above. Another approach, the non-equilibrium linked cluster expansion (NLCE), is based on generalization of the linked cluster expansion to nonequilibrium situations 46 . This approach takes the contact population into account, but appears to be unstable for diagrammatic expansion beyond the lowest order.…”

Green Function Techniques in the Treatment of Quantum Transport at the Molecular Scale

“…The existing approaches are mean-field [131,132,133], or start from the exact solution for the isolated system and then treat tunneling as a perturbation [134,135,136,137,138,139,140]. The fluctuations beyond mean-field approximations were considered in Refs.…”

Resonant tunneling in a pulsed phonon field

“…The analysis has been conducted by the nonequilibrium linked cluster expansion, 12 generalized to the time domain. The distribution function for the pulsed phonon field, with a zero coherent component, has been constructed and the phonon correlation functions were described by the GKB Ansatz.…”

“…In the firstorder linked cluster approximation, NLCE gives reliable results for moderate interaction strengths. 12 For electrons coupled to LO phonons, the dimensionless electron-phonon coupling constant g, defined below Eq. ͑4͒, should satisfy g Ϸ0.3Ϫ1 ͑depending on the temperature͒.…”