We present a combined theoretical approach to study the nonequilibrium transport properties of nanoscale systems coupled to metallic electrodes and exhibiting strong electron-phonon interactions. We use the Keldysh Green function formalism to generalize beyond linear theory in the applied voltage an equation of motion method and an interpolative self-energy approximation previously developed in equilibrium. We analyze the specific characteristics of inelastic transport appearing in the intensity versus voltage curves and in the conductance, providing qualitative criteria for the sign of the step-like features in the conductance. Excellent overall agreement between both approaches is found for a wide range of parameters.
Introduction (2) Experimental background: Test beds (8) Theoretical approaches: A microscopic model(10) The electron-phonon coupling(14)Time and energy scales(15) Theoretical methods(19)Numerical calculations(28) Incoherent vs. coherent transport (28) Inelastic tunneling spectroscopy: Experimental background(31) Theoretical considerations:the weak coupling limit(36) Theoretical considerations: moderately strong coupling(41)Comparison of approximation schemes(48)Asymmetry in IETS(51)The origin of dips in IETS signals(53)Computational approaches (56) Effects of electron-electron(e-e)interactions (63) Noise (66) Non-linear conductance phenomena (73) Heating and heat conduction: General considerations(77) Heat generation(81) Heat conduction(85) Junction temperature(88) Current induced reactions (91) Summary and outlook (91)
In the present work, we theoretically analyze the steady-state thermoelectric transport through a single-molecule junction with a vibrating bridge. Thermally induced charge current in the system is explored using a nonequilibrium Greens functions formalism. We study combined effects of Coulomb interactions between charge carriers on the bridge and electron-phonon interactions on the thermocurrent beyond the linear response regime. It is shown that electron-vibron interactions may significantly affect both magnitude and direction of the thermocurrent, and vibrational signatures may appear.
The efficiency of optical emitters can be dramatically enhanced by reducing the effective mode volume (the Purcell effect). Here we predict an analogous enhancement for electron-phonon (el-ph) scattering, achieved by compressing the electronic Wannier orbitals. Reshaping of Wannier orbitals is a prominent effect in graphene moire superlattices (SLs) where the orbitals are tunable by the twist angle. A reduction of the orbital effective volume leads to an enhancement in the effective el-ph coupling strength, yielding the values considerably bigger than those known for pristine monolayer graphene. The enhanced coupling boosts the el-ph scattering rates, pushing them above the values predicted from the enhanced spectral density of electronic excitations. The enhanced phonon emission and scattering rates are manifest in the observables such as electron-lattice cooling and the linear-$T$ resistivity, both of which are directly tunable by the moire twist angle.
Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are direct (n=0) and exchange (n different from 0) terms, which are algebraically small in a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.
We develop a numerically exact scheme for resumming certain classes of Feynman diagrams in the self-consistent perturbation expansion for the electron and magnon self-energies in the nonequilibrium Green function formalism applied to a coupled electron-magnon (mbox{e-m}) system which is driven out of equilibrium by the applied finite bias voltage. Our scheme operates with the electronic and magnonic GFs and the corresponding self-energies viewed as matrices in the Keldysh space, rather than conventionally extracting their retarded and lesser components. This is employed to understand the effect of inelastic mbox{e-m} scattering on charge and spin current vs. bias voltage $V_b$ in F/I/F magnetic tunnel junctions (MTJs), which are modeled on a one-dimensional (1D) tight-binding lattice for the electronic subsystem and 1D Heisenberg model for the magnonic subsystem. For this purpose, we evaluate Fock diagram for the electronic self-energy and the electron-hole polarization bubble diagram for the magnonic self-energy. The respective electronic and magnonic GF lines within these diagrams are the fully interacting ones, thereby requiring to solve the ensuing coupled system of nonlinear integral equations self-consistently. Despite using the 1D model and treating mbox{e-m} interaction in many-body fashion only within a small active region consisting of few lattice sites around the F/I interface, our analysis captures essential features of the so-called zero-bias anomaly observed in both MgO- and AlO$_x$-based realistic 3D MTJs where the second derivative $d^2 I/dV_b^2$ (i.e., inelastic electron tunneling spectrum) of charge current exhibits sharp peaks of opposite sign on either side of the zero bias voltage.