Current-conserving and gauge-invariant quantum ac transport theory in the presence of phonon

Abstract

Using the nonequilibrium Green's function (NEGF) approach, we develop a microscopic ac transport theory in the presence of electron-phonon interaction. Taking into account the self-consistent Coulomb interaction, the displacement current is included. This ensures that our theory satisfies the current-conserving and gauge-invariant conditions. Importantly, the inclusion of self-consistent Coulomb interaction naturally connects the NEGF formalism to the density functional theory (DFT). This allows us to calculate the self-consistent Hamiltonian using DFT within the NEGF framework, which paves the way for first principles ac transport calculation of nanoelectronic devices in the presence of electron-phonon interaction. It is known that the inelastic electron tunneling spectroscopy (IETS) is a powerful tool in studying the inelastic dc quantum transport in molecular devices. The basic idea of IETS is to obtain the information of vibrational spectrum of molecular devices by measuring the second derivative of the dc current with respect to the bias voltage. In the ac transport, we find that the phonon spectrum and electron-phonon coupling strength can be obtained from the second derivative of the admittance with respect to the frequency which is the working principle of the inelastic electron admittance spectroscopy (IEAS). Hence we propose to use IEAS to probe the effect of the phonon in ac transport. As an example, dynamic conductance of a quantum dot is discussed in detail and the concept of IEAS is demonstrated.

Efficient quantum modeling of inelastic interactions in nanodevices

“…Among them the non-equilibrium Green's function (NEGF) formalism appears as one of the most efficient methods to include interactions in quantum transport codes using the concept of self-energies 7 . This approach has been successfully applied to various nano-structures and devices, including quantum dots 8,9 , molecular junctions 10 , 2D materials 11 , resonant tunneling diodes 12 , semiconductor transistors [13][14][15][16][17][18][19] and solar cells [20][21][22] . Despite significant improvements the NEGF method still requires heavy computational resources when dealing with interactions in realistic nanostructures.…”

Current conserving theory for frequency dependent noise power under dc bias

“…The continuity equation can also be obtained from the equation of motion showing the consistency of our theory (see equation(65)of[18]). …”

Are Current Discontinuities in Molecular Devices Experimentally Observable?

“…For example, if a fraction η of a charge q oscillating along the z-axis over a distance 2a lacks a corresponding current, the predicted maximum longitudinal field (along z) is E L,max = 2ηω 2 qa/(c 2 r). It is tempting to speculate that this kind of oscillations could happen in graphene-based nanojunctions or carbon nanowires [21,22,[44][45][46].…”