Inelastic transient electrical currents and phonon heating in a single-level quantum dot system

Abstract

We present a theoretical study on inelastic transient electrical currents and the effects of phonon heating in a single-level quantum dot system weakly coupled to a localized vibration degree of freedom, using the nonequilibrium Green's function method under the wide-band-limit and the lowest-order-expansion approximations. The energy transfer between electron and phonon systems is evaluated using both approximations, which separately are exact in the limits of the equilibrium state (t < 0) and steady state (t→∞). The time-dependent phonon number, which determines the system temperature and heating effects on the inelastic current, is calculated using a phenomenological method employing the time-dependent power transfer. The two approximations are shown to provide qualitatively similar dynamical behaviors for the system temperature, which can be grouped under two responses: if the energy corresponding to the applied bias voltage is smaller than or equal to the phonon energy, the temperature first increases because of phonon emission, and then decreases because of phonon absorption; alternatively, if the energy corresponding to the bias voltage is larger than the phonon energy, the temperature increases monotonically until a steady state is reached. The total electrical current is suppressed by phonon heating, while heat transferring between dot and environment mitigates the effects of such heating. Furthermore, the relaxation time of the current is extended by phonon scattering and heating.

Spin polarized currents through a quantum dot: Non-equilibrium Green’s function simulations under Hartree approximation

“…For this model, we simulate the TD current using the NEGF technique under the wide band limit approximation, 6,7,10,[13][14][15]17,18) in which the level broadening due to ¡ electrode, À ; , is independent of energy ( ¼ L, R). In this technique, the spin component of the TD current from the QD into ¡ electrode is expressed as…”

“…Actually, nanosecond dynamics has been experimentally observed in a quantum capacitor, 1) a quantum point contact, [2][3][4] and a single-atom contact. 5) On the other hand, the simulation methods for time-dependent quantum transport have been developed, such as the non-equilibrium Green's function (NEGF) method, [6][7][8][9][10][11][12][13][14][15][16][17][18] Liouville equation, [19][20][21] and time-dependent density functional theory (TD-DFT). [22][23][24] Many of computational works have shown that the temporal oscillations of electrical current appear right after the sudden switching-on of voltage in a variety of nano-scale systems.…”

A many-body approach to transport in quantum systems: from the transient regime to the stationary state

“…In this context, also the partitioning protocols between the dot and the leads have been investigated [327] disentangling dynamical charge rearrangements due to the dot-lead contacting. Phonons or vibrons may also induce or mediate dynamical effects, such as spin-flip processes [478], heating [479,480] or electron correlations [481].…”

A many-body approach to transport in quantum systems: From the transient regime to the stationary state

“…In this context, also the partitioning protocols between the dot and the leads have been investigated [280] disentangling dynamical charge rearrangements due to the dot-lead contacting. Phonons or vibrons may also induce or mediate dynamical effects, such as spin-flip processes [434], heating [435,436] or electron correlations [437] Modeling the electron-phonon coupling can also be extended to larger systems. Nuclear dynamics in a quantum transport setup of atomic-ring structures were investigated in Ref.…”