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Physical Review Letters

Interaction Induced Electron Self-Interference in a Semiconductor: The Phonon Staircase Effect

J. A. Kenrow, K. El Sayed, C. J. Stanton

Published Jun 23, 1997• 13 citations
Publisher

Abstract

The exact quantum mechanics of a model semiconductor system of an electron with a discrete and equidistant energy spectrum interacting with a single phonon mode is presented. An electron initially excited into a coherent superposition of states interacts with phonons thereby creating a self-interference in time which reduces the emission of phonons to isolated bursts. This self-interference effect gives rise to steplike behavior in the relaxation kinetics of the electron and phonons. We show that this ``phonon staircase'' effect is a consequence of a correlated initial electron distribution and the violation of energy conservation in the electron-phonon interaction on short time scales.

DOI
10.1103/physrevlett.78.4873

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The exact quantum mechanics of a model semiconductor system of an electron with a discrete and equidistant energy spectrum interacting with a single phonon mode is presented. An electron initially excited into a coherent superposition of states interacts with phonons thereby creating a self-interference in time which reduces the emission of phonons to isolated bursts. This self-interference effect gives rise to steplike behavior in the relaxation kinetics of the electron and phonons. We show that this ``phonon staircase'' effect is a consequence of a correlated initial electron distribution and the violation of energy conservation in the electron-phonon interaction on short time scales.
We study the relaxation of the Holstein model after a sudden switch-on of the interaction by means of the nonequilibrium dynamical mean field theory, with the self-consistent Migdal approximation as an impurity solver. We show that there exists a qualitative change in the thermalization dynamics as the interaction is varied in the weak-coupling regime. On the weaker interaction side of this crossover, the phonon oscillations are damped more rapidly than the electron thermalization time scale, as determined from the relaxation of the electron momentum distribution function. On the stronger interaction side, the relaxation of the electrons becomes faster than the phonon damping. In this regime, despite long-lived phonon oscillations, a thermalized momentum distribution is realized temporarily. The origin of the ``thermalization crossover'' found here is traced back to different behaviors of the electron and phonon self-energies as a function of the electron-phonon coupling. In addition, the importance of the phonon dynamics is demonstrated by comparing the self-consistent Migdal results with those obtained with a simpler Hartree-Fock impurity solver that neglects the phonon self-energy. The latter scheme does not properly describe the evolution and thermalization of isolated electron-phonon systems.
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We present a new approach to quantum kinetics based on a Schr\"odinger's equation formalism. As an example we apply this method to a coupled electron-LO phonon system in a semiconductor. We demonstrate that it is possible to compute the full many-body wave function of the electron-phonon system for short times. The time-dependent electron probability distribution, extracted from the many-body wave function, illustrates the non-Markovian nature of the early time kinetics. The retarded onset of dissipation and kinetic energy overshoots are explained through virtual, nonresonant transitions.
We study theoretically electron transients in semiconductor alloys excited by light pulses shorter than 100 fs and tuned above the absorption edge during and shortly after the pulse, when disorder scattering is dominant. We use nonequilibrium Green functions employing the field-dependent self-consistent Born approximation. The propagators and the particle correlation function are obtained by a direct numerical solution of the Dyson equations in differential form. For the purely elastic scattering in our model system the solution procedures for the retarded propagator and for the correlation function can be decoupled. The propagator is used as an input in calculating the correlation function. Numerical results combined with a cumulant expansion permit one to separate in a consistent fashion the dark and the induced parts of the self-energy. The dark behavior reduces to propagation of strongly damped quasiparticles; the field induced self-energy leads to an additional time nonlocal coherence. The particle correlation function is formed by a coherent transient and an incoherent back-scattered component. The particle number is conserved only if the field induced coherence is fully incorporated. The transient polarization and the energy balance are also obtained and interpreted.
Abstract. We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction. 1. Introduction and
We study electron-phonon interaction induced decoherence between two-electron singlet and triplet states in a semiconductor double quantum dot using a spin-boson model. We investigate the onset and time evolution of this dephasing, and study its dependence on quantum dot parameters such as dot size and double dot separations, as well as the host materials (GaAs and Si). At the short time limit, electron-phonon interaction only causes an incomplete initial Gaussian decay of the off-diagonal density matrix element in the singlet-triplet Hilbert space; a complete long-time exponential decay due to phonon relaxation would eventually dominate over two-spin decoherence. We analyze two-spin decoherence in both symmetric and biased double quantum dots, identifying their difference in electron-phonon coupling and the relevant consequences.