Interplay between energy dissipation and reservoir-induced thermalization in nonequilibrium quantum nanodevices

A solid state electronic nanodevice is an intrinsically open quantum system, exchanging both energy with the host material and carriers with connected reservoirs. Its out-of-equilibrium behavior is determined by a nontrivial interplay between electronic dissipation and decoherence induced by inelastic processes within the device, and the coupling of the latter to metallic electrodes. We propose a unified description, based on the density matrix formalism, that accounts for both these aspects, enabling us to predict various steady-state as well as ultrafast nonequilibrium phenomena, nowadays experimentally accessible. More specifically, we derive a generalized density-matrix equation, particularly suitable for the design and optimization of a wide class of electronic and optoelectronic quantum devices. The power and flexibility of this approach is demonstrated with the application to a photoexcited triple-barrier nanodevice.

Figure 1

A nanodevice as an intrinsically open quantum system, which can exchange energy with the host material (environment), and carriers with external reservoirs. Its nonequilibrium properties are determined by the nontrivial interplay between these two types of interactions.

Figure 2

Time evolution of the photoexcited carrier density across a realistic GaAs/AlGaAs triple-barrier nanodevice (well width $a_w=8$ nm, barrier width $a_b=2$ nm, and height $V_0=300$ meV). At $t=0$ photoexcited carriers are fully localized in the left well (lower panel). The subsequent transient dynamics (upper panel), corresponding to the solid-curve result in Fig. 3b, clearly shows an interwell tunneling dynamics characterized by a strong interplay between phase coherence and energy dissipation and decoherence processes (see text).

Figure 3

Ultrafast electro-optical response of a realistic GaAs/AlGaAs triple-barrier nanodevice (see lower panel in Fig. 2) sandwiched between its electric contacts: Current density $j$ across the central barrier (in units of its Landauer-Büttiker value $j_0$) as a function of time corresponding to an initial coherent superposition of the two resonant electronic states of the triple-barrier structure (${\epsilon }_1\simeq 48$ meV, ${\epsilon }_2\simeq 56$ meV) and to a quasiequilibrium carrier injection from the left contact only (total charge density $n\simeq 7\times {10}^{16}$ cm${}^{-3}$) in the mesoscopic limit (a), and in the presence of inelastic scattering processes (b), for three different values of the effective device length [$l=50$ nm (dashed curves), $l=1\mu$m (solid curves), and $l=20\mu$m (dotted curves)].