Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira–Leggett Hamiltonian

Abstract

The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of non-perturbative and non-Markovian treatment. We employ a Caldeira-Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study non-Markovian and nonperturbative thermal effects at finite temperature in a rigorous manner. We study current variation in time and the current-voltage (I -V ) relation of the resonant tunneling diode for several widths of the contact region, which consists of doped GaAs. Hysteresis and both single and double plateau-like behavior are observed in the negative differential resistance (NDR) region. While all of the current oscillations decay in time in the NDR region in the case of a strong system-bath coupling, there exist self-excited high-frequency current oscillations in some parts of the plateau in the NDR region in the case of weak coupling. We find that the effective potential in the oscillating case possesses a basin-like form on the emitter side (emitter basin) and that the current oscillation results from tunneling between the emitter basin and the quantum well in the barriers.

Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities

“…[62][63][64] Because the HEOM approach is computationally heavy, a variety of algorisms have been developed to deal with dissipative dynamics in realistic situations. [65][66][67][68][69][70][71][72] It has been applied to the study of multi-dimensional vibrational spectroscopies, [52][53][54][55] photosynthetic antenna systems, [58][59][60][73][74][75][76] fermion systems, [77][78][79] quantum ratchets, 80 resonant tunneling diodes, 81,82 and dissociation of tightly bounded electron-hole pairs. 83 While the applicability of the HEOM approach continues to expand, the basic nature of the hierarchy elements has not been thoroughly explored.…”

Coulomb-driven terahertz-frequency intrinsic current oscillations in a double-barrier tunneling structure

“…To get a qualitative picture of the mechanism behind the current oscillations, several authors have previously solved the time-independent Schrödinger equation (obtained eigenstates and energies) for a sub-region of the device in question 17,18,40 . Here, we do the same.…”

“…In contrast, as shown earlier in this section, we found that current oscillations are driven by the time-dependent potential difference between the EQW and MQW. Sakurai and Tanimura worked within a hierarchy-equationof-motion formalism and also observed intrinsic current oscillations in RTDs 18,19 . To explain their results, they performed a similar bound-state analysis.…”

“…Zhao et al 17 proposed a mechanism that emphasized the importance of the formation of a quantum well on the emitter side of the device (the emitter quantum well, EQW) and connected the frequency of the oscillations to the average energy spacing between the bound states in the EQW and the main quantum well (MQW). The work of Jensen and Buo 13 and others [14][15][16]18,19 on intrinsic current oscillations focused on RTDs with a traditional doping profile (no doping in the region around the well and barriers), where the EQW only forms at low temperature (77 K or below) and in a narrow bias window. For this reason, and due to thermal broadening effects, it has been argued that intrinsic current oscillations could only occur at low temperatures 17 .…”

Efficient method to generate time evolution of the Wigner function for open quantum systems

“…Both forms are difficult to solve and, as a result, a plethora of numerical methods for evolving the Wigner function propagation have been developed. These have involved (i) the integral form of Moyal's equation [20][21][22][23][24][25], (ii) reduction of the Moyal equation to a Boltzmann-like equation [26,27], (iii) propagation of Gaussian and coherent states [28][29][30][31], (iv) Monte Carlo schemes in which the Wigner function is contracted by averaging over stochastic trajectories of pure-states [32][33][34][35], and (v) evolving the density matrix in the coordinate representation [36,37].…”