Effect of temperature on resonant electron transport through stochastic conduction channels in superlattices

Abstract

We show that resonant electron transport in semiconductor superlattices with an applied electric and tilted magnetic field can, surprisingly, become more pronounced as the lattice and conduction electron temperature increases from 4.2 K to room temperature and beyond. It has previously been demonstrated that at certain critical field parameters, the semiclassical trajectories of electrons in the lowest miniband of the superlattice change abruptly from fully localised to completely unbounded. The unbounded electron orbits propagate through intricate web patterns, known as stochastic webs, in phase space, which act as conduction channels for the electrons and produce a series of resonant peaks in the electron drift velocity versus electric field curves. Here, we show that increasing the lattice temperature strengthens these resonant peaks due to a subtle interplay between thermal population of the conduction channels and transport along them. This enhances both the electron drift velocity and the influence of the stochastic webs on the current-voltage characteristics, which we calculate by making self-consistent solutions of the coupled electron transport and Poisson equations throughout the superlattice. These solutions reveal that increasing the temperature also transforms the collective electron dynamics by changing both the threshold voltage required for the onset of self-sustained current oscillations, produced by propagating charge domains, and the oscillation frequency.

Effects of classical stochastic webs on the quantum dynamics of cold atomic gases in a moving optical lattice

“…Perturbing a simple harmonic oscillator by a plane wave whose frequency is commensurate with the oscillator frequency has been shown to rapidly excite the oscillator [17][18][19][20][21][22][23][24][25][26]. This resonant heating manifests itself experimentally in, for example, enhanced electron transport in semiconductor superlattices [20][21][22][23][24][25][26][27] and heating in Tokamak fusion reactors [17][18][19]28].…”

“…It is well known that the phase space of a harmonic oscillator driven by a plane wave whose angular frequency is an integer multiple of the unperturbed harmonic-oscillator frequency is threaded by a continuous stochastic web within which the motion is unstable [17][18][19][20][21][22][23][24][25][26]29]. Each stochastic web is characterized by an infinite number of circular filaments connected by 2R radial filaments.…”

“…Stochastic webs have analytically defined structures that can be determined by expanding the Hamiltonian of the driven harmonic oscillator into Bessel functions and finding the stationary points of the system [29]. The concentric ring-shaped filaments have radii given Stochastic webs are important in many branches of physics, including plasma dynamics, Tokamak fusion, quasi crystals, condensed-matter quantum devices, and analogous optical and atomic systems [17][18][19][20][21][22][23][24][25][26]29]. One reason for this interest is that the radial filaments provide chaotic pathways along which the oscillator can diffuse, thus attaining higher ρ values and gaining energy from the plane wave.…”

“…This resonant heating manifests itself experimentally in, for example, enhanced electron transport in semiconductor superlattices [20][21][22][23][24][25][26][27] and heating in Tokamak fusion reactors [17][18][19]28]. The excitation of the oscillator is due to the resonant creation of intricate phase-space structures known as "stochastic webs" [17][18][19][20][21][22][23][24][25][26]29], which enable the oscillator to diffuse through the web filaments away from the web center, thereby gaining energy and becoming delocalized in real space.…”

Sub-terahertz amplification in a semiconductor superlattice with moving charge domains

“…Equation (3) is obtained by averaging of the Esaki-Tsu formula for drift velocity 12 with respect to the MaxwellBoltzmann distribution of the initial electron momentums at the given temperature T. 33 Here, I 0,1 (.) are the modified Bessel functions of the first kind, k B and h are the Boltzmann and the Planck constants, and d is the spatial period of the SL.…”