Warming in systems with a discrete spectrum: Spectral diffusion of two-dimensional electrons in a magnetic field

Abstract

Warming in complex physical systems, in particular global warming, attracts significant contemporary interest. It is essential, therefore, to understand basic physical mechanisms leading to overheating. It is well known that application of an electric field to conductors heats electric charge carriers. Often an elevated electron temperature describes the result of the heating. This paper demonstrates that an electric field applied to a conductor with discrete electron spectrum produces a non-equilibrium electron distribution, which cannot be described by temperature. Such electron distribution changes dramatically the conductivity of highly mobile two dimensional electrons in a magnetic field, forcing them into a state with a zero differential resistance. Most importantly the results demonstrate that, in general, the effective overheating in the systems with discrete spectrum is significantly stronger than the one in systems with continuous and homogeneous distribution of the energy levels at the same input power.

Nonlinear resistance of two-dimensional electrons in crossed electric and magnetic fields

“…The effect, existing in a broad range of temperatures, can not be explained by an increase of the electron temperature due to the heating by the electric field E [11,54]. In the paper [11] the effect is attributed to a non-uniform spectral diffusion of the 2D electrons induced by the electric field [28].…”

“…Despite the apparent applicability of the T e approximation to the overheated electron systems, recent studies have revealed an inadequacy of the temperature description of the nonlinear transport of highly mobile 2D carriers [11,52,54]. Instead of the T e approximation in this paper we use a different approach [28].…”

Dynamics of quantal heating in electron systems with discrete spectra

“…This effect, called quantal heating, does not exist in classical electron systems. The most essential property of quantal heating is the conservation of the total number of quantum states participating in the electron transport and, thus, the conservation of the overall broadening of the electron distribution 2,3 . In contrast to classical Joule heating, quantal heating leads to outstanding nonlinear transport properties of highly mobile 2D electrons, driving them into exotic nonlinear states in which voltage (current) does not depend on current 4 (voltage) 5 .…”

“…Recently it was shown that the quantum properties of matter significantly affect the heating 1,2 , giving rise to a thermal stratification (quantization) of the electron distribution in energy space 3 . This effect, called quantal heating, does not exist in classical electron systems.…”

Zero-differential conductance of two-dimensional electrons in crossed electric and magnetic fields

“…At I dc > I th the differential resistance stays at zero value in a broad range of electric currents I dc > I th , significantly exceeding the threshold value I th . The initial drop of the resistance is associated with a quantal heating induced by the spectral diffusion of 2D electrons in crossed electric and magnetic fields [7][8][9][10] . The transition into the ZDR state is attributed to the local instability of the electric current at I dc > I th 11 .The local instability is considered to be the origin of another spectacular phenomenon -the zero resistance state observed in highly mobile 2D electron systems under a microwave irradiation [12][13][14] .…”