Electron-electron scattering and resistivity of ballistic multimode channels

Abstract

We show that electron-electron scattering gives a positive contribution to the resistivity of ballistic multimode wires whose width is much smaller than their length. This contribution is not exponentially small at low temperatures and therefore may be experimentally observable. It scales with temperature as T 2 for three-dimensional channels and as T 5/2 for two-dimensional ones.

Statistical theory of relaxation of high-energy electrons in quantum Hall edge states

“…where the superscript F indicates the use of the Ansatz (40). Thus, the energy smearing around the inner and outer ES's Fermi level is simply the effective temperature, also out-ofequilibrium for x > 0.…”

“…(39) to build the basic equations for the effective temperatures T i (x) and T o (x). The Ansatz (40) allows us to evaluate the left-hand sides of Eqs. (39b) and (39c), i.e.…”

“…21 Similar models for other quasi-one-dimensional systems have also recently been studied. 28,[31][32][33][34][35][36][37][38][39][40][41][42][43] Here we discuss the relaxation of high energy electrons injected locally by a side-coupled QD into one of two ESs (ν = 2). This gives a narrow peak in the ES's energy distribution high above the Fermi level [Fig.…”

Electron-electron scattering and conductance of long many-mode channels

“…This suggests that the electron-electron scattering may affect the current in finite-length conducting channels even in the case of a specular reflection from the walls. Recently, the correction to the conductance of a narrow multichannel ballistic conductor was calculated for the weak electron-electron scattering [10]. This correction appeared to be negative and resulted from pairwise collisions that changed the number of electrons moving to the right and to the left, i. e. whose projection of the velocity on the channel axis was positive or negative (see Fig.…”

“…As the calculations in Ref. [10] were performed in the lowest approximation in the electron-electron scattering, the resulting correction to the conductance was proportional to the length of the channel. However, it was not clear whether the conductance tends to zero with increasing length of the channel or stops to decrease at some finite value.…”