Possible mechanism of the fractional conductance quantization in a one-dimensional constriction

Abstract

As it is well known there may arise situations when an interaction between electrons is attractive. A weak attraction should manifest itself strongly in 1D systems, since it can create two-electron bound states. This paper interprets the 0.7 $(2e^2/h)$ conductance structure, observed recently in a one-dimensional constriction, as a manifestation of two-electron bound states formed in a barrier saddle-point. The value 0.75 $(2e^2/h)$ follows naturally from the 3:1 triplet-singlet statistical weight ratio for the two-electron bound states, if the triplet energy is lower. Furthermore, the value 0.75 has to be multiplied by the probability T of the bound state formation during adiabatic transmission of two electrons into 1D channel ($T\simeq 1$). If the binding energy is larger than the sub-band energy spacing the 0.7 structure can be seen even when the integer steps are smeared away by the temperature. Bound states of several electrons, if they exist, may give different steps at 1/2, 5/16, 3/16 etc in the conductance. The latter results are sensitive to the length of 1D system and the electron density at the barrier. It is not excluded that the fractional conductance quantization may also appear for a repulsive interaction between electrons. In this case the electron level splitting is due to the exchange interaction with two nearest neighbors in a 1D Wigner crystal.