Quantized Conductance by Accelerated Electrons

Abstract: One-dimensional quantized conductance is derived from the electrons in a homogeneous electric field by calculating the traveling time of the accelerated motion and the number of electrons in the one-dimensional region. As a result, the quantized conductance is attributed to the finite time required for ballistic electrons to travel a finite length. In addition, even if the conductance is finite, it is possible to say that this model requires no Joule heat dissipation, because the electrical power is converted to kinetic energy of electrons. Furthermore, the relationship between the non-equilibrium source-drain bias $V_\mathrm{sd}$ and the wavenumber $k$ in a one-dimensional conductor is shown as $k \propto \sqrt{V_\mathrm{sd}}$. This correspondence explains the wavelength of the coherent electron flows emitted from a quantum point contact. It also explains the anomalous $0.7 \cdot 2e^2/h$ ($e$ is the elementary charge, and $h$ is the Plank's constant) conductance plateau as a consequence of the perturbation gap at the crossing point of the wavenumber-direction-splitting dispersion relation. We propose that this splitting is caused by the Rashba spin-orbit interaction induced by the potential gradient of the quantum well at quantum point contacts.