Dissipation and quantum noise in chiral circuitry

• Main Authors: Wadhawan, Disha, Das, Sourin
• Format: Journal Article
• Language: English
• Published: 25-07-2020
• Subjects: Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.1811.07289

Physica E: Low-dimensional Systems and Nanostructures 121, 114117
(2020) We obtain an empirical relation between the zero temperature, zero frequency
quantum noise ${\small{(}}S{\small{(}}\omega=0{\small{)}}{\small{)}}$ and the
related power dissipation ${\small{(}}D{\small{)}}$ for chiral circuitry. We
consider the case of single quantum point contact (QPC) which induces
inter-edge scattering of electrons among $"n"$ number of chiral edges of
$\nu=1$ quantum Hall state. The ratio of total maximum power dissipation
generated at the QPC ($D_{total}$) to the sum of auto-correlated noise
generated in the chiral edge channels emanating out of the QPC region
($S_{total}$) is shown to be,
$D_{total}/S_{total}{\small{(}}\omega=0{\small{)}} = V/{\small{}}4 e{\small{}}$
where $e$ is the electronic charge and $V$ is the voltage imposed on any one of
the "$n$" incoming edge channels while keeping remaining "$n-1$" edge channels
grounded. This implies that this ratio is universal except for a linear voltage
bias dependence, i.e., it is independent of details of the scattering matrix
($S$-matrix) of the QPC region. Here the maximum power dissipation in each
chiral edge is defined as the rate at which energy would be lost if the
non-equilibrium distribution of electrons generated by the QPC region in each
chiral edge is equilibrated to the corresponding zero temperature Fermi
distribution. Further, for ${\cal Z}_n$ symmetric $S$-matrix, we show that the
universal behaviour persists even when all the bias voltages imposed on the
incoming edge channels are kept finite and distinct.