Resonant tunneling through a quantum dot weakly coupled to quantum wires or quantum Hall edge states

TL;DR

This paper analyzes resonant tunneling through a quantum dot coupled to Tomonaga-Luttinger liquids, deriving conductance formulas and exploring effects of temperature, interaction parameter g, and cotunneling, relevant for fractional quantum Hall edge states.

Contribution

It provides a detailed conductance calculation for quantum dots coupled to Luttinger liquids, including cotunneling effects, applicable to fractional quantum Hall edge states.

Findings

Resonant tunneling is incoherent for g<1/2 at all temperatures.

Conductance peaks scale with temperature as T^{(1/g)-2} and T.

The formula applies to fractional quantum Hall edge states with filling factor nu=1/(2m+1).

Abstract

Resonant tunneling through a quantum dot weakly coupled to Tomonaga-Luttinger liquids is discussed. The linear conductance due to sequential tunneling is calculated by solving a master equation for temperatures below and above the average level spacing in the dot. When the parameter g characterizing the Tomonaga-Luttinger liquid is smaller than 1/2, the resonant tunneling process is incoherent down to zero temperature. At low temperature T the height and width of the conductance peaks in the Coulomb blockade oscillations are proportional to T^{(1/g)-2} and T, respectively. The contribution from tunneling via a virtual intermediate state (cotunneling) is also included. The resulting conductance formula can be applied for the resonant tunneling between edge states of fractional quantum Hall liquids with filling factor nu=1/(2m+1)=g.