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

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 ${T}^{1/g\ensuremath{-}2}$ 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 $\ensuremath{\nu}=1/(2m+1)=g$.