Multiterminal open quantum dot circuit operating in the fractional quantum Hall regime

Abstract

We study theoretically a large quantum dot in the fractional quantum Hall regime that is strongly coupled to $\mathcal{M}$ leads via single-mode quantum point contacts. In the case $\mathcal{M}=2$, when the system is mapped onto the two-channel charge Kondo problem, we predict a universal expression for the conductance in the vicinity of a strong-coupling fixed point. The power of the leading temperature correction to the maximal conductance is determined by the fractional filling factor $\ensuremath{\nu}=1/m$. For $\mathcal{M}>2$, we examine the case in which $\mathcal{M}\ensuremath{-}1$ quantum point contacts are fully open, reproducing a single-channel circuit coupled to a dissipative Ohmic environment. The system is treated as a Luttinger liquid with an impurity, whose effective interaction parameter is defined as $K=\ensuremath{\nu}(\mathcal{M}\ensuremath{-}1)/\mathcal{M}$. Conductance scaling in the weak and strong tunnel regimes is used to discuss the low-temperature transport behavior of multichannel single- and double-charge Kondo devices.