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Journal of Physics Condensed Matter

From quantum critical to two-channel Kondo physics via charge fluctuations in a quantum dot

Eugene H. Kim, Yong Baek Kim, Catherine Kallin

Published Oct 3, 2003• 7 citations
Publisher

Abstract

We consider charge fluctuations in a quantum dot coupled to an interacting one-dimensional electron liquid. By tuning the coupling between the dot and the one-dimensional electron liquid, one can access the various regimes which arise, which include a quantum critical and a two-channel Kondo regime. The differential capacitance is computed and is shown to contain detailed information about the system.

DOI
10.1088/0953-8984/15/41/012

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We consider charge fluctuations in a quantum dot coupled to an interacting one-dimensional electron liquid. By tuning the coupling between the dot and the one-dimensional electron liquid, one can access the various regimes which arise, which include a quantum critical and a two-channel Kondo regime. The differential capacitance is computed and is shown to contain detailed information about the system.
In this document we present a study of the thermodynamic and transport properties of two kinds of quantum impurity systems in the Kondo regime.The first system consists of a spin-1 molecule in which mechanical stretching along the transport axis produces a magnetic anisotropy.We find that a generic coupling between a vibrational mode along this axis and the molecular spin induces a correction to the magnetic anisotropy, driving the ground state of the system into a non-Fermi-liquid phase.A transition into a Fermi-liquid ground state can then be induced by means of stretching, going through an underscreened spin-1 Kondo ground state at zero effective anisotropy.In the second system we study the effects of a charge detector, implemented by a quantum point-contact (QPC), on the Kondo state of a nearby spin-1/2 quantum dot (QD).While making the charge detection possible, the Coulomb interaction between the electrons traversing the QPC and those within the QD contribute to decoherence of the Kondo state.By modeling the QPC as two metallic terminals connected to an intermediate localized level, we can explore three transport regimes of the detector: a zero-conductance regime, a finite-conductance regime in mixed valence, and unitary conductance in a Kondo ground state that has been suggested as an explanation to the "0.7 anomaly" in QPCs.Transitions between these different ground states can be achieved by tuning the strength of a capacitive coupling that parameterizes the electrostatic interaction.
We consider the simplest example of a double quantum dot system: two equivalent, capacitively coupled single-level dots, each coupled to its own lead. Focussing on a regime of two electrons on the double dot, a rich range of behaviour is found on increasing the interdot coupling: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom; followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi liquid 'charge-ordered' phase with finite residual entropy and anomalous transport properties. The numerical renormalization group method, coupled with simple physical arguments, is employed to obtain a detailed understanding of the problem.
We propose a design for a one-dimensional quantum box device where the charge fluctuations are described by an anisotropic two-channel Kondo model. The device consists of a quantum box in the Coulomb blockade regime, weakly coupled to a quantum wire by a single-mode point contact. The electron correlations in the wire produce strong backscattering at the contact, significantly increasing the Kondo temperature as compared to the case of non-interacting electrons. By employing boundary conformal field theory techniques we show that the differential capacitance of the box exhibits manifest two-channel Kondo scaling with temperature and gate voltage, uncontaminated by the one-dimensional electron correlations. We discuss the prospect to experimentally access the Kondo regime with this type of device.
We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling, a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom, followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi-liquid "charge-ordered" phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormalization group methods are employed to obtain a detailed understanding of the problem.
The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U', in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) is found to persist robustly with increasing U'/U, before a rapid but continuous crossover to (a) the SU(4) point U'=U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U'_c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U,U')-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.