Quantum phase transition in capacitively coupled double quantum dots

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.Comment: 4 pages, 3 figure

Two-channel Kondo physics in tunnel-coupled double quantum dots

We investigate theoretically the possibility of observing two-channel Kondo (2CK) physics in tunnel-coupled double quantum dots (TCDQDs), at both zero and finite magnetic fields; taking the two-impurity Anderson model (2AIM) as the basic TCDQD model, together with effective low-energy models arising from it by Schrieffer-Wolff transformations to second and third order in the tunnel couplings. The models are studied primarily using Wilson's numerical renormalization group. At zero-field our basic conclusion is that while 2CK physics arises in principle provided the system is sufficiently strongly-correlated, the temperature window over which it could be observed is much lower than is experimentally feasible. This finding disagrees with recent work on the problem, and we explain why. At finite field, we show that the quantum phase transition known to arise at zero-field in the two-impurity Kondo model (2IKM), with an essentially 2CK quantum critical point, persists at finite fields. This raises the prospect of access to 2CK physics by tuning a magnetic field, although preliminary investigation suggests this to be even less feasible than at zero field.Comment: 10 pages, 8 figures. Version as published in PR

Magnetic field effects in few-level quantum dots: theory, and application to experiment

We examine several effects of an applied magnetic field on Anderson-type models for both single- and two-level quantum dots, and make direct comparison between numerical renormalization group (NRG) calculations and recent conductance measurements. On the theoretical side the focus is on magnetization, single-particle dynamics and zero-bias conductance, with emphasis on the universality arising in strongly correlated regimes; including a method to obtain the scaling behavior of field-induced Kondo resonance shifts over a very wide field range. NRG is also used to interpret recent experiments on spin-1/2 and spin-1 quantum dots in a magnetic field, which we argue do not wholly probe universal regimes of behavior; and the calculations are shown to yield good qualitative agreement with essentially all features seen in experiment. The results capture in particular the observed field-dependence of the Kondo conductance peak in a spin-1/2 dot, with quantitative deviations from experiment occurring at fields in excess of $\sim$ 5 T, indicating the eventual inadequacy of using the equilibrium single-particle spectrum to calculate the conductance at finite bias.Comment: 15 pages, 12 figures. Version as published in PR

A local moment approach to the degenerate Anderson impurity model

The local moment approach is extended to the orbitally-degenerate [SU(2N)] Anderson impurity model (AIM). Single-particle dynamics are obtained over the full range of energy scales, focussing here on particle-hole symmetry in the strongly correlated regime where the onsite Coulomb interaction leads to many-body Kondo physics with entangled spin and orbital degrees of freedom. The approach captures many-body broadening of the Hubbard satellites, recovers the correct exponential vanishing of the Kondo scale for all N, and its universal scaling spectra are found to be in very good agreement with numerical renormalization group (NRG) results. In particular the high-frequency logarithmic decays of the scaling spectra, obtained here in closed form for arbitrary N, coincide essentially perfectly with available numerics from the NRG. A particular case of an anisotropic Coulomb interaction, in which the model represents a system of N `capacitively-coupled' SU(2) AIMs, is also discussed. Here the model is generally characterised by two low-energy scales, the crossover between which is seen directly in its dynamics.Comment: 23 pages, 7 figure

Correlated electron physics in multilevel quantum dots: phase transitions, transport, and experiment

We study correlated two-level quantum dots, coupled in effective 1-channel fashion to metallic leads; with electron interactions including on-level and inter-level Coulomb repulsions, as well as the inter-orbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics and electronic transport properties are considered; and direct comparison is made to conductance experiments on lateral quantum dots. Two distinct phases arise generically, one characterised by a normal Fermi liquid fixed point (FP), the other by an underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of non-integral dot charge, are found to consist of continuous lines of Kosterlitz-Thouless transitions, separated by first order level-crossing transitions at high symmetry points. A `Friedel-Luttinger sum rule' is derived and, together with a deduced generalization of Luttinger's theorem to the USC phase (a singular Fermi liquid), is used to obtain a general result for the T=0 zero-bias conductance, expressed solely in terms of the dot occupancy and applicable to both phases. Relatedly, dynamical signatures of the QPT show two broad classes of behavior, corresponding to the collapse of either a Kondo resonance, or antiresonance, as the transition is approached from the Fermi liquid phase; the latter behavior being apparent in experimental differential conductance maps. The problem is studied using the numerical renormalization group method, combined with analytical arguments.Comment: 22 pages, 18 figures, submitted for publicatio

Dynamics of capacitively coupled double quantum dots

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime; and then towards and through the quantum phase transition to a charge-ordered (CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.Comment: 14 pages, 6 figure

Interplay between Kondo physics and spin-orbit coupling in carbon nanotube quantum dots

We investigate the influence of spin-orbit coupling on the Kondo effects in carbon nanotube quantum dots, using the numerical renormalization group technique. A sufficiently large spin-orbit coupling is shown to destroy the SU(4) Kondo effects at zero magnetic field, leaving only two SU(2) Kondo effects in the one- and three-electron Coulomb blockade valleys. On applying a finite magnetic field, two additional, spin-orbit induced SU(2) Kondo effects arise in the three- and two-electron valleys. Using physically realistic model parameters, we calculate the differential conductance over a range of gate voltages, temperatures and fields. The results agree well with measurements from two different experimental devices in the literature, and explain a number of observations that are not described within the standard framework of the SU(4) Anderson impurity model.Comment: 15 pages, 11 figure

Conductance fingerprint of Majorana fermions in the topological Kondo effect

We consider an interacting nanowire/superconductor heterostructure attached to metallic leads. The device is described by an unusual low-energy model involving spin-1 conduction electrons coupled to a nonlocal spin-1/2 Kondo impurity built from Majorana fermions. The topological origin of the resulting Kondo effect is manifest in distinctive non-Fermi-liquid (NFL) behavior, and the existence of Majorana fermions in the device is demonstrated unambiguously by distinctive conductance lineshapes. We study the physics of the model in detail, using the numerical renormalization group, perturbative scaling and abelian bosonization. In particular, we calculate the full scaling curves for the differential conductance in AC and DC fields, onto which experimental data should collapse. Scattering t-matrices and thermodynamic quantities are also calculated, recovering asymptotes from conformal field theory. We show that the NFL physics is robust to asymmetric Majorana-lead couplings, and here we uncover a duality between strong and weak coupling. The NFL behavior is understood physically in terms of competing Kondo effects. The resulting frustration is relieved by inter-Majorana coupling which generates a second crossover to a regular Fermi liquid.Comment: 17 pages, 8 figure