Martin R. Galpin

Zero-bias conductance in carbon nanotube quantum dots.

We present numerical renormalization group calculations for the zero-bias conductance of quantum dots made from semiconducting carbon nanotubes. These explain and reproduce the thermal evolution of the conductance for different groups of orbitals, as the dot-lead tunnel coupling is varied and the system evolves from correlated Kondo behavior to more weakly correlated regimes. For integer fillings N=1, 2, 3 of an SU(4) model, we find universal scaling behavior of the conductance that is distinct from the standard SU(2) universal conductance, and concurs quantitatively with experiment. Our results also agree qualitatively with experimental differential conductance maps.

Local moment formation and Kondo screening in impurity trimers.

We study theoretically a triangular cluster of three magnetic impurities, hybridizing locally with conduction electrons of a metallic host. Such a cluster is the simplest to exhibit frustration, an important generic feature of many complex molecular systems in which different interactions compete. Here, low-energy doublet states of the trimer are favored by effective exchange interactions produced by strong electronic repulsion in localized impurity orbitals. Parity symmetry protects a level crossing of such states on tuning microscopic parameters, while an avoided crossing arises in the general distorted case. Upon coupling to a metallic host, the behavior is shown to be immensely rich because collective quantum many-body effects now also compete. In particular, impurity degrees of freedom are totally screened at low temperatures in a Kondo-screened Fermi liquid phase, while degenerate ground states persist in a local moment phase. Local frustration drives the quantum phase transition between the two, which may be first order or of Kosterlitz-Thouless type, depending on symmetries. Unusual mechanisms for local moment formation and Kondo screening are found due to the orbital structure of the impurity trimer. Our results are of relevance for triple quantum dot devices. The problem is studied by a combination of analytical arguments and the numerical renormalization group.

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.

Correlated electron physics in two-level quantum dots: Phase transitions, transport, and experiment

We study correlated two-level quantum dots, coupled in effective one-channel fashion to metallic leads, with electron interactions including on-level and interlevel Coulomb repulsions, as well as the interorbital 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 characterized by a normal Fermi liquid fixed point FP and the other by an underscreened USC spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of nonintegral 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. DOI: 10.1103/PhysRevB.80.125117

Tunable Kondo Physics in a Carbon Nanotube Double Quantum Dot

We investigate a tunable two-impurity Kondo system in a strongly correlated carbon nanotube double quantum dot, accessing the full range of charge regimes. In the regime where both dots contain an unpaired electron, the system approaches the two-impurity Kondo model. At zero magnetic field the interdot coupling disrupts the Kondo physics and a local singlet state arises, but we are able to tune the crossover to a Kondo screened phase by application of a magnetic field. All results show good agreement with a numerical renormalization group study of the device.

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.

Generalized Wilson chain for solving multichannel quantum impurity problems

The Numerical Renormalization Group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within DMFT. Here we present a simple generalization of the Wilson Chain, which improves the scaling of computational cost with the number of channels/bands, bringing new problems within reach. The method is applied to calculate the t-matrix of the three-channel Kondo model at T=0, which shows universal crossovers near non-Fermi liquid critical points. A non-integrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening/overscreening mechanisms.

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 Wilsons 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.

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 we 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-

Dynamics of capacitively coupled double quantum dots

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