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Abstract:

We study theoretically a ring of three quantum dots mutually coupled by antiferromagnetic exchange interactions and tunnel-coupled to two metallic leads: the simplest model in which the consequences of local frustration arising from internal degrees of freedom may be studied within a two-channel environment. Two-channel Kondo (2CK) physics is found to predominate at low energies in the mirror-symmetric models considered, with a residual spin- 1 2 overscreened by coupling to both leads. It is however shown that two distinct 2CK phases, with different ground-state parities, arise on tuning the interdot exchange couplings. In consequence a frustration-induced quantum phase transition occurs, the 2CK phases being separated by a quantum critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasidegenerate local trimer states acts to destabilize the 2CK fixed points; and the critical fixed point is shown to consist of a free pseudospin together with effective one-channel spin quenching, itself reflecting underlying channel anisotropy in the inherently two-channel system. Numerical renormalization group techniques and physical arguments are used to obtain a detailed understanding of the problem, including study of both thermodynamic and dynamical properties of the system. © 2010 The American Physical Society.

Abstract:

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, focusing 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 and 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 characterized by two low-energy scales, the crossover between which is seen directly in its dynamics.

Abstract:

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.

Abstract:

This paper provides a theoretical description of sequential tunneling transport and spectroscopy, in carbon nanotube quantum dots weakly tunnel coupled to metallic leads under a voltage bias. The effects of Coulomb blockade charging, spin-orbit fine structure, and orbital- and spin-Zeeman effects arising from coupling to applied magnetic fields are considered; and the dependence of the conductance upon applied gate voltage, bias voltage, and magnetic fields is determined. The work is motivated by recent experiments on ultraclean carbon nanotube dots [Kuemmeth et al., Nature (London) 452, 448 (2008)], to which comparison is made.