We investigate a quantum dot (Anderson impurity) coupled to metallic leads, with a time-periodic voltage bias across the device. Using a time-dependent Schrieffer-Wolff transformation, we show that the Floquet Hamiltonian of the model can be mapped onto a two-channel Kondo model, in which the impurity is screened by separate conduction bands corresponding to parity-even and odd superpositions of the metallic leads. By changing the frequency and amplitude of the perturbation, one can tune the system to a quantum critical point with symmetric coupling of the impurity to both channels. For the understanding of the driven state, energy absorption from the drive must be considered: Although the absorption at the impurity is balanced by the energy flow into the conduction band, locally it leads to non-thermal distribution functions which can have a detrimental effect on the Kondo physics. However, a numerical simulation demonstrates that the absorption can be systematically suppressed at a fixed value of the induced couplings by increasing the frequency, so that the time-averaged dynamics in the driven one-channel Anderson model can be used to study the critical behavior of the two-channel model.
We investigate a quantum dot (Anderson impurity) coupled to metallic leads, with a time-periodic voltage bias across the device. Using a time-dependent Schrieffer-Wolff transformation, we show that the Floquet Hamiltonian of the model can be mapped onto a two-channel Kondo model, in which the impurity is screened by separate conduction bands corresponding to parity-even and odd superpositions of the metallic leads. By changing the frequency and amplitude of the perturbation, one can tune the system to a quantum critical point with symmetric coupling of the impurity to both channels. For the understanding of the driven state, energy absorption from the drive must be considered: Although the absorption at the impurity is balanced by the energy flow into the conduction band, locally it leads to non-thermal distribution functions which can have a detrimental effect on the Kondo physics. However, a numerical simulation demonstrates that the absorption can be systematically suppressed at a fixed value of the induced couplings by increasing the frequency, so that the time-averaged dynamics in the driven one-channel Anderson model can be used to study the critical behavior of the two-channel model.
Whether a small quantum mechanical system is able to equilibrate with its environment once an external local perturbation drives it out of thermal equilibrium is a central question which cuts across many different fields of science. Here we consider such a problem for a correlated quantum impurity coupled to a fermionic reservoir and driven out of equilibrium by local quantum quenches such as those recently realized in optical absorption experiments on single quantum dots. We argue that equilibration in this problem is deeply connected to the occurrence of the Kondo effect at low energy and that a highly nontrivial dynamical behavior may emerge whenever a local quantum critical point intrudes between a conventional Kondo screened phase and a Kondo unscreened one. We discuss this issue in the context of the Anderson impurity model coupled to a pseudogap reservoir by using a correlated time-dependent variational wave function that is able to qualitatively describe this physics
We investigate systems comprising chains and rings of quantum dots, coupled to two metallic leads. Such systems allow to study the competition between orbital and spin degrees of freedom in a nanodevice, and the effect this subtle interplay has on two-channel Kondo (2CK) physics. We demonstrate that a rich range of strongly correlated electron behaviour results, with non-Fermi liquid 2CK phases and non-trivial phase transitions accessible. We employ physical arguments and the numerical renormalization group (NRG) technique to analyse these systems in detail, examining in particular both thermodynamic and dynamical properties. When leads are coupled to either end of a chain of dots, we show that the resulting behaviour on low temperature/energy scales can be understood in terms of simpler paradigmatic quantum `impurity' models. An effective low-energy single-spin 2CK model is derived for all odd-length chains, while the behaviour of even-length chains is related fundamentally to that of the classic `two-impurity Kondo' model. In particular, for small interdot coupling, we show that an effective coupling mediated though incipient single-channel Kondo states drives all odd chains to the 2CK fixed point (FP) on the lowest temperature/energy scales. A theory is also developed to describe a phase transition in even chains. We derive an effective channel-anisotropic 2CK model, which indicates that the critical FP of such models must be the 2CK FP. This physical picture is confirmed using NRG for various chain systems. We also examine the effect of local frustration on 2CK physics in mirror-symmetric ring systems. The importance of geometry and symmetry is demonstrated clearly in the markedly different physical behaviour that arises in systems where two leads are either connected to the same dot, or to neighbouring dots. In the latter case, we show for all odd-membered rings that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot couplings. A frustration-induced phase transition thus occurs, the 2CK phases being separated by a novel 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 destabilise the 2CK FPs, and the critical FP is shown to consist of a free pseudospin together with effective single-channel spin quenching. While connecting both leads to the same dot again results in two parity-distinct phases, a simple level-crossing transition now results due to the symmetry of the setup. The proposed geometry also allows access to a novel ferromagnetically-coupled two-channel local moment phase. Driven by varying the interdot couplings and occurring at the point of inherent magnetic frustration, such transitions in ring structures provide a striking example of the subtle interplay between internal spin and orbital degrees of freedom in coupled quantum dot systems, and the resulting effect on Kondo physics.
The system of several (N) quantum dots coupled in parallel to the same single-mode conduction channel can be modeled as a single-channel N-impurity Anderson model. Using the generalized Schrieffer-Wolff transformation we show that near the particle-hole symmetric point, the effective Hamiltonian in the local moment regime is the N-impurity S=1∕2 Kondo model. The conduction-band-mediated RKKY exchange interaction between the dots is ferromagnetic and at intermediate temperatures locks the moments into a maximal spin S=N∕2 ground state. We provide an analytical estimate for the RKKY interaction. At low temperatures the spin is partially screened by the conduction electrons to $N∕2\ensuremath{-}1∕2$ due to the Kondo effect. By comparing accurate numerical renormalization group results for magnetic susceptibility of the N-impurity Anderson model to the exact Bethe ansatz results of a S=N∕2 SU(2) Kondo system we show that at low-temperature the quantum dots can be described by the effective S=N∕2 Kondo model. Moreover, the Kondo temperature is independent of the number of impurities N. We demonstrate the robustness of the spin N∕2 ground state as well as of the associated S=N∕2 Kondo effect by studying the stability of the system with respect to various experimentally relevant perturbations. We finally explore various quantum phase transitions driven by these perturbations.
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 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, 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.
We study odd-membered chains of spin-21 impurities, with each end connected to its own metallic lead. For antiferromagnetic exchange coupling, universal two-channel Kondo (2CK) physics is shown to arise at low energies. Two overscreening mechanisms are found to occur depending on coupling strength, with distinct signatures in physical properties. For strong interimpurity coupling, a residual chain spin-21 moment experiences a renormalized effective coupling to the leads, while in the weak-coupling regime, Kondo coupling is mediated via incipient single-channel Kondo singlet formation. We also investigate models in which the leads are tunnel-coupled to the impurity chain, permitting variable dot filling under applied gate voltages. Effective low-energy models for each regime of filling are derived, and for even fillings where the chain ground state is a spin singlet, an orbital 2CK effect is found to be operative. Provided mirror symmetry is preserved, 2CK physics is shown to be wholly robust to variable dot filling; in particular, the single-particle spectrum at the Fermi level, and hence the low-temperature zero-bias conductance, is always pinned to half-unitarity. We derive a Friedel-Luttinger sum rule and from it show that, in contrast to a Fermi liquid, the Luttinger integral is nonzero and determined solely by the ``excess'' dot charge as controlled by gate voltage. The relevance of the work to real quantum dot devices, where interlead charge-transfer processes fatal to 2CK physics are present, is also discussed. Physical arguments and numerical renormalization-group techniques are used to obtain a detailed understanding of these problems.
Quantum dot devices may be tuned to Kondo models which have non-interacting limits such as the Toulouse limit. At sufficiently low temperatures the Toulouse limit can be used to make predictions for charge transport in the devices driven away from equilibrium, e.g. with an ac bias. We investigate non-equilibrium transport in a resonant level model with a single lead which may be mapped onto the Toulouse limit of the one-channel Kondo model. The main results are expressions for the charge current that are exact in the tunnelling couplings, while remaining in the linear response regime of the time-dependent voltage bias. We also show how the line of enquiry directly extends to the tunnelling junction studied by A.~Schiller and S.~Hershfield in which a Kondo impurity interacts separately with two leads.