Local Quantum Critical Point in the Pseudogap Anderson Model: Finite-T Dynamics and ω/T Scaling

Nonequilibrium Kondo effect in a graphene-coupled quantum dot in the presence of a magnetic field

Background: Quantum dots connected to larger systems containing a continuum of states like charge reservoirs allow the theoretical study of many-body effects such as the Coulomb blockade and the Kondo effect. Results: Here, we analyze the nonequilibrium Kondo effect and transport phenomena in a quantum dot coupled to pure monolayer graphene electrodes under external magnetic fields for finite on-site Coulomb interaction. The system is described by the pseudogap Anderson Hamiltonian. We use the equation of motion technique to determine the retarded Green's function of the quantum dot. An analytical formula for the Kondo temperature is derived for electron and hole doping of the graphene leads. The Kondo temperature vanishes in the vicinity of the particle-hole symmetry point and at the Dirac point. In the case of particle-hole asymmetry, the Kondo temperature has a finite value even at the Dirac point. The influence of the on-site Coulomb interaction and the magnetic field on the transport properties of the system shows a tendency similar to the previous results obtained for quantum dots connected to metallic electrodes. Most remarkably, we find that the Kondo resonance does not show up in the density of states and in the differential conductance for zero chemical potential due to the linear energy dispersion of graphene. An analytical method to calculate self-energies is also developed which can be useful in the study of graphene-based systems. Conclusion: Our graphene-based quantum dot system provides a platform for potential applications of nanoelectronics. Furthermore, we also propose an experimental setup for performing measurements in order to verify our model.

Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model

The paramagnetic phase of the one-band Hubbard model is studied at zero-temperature, within the framework of dynamical mean-field theory, and for general particle-hole asymmetry where a doping-induced Mott transition occurs. Our primary focus is the Mott insulator (MI) phase, and our main aim to establish what can be shown exactly about it. To handle the locally doubly-degenerate MI requires two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the standard single self-energy. Exact results are obtained for the local charge, local magnetic moment and associated spin susceptibilities, the interaction-renormalised levels, and the low-energy behaviour of the self-energy in the MI phase. The metallic phase is also considered briefly, and shown to acquire an emergent particle-hole symmetry as the Mott transition is approached. Throughout the metal, Luttinger's theorem is reflected in the vanishing of the Luttinger integral; for the generic MI by contrast this is shown to be non-vanishing, but again to have a universal magnitude. Numerical results are also obtained using NRG, for the metal/MI phase boundary, the scaling behaviour of the charge as the Mott transition is aproached from the metal, and associated universal scaling of single-particle dynamics as the low-energy Kondo scale vanishes.

Steady-State Dynamics and Effective Temperature for a Model of Quantum Criticality in an Open System

We study the thermal and nonthermal steady-state scaling functions and the steady-state dynamics of a model of local quantum criticality. The model we consider, i.e., the pseudogap Kondo model, allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points. In the vicinity of each fixed point we establish the existence of an effective temperature-different at each fixed point-such that the equilibrium fluctuation-dissipation theorem is recovered. Most notably, steady-state scaling functions in terms of the effective temperatures coincide with the equilibrium scaling functions. This result extends to higher correlation functions as is explicitly demonstrated for the Kondo singlet strength. The nonlinear charge transport is also studied and analyzed in terms of the effective temperature.

Critical Kondo destruction in a pseudogap Anderson model: scaling and relaxational dynamics

We study the pseudogap Anderson model as a prototype system for critical Kondo destruction. We obtain finite-temperature (T) scaling functions near its quantum-critical point, by using a continuous-time quantum Monte Carlo method and also considering a dynamical large-N limit. We are able to determine the behavior of the scaling functions in the typically difficult to access quantum-relaxational regime (ℏω<k(B)T) and conclude that the relaxation rates for both the spin and single-particle excitations are linear in temperature. We discuss the implications of these results for the quantum-critical phenomena in heavy-fermion metals.

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, 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.