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Register a new userExploring the phase diagram of the two-impurity Kondo problem
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A system of two exchange-coupled Kondo impurities in a magnetic field gives rise to a rich phase space hosting a multitude of correlated phenomena. Magnetic atoms on surfaces probed through scanning tunnelling microscopy provide an excellent platform to investigate coupled impurities, but typical high Kondo temperatures prevent field-dependent studies from being performed, rendering large parts of the phase space inaccessible. We present an integral study of pairs of Co atoms on insulating Cu2N/Cu(100), which each have a Kondo temperature of only 2.6 K. In order to cover the different regions of the phase space, the pairs are designed to have interaction strengths similar to the Kondo temperature. By applying a sufficiently strong magnetic field, we are able to access a new phase in which the two coupled impurities are simultaneously screened. Comparison of differential conductance spectra taken on the atoms to simulated curves, calculated using a third order transport model, allows us to independently determine the degree of Kondo screening in each phase.
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We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling $J_K$, longitudinal anisotropy $D$, and transverse anisotropy $E$. In the isotropic case, two impurities on opposite(same) sublattices have a singlet(triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively four-fold degenerate ground state, i.e., two decoupled impurities. For large enough $J_K$ the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear non-perturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persists and the two effects coexist: the impurities are underscreened, and the dangling spin-$1/2$ degrees of freedom are responsible for the inter-impurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasi-classical correlations.
The archetypal two-impurity Kondo problem in a serially-coupled double quantum dot is investigated in the presence of a thermal bias $theta$. The slave-boson formulation is employed to obtain the nonlinear thermal and thermoelectrical responses. When the Kondo correlations prevail over the antiferromagnetic coupling $J$ between dot spins we demonstrate that the setup shows negative differential thermal conductance regions behaving as a thermal diode. Besides, we report a sign reversal of the thermoelectric current $I(theta)$ controlled by $t/Gamma$ ($t$ and $Gamma$ denote the interdot tunnel and reservoir-dot tunnel couplings, respectively) and $theta$. All these features are attributed to the fact that at large $theta$, both $Q(theta)$ (heat current) and $I(theta)$ are suppressed regardless the value of $t/Gamma$ because the double dot decouples at high thermal biases. Eventually, and for a finite $J$, we investigate how the Kondo-to-antiferromagnetic crossover is altered by $theta$.
We calculate the differential conductance (dI/dV) corresponding to scanning tunneling spectroscopy (STS) measurements for two magnetic atoms adsorbed on a metal surface with the aid of the numerical renormalization group (NRG) technique. We find that the peak structure of the dI/dV spectra near the Fermi level changes gradually as a function of the adatom separation and the coupling between the adatoms and the metal surface conduction band. When the coupling becomes small, the peak disappears and, instead, a dip structure appears near the Fermi level. This dip structure is the manifestation of the strong antiferromagnetic correlation between the localized spins. The gradual change of the dI/dV structure from a peak structure to a dip structure originates from the crossover transition in the two impurity Kondo problem.
Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale $T_{text{FL}}$ is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, $T_{text{FL}}$ becomes arbitrarily small close to two new quantum critical points (QCPs) which we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin ($omega^{-1/5}$), orbital ($omega^{1/5}$) and spin-orbital ($omega^1$) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.
We consider a quantum dot with ${cal K}{geq} 2$ orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multi-level Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel $S{=}1$ Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi-liquid. Using non-equilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.
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