We study equilibrium and nonequilibrium properties of the single-impurity Anderson model with a power-law pseudogap in the density of states. In equilibrium, the model is known to display a quantum phase transition from a generalized Kondo to a local moment phase. In the present work, we focus on the extension of these phases beyond equilibrium, i.e. under the influence of a bias voltage. Within the auxiliary master equation approach combined with a scheme based on matrix product states (MPS) we are able to directly address the current-carrying steady state. Starting with the equilibrium situation, we first corroborate our results by comparing with a direct numerical evaluation of ground state spectral properties of the system by MPS. Here, a scheme to locate the phase boundary by extrapolating the power-law exponent of the self energy produces a very good agreement with previous results obtained by the numerical renormalization group. Our nonequilibrium study as a function of the applied bias voltage is then carried out for two points on either side of the phase boundary. In the Kondo regime the resonance in the spectral function is splitted as a function of the increasing bias voltage. The local moment regime, instead, displays a dip in the spectrum near the position of the chemical potentials. Similar features are observed in the corresponding self energies. The Kondo split peaks approximately obey a power-law behavior as a function of frequency, whose exponents depend only slightly on voltage. Finally, the differential conductance in the Kondo regime shows a peculiar maximum at finite voltages, whose height, however, is below the accuracy level.
We predict a resonance impurity state generated by the substitution of one Cu atom with a nonmagnetic atom, such as Zn, in the pseudogap state of a high-T_c superconductor. The precise microscopic origin of the pseudogap is not important for this state to be formed, in particular this resonance will be present even in the absence of superconducting fluctuations in the normal state. In the presence of superconducting fluctuations, we predict the existence of a counterpart impurity peak on a symmetric bias. The nature of impurity resonance is similar to the previously studied resonance in the d-…
The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi liquid and local moment phases, via the local moment approach. Both phases are shown to be characterized by a low-energy scale that vanishes at the QCP; and the universal scaling spectra, on all energy scales, are obtained analytically. The spectrum precisely at the QCP is also obtained; its form showing clearly the non-Fermi liquid, interacting nat…
We study a pseudogap Anderson-Holstein model of a magnetic impurity level that hybridizes with a conduction band whose density of states vanishes in power-law fashion at the Fermi energy, and couples, via its charge, to a nondispersive bosonic mode (e.g., an optical phonon). The model, which we treat using poor-man's scaling and the numerical renormalization group, exhibits quantum phase transitions of different types depending on the strength of the impurity-boson coupling. For weak impurity-boson coupling, the suppression of the density of states near the Fermi energy leads to quantum phase …
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, 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 (hbar w < 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 cr…
The pseudogap Anderson impurity model is a paradigm for locally critical quantum phase transitions. Within the framework of the local moment approach we study its finite-T dynamics, as embodied in the single-particle spectrum, in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi-liquid (Kondo screened) and local moment phases. The scaling spectra in both phases, and at the QCP itself, are obtained analytically. A key result is that pure omega/T-scaling obtains at the QCP, where the Kondo resonance has just collapsed. The connection between the scaling spec…
We investigate the dynamical properties of the two-channel Anderson model using the noncrossing approximation (NCA) supplemented by numerical renormalization-group calculations. We provide evidence supporting the conventional wisdom that the NCA gives reliable results for the standard two-channel Anderson model of a magnetic impurity in a metal. We extend the analysis to the pseudogap two-channel model describing a semi-metallic host with a density of states that vanishes in power-law fashion at the Fermi energy. This model exhibits continuous quantum phase transitions between weak- and strong…
We analyze the consequences of a first-order (in the effective Kondo coupling) inter-impurity correlation present in the Two-Impurity Anderson Hamiltonian. This correlation generates a pair of Kondo Doublet states which are responsible for the first (higher energy) Kondo stage of these systems. Applied to systems of quantum dots in a semiconductor heterolayer, these Doublets predict a mainly ferromagnetic dot-dot spin correlation which is different than the expected from the second-order RKKY interaction. In order to effectively screen both dots, a parallel alignment of the dot-spins is favore…
Impurity moments coupled to fermions with a pseudogap density of states display a quantum phase transition between a screened and a free moment phase upon variation of the Kondo coupling. We describe the universal theory of this transition for the experimentally relevant case of particle-hole asymmetry. The theory takes the form of a crossing between effective singlet and doublet levels, interacting with low-energy fermions. Depending on the pseudogap exponent, this interaction is either relevant or irrelevant under renormalization group transformations, establishing the existence of an upper-…
The pseudogap Anderson impurity model provides a paradigm for understanding local quantum phase transitions, in this case between generalised fermi liquid and degenerate local moment phases. Here we develop a non-perturbative local moment approach to the generic asymmetric model, encompassing all energy scales and interaction strengths and leading thereby to a rich description of the problem. We investigate in particular underlying phase boundaries, the critical behaviour of relevant low-energy scales, and single-particle dynamics embodied in the local spectrum. Particular attention is given t…
The quantum criticality of the two-lead two-channel pseudogap Anderson model is studied. Based on the non-crossing approximation, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, $\propto |ω-μ_F|^r$ ($0<r<1$) near the Fermi energy. Equilibrium and non-equilibrium quantum critical properties at the two-channel Kondo (2CK) to local moment (LM) phase transition are addressed by extracting universal scaling functions in both linear and non-linear conductances, respectively…
We propose an efficient algorithm to numerically solve Anderson impurity problems using matrix product states. By introducing a modified chain mapping we obtain significantly lower entanglement, as compared to all previous attempts, while keeping the short-range nature of the couplings. Our approach naturally extends to finite temperatures, with applications to dynamical mean field theory, non-equilibrium dynamics and quantum transport.
The strongly correlated two-electron transport in one-dimensional channel coupled with an Anderson-type impurity is solved exactly via a Bethe ansatz approach. We show that the transport properties are fundamentally different for spin singlet and triplet states, thus the impurity acts as a novel filter that operates based on the total spin angular momentum of the electron pairs, but not individual spins. The filter provides a deterministic generation of electron entanglement in spin, as well as energy and momentum space.
In a recent Comment, Kolf et al. (cond-mat/0503669) state that our analysis of the Fano resonance for Anderson impurity systems [Luo et al., Phys. Rev. Lett 92, 256602 (2004)] is incorrect. Here we want to point out that their comments are not based on firm physical results and their criticisms are unjustified and invalid.
Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models (see A. Weichselbaum and J. von Delft) by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller (2005). While these developments prove particularly useful in the calculation of transient response and finite temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to t…
We analyze the anomalies of superconducting state (both s- and d-wave pairing) in the model of the pseudogap state induced by Heisenberg spin fluctuations of antiferromagnetic short-range order, and based on the scenario of strong scattering near the "hot spots" on the Fermi surface. We present microscopic derivation of Ginzburg-Landau expansion, taking into account all Feynman graphs of perturbation theory for electron interaction with fluctuations of short-range order and in the "ladder" approximation for electron scattering by normal (nonmagnetic) impurities. We determine the dependence of …
We compute exactly the low-energy single-electron Green's function, the impurity and electron self-energies, and the resistivity for the two-channel Anderson impurity model. These results are obtained by exploiting the boundary conformal field theory identified from the Bethe Ansatz solution of the model. Using that solution we can make contact with the parameters of the original Hamiltonian and provide the detailed crossover between the two integer valence limits. Our results generalize those obtained previously in the context of the two-channel Kondo model.
The $S=1/2$ antiferromagnetic Heisenberg spin chain compound Sr$_2$CuO$_3$ doped with $1 \%$ and $2 \%$ of Ni impurities has been studied by means of $^{63}$Cu nuclear magnetic resonance. A strong decrease of the spin-lattice relaxation rate $T_1^{-1}$ at low temperatures points toward a spin gap, while a stretching exponent $λ< 1$ and a frequency dependence of $T_1^{-1}$ indicate that this spin gap varies spatially and should rather be characterized as a spin pseudogap. The magnitude of the spin pseudogap scales with doping level. Our results therefore evidence the finite-size character of th…
In a recent letter, Chatterjee et al. (Nature Phys. 4, 108 (2008)) reported tunnelling data obtained below and above the critical temperature (Tc = 15 K) by STM in overdoped Bi2-yPbySr2CuO6+x (Bi2201) and some interpretations of the data1. The main experimental findings of their work are observations of native-impurity resonances which coexist spatially with the superconducting (SC) gap below Tc and survive unchanged on warming through Tc. No doubts, the data in the letter are an important piece of information for assembling the high-Tc SC jigsaw puzzle; however, there are inaccuracies in the …
Transient and steady state currents through dc-biased quantum impurity models beyond the linear response regime are of considerable interest, both from an experimental and a theoretical point of view. Here we present a new analytical approach for the calculation of such currents based on the flow equation method (method of infinitesimal unitary transformations). Specifically, we analyze the Anderson impurity model in its mixed valence regime where the coupling to the leads is switched on suddenly at time $t=0$. We observe the real time buildup of the current until it reaches its steady state l…
The Anderson model of an $s$-wave single-orbital correlated impurity placed on a noninteracting honeycomb lattice, a simplified model for studying an impurity on graphene, is used to investigate pseudogap Kondo problem. In this model, there are two quantum phases: the phase of free impurity local moment and the Kondo phase where this local moment is fully screened. The transition between these two phases is under investigation. The work focuses mostly on the case where the impurity is placed on top of a lattice site. In this case, the full phase diagram is constructed using three parameters: t…
We reobtain the Kondo-Doublet interaction by means of the Brillouin-Wigner Perturbation theory. By applying the same method to the single impurity case we show that the Kondo-Doublet interaction is a direct consequence of the Kondo screening cloud. We fully confirm our previous results on this novel interaction. In particular, we found that for values of the system parameters typical of semiconductor Quantum Dots heterostructures, the ferromagnetic Kondo-Doublet interaction dominates over the RKKY one.
Magnetic impurities coupled to both fermionic and bosonic baths or to a fermionic bath with pseudogap density of states, described by the Fermi-Bose Kondo and pseudogap Kondo models, display non-trivial intermediate coupling fixed points associated with critical local-moment fluctuations and local non-Fermi liquid behavior. Based on renormalization group together with a renormalized perturbation expansion around the free-impurity limit, we calculate various impurity properties in the vicinity of those intermediate-coupling fixed points. In particular, we compute the conduction electron T matri…
We use the poor man's scaling approach to study the phase boundaries of a pair of quantum impurity models featuring a power-law density of states $ρ(ω)\propto|ω|^r$ that gives rise to quantum phase transitions between local-moment and Kondo-screened phases. For the Anderson model with a pseudogap (i.e., $r>0$), we find the phase boundary for (a) $0<r<1/2$, a range over which the model exhibits interacting quantum critical points both at and away from particle-hole symmetry, and (b) $r>1$, where the phases are separated by first-order quantum phase transitions. For the particle-hole-symmetric K…
We study the Anderson model in which a configuration with a doublet is hybridized with another with a singlet and a triplet. We calculate the conductance through the system as a function of temperature and bias voltage, near the quantum critical line for which the system is exactly solvable. The results explain recent transport measurements in a single-molecule quantum dot.
We study the dynamics of the quenched Anderson model at finite temperature using matrix product states. Exploiting a chain mapping for the electron bath, we investigate the entanglement structure in the MPS for various orderings of the two chains, which emerge from the thermofield transformation employed to deal with nonzero temperature. We show that merging both chains can significantly lower the entanglement at finite temperatures as compared to an intuitive nearest-neighbor implementation of the Hamiltonian. Analyzing the population of the free bath modes -- possible when simulating the ful…
Quantum transport is studied for the nonequilibrium Anderson impurity model at zero temperature employing the multilayer multiconfiguration time-dependent Hartree theory within the second quantization representation (ML-MCTDH-SQR) of Fock space. To adress both linear and nonlinear conductance in the Kondo regime, two new techniques of the ML-MCTDH-SQR simulation methodology are introduced: (i) the use of correlated initial states, which is achieved by imaginary time propagation of the overall Hamiltonian at zero voltage and (ii) the adoption of the logarithmic discretization of the electronic …
The scaling behavior of Anderson impurity models each of which with a different site energy epsilon_i is examined close to the Mott-Anderson transition. Depending on the impurity energy epsilon_i, in the critical regime the site turns into a local magnetic moment, as indicated by a vanishing quasiparticle weight Z -> 0, or remains nearly doubly occupied or nearly empty, corresponding to Z -> 1. In this paper, we present the scaling behavior of Z as a function of the on-site energy epsilon_i and the distance t to the transition, and interpret our result in terms of an appropriate beta function …
It is shown that the calculation of the magnetic moment of a Friedel-Anderson impurity in mean-field theory is unreliable. A class of approximate solutions, which contains the mean-field solution as an element, is expressed in rotated Hilbert space and optimized. The optimal state has considerably lower energy than the mean field solution and requires almost twice the Coulomb exchange U to become magnetic. Since most moment calculations of magnetic impurities, for example the spin-density-functional theory, use the mean-field approximation the resulting magnetic moments have to be critically r…
Using the Bethe ansatz method, we study the ground state properties of a $U\to\infty$ Anderson impurity in a ``gapless'' host, where a density of band states vanishes at the Fermi level $ε_F$ as $|ε-ε_F|$. As in metals, the impurity spin is proven to be screened at arbitrary parameters of the system. However, the impurity occupancy as a function of the bare impurity energy is shown to acquire novel qualitative features which demonstrate a nonuniversal behavior of the system. The latter explains why the Kondo screening is absent (or exists only at quite a large electron-impurity coupling) in ea…
The Friedel oscillations in the vicinity of a Friedel-Anderson (FA) impurity are investigated numerically. For an FA impurity in the local moment limit the normalized amplitude A(ξ) is S-shaped, approximately zero at short distances, approaching two at large distances and crossing the value one at the characteristic length ξ_{1/2}. Surprisingly, the Friedel oscillations of a simple non-interacting Friedel impurity with a narrow resonance at the Fermi level show a very similar behavior of their amplitude A(ξ). A comparison correlates the resonance width and the Kondo energy of the FA impurity w…
We analyze the spectrum of the electric-current autocorrelation function (noise power) in the Anderson impurity model biased by a finite transport voltage. Special emphasis is placed on the interplay of non-equilibrium effects and electron-electron interactions. Analytic results are presented for a perturbation expansion in the interaction strength $U$. Compared to the non-interacting setup we find a suppression of noise for finite frequencies in equilibrium and an amplification in non-equilibrium. Furthermore, we use a diagrammatic resummation scheme to obtain non-perturbative results in the …
We present an extension of the non-crossing approximation (NCA), which is widely used to calculate properties of Anderson impurity models in the limit of infinite Coulomb repulsion $U\to\infty$, to the case of finite $U$. A self-consistent conserving pseudo-particle representation is derived by symmetrizing the usual NCA diagrams with respect to empty and doubly occupied local states. This requires an infinite summation of skeleton diagrams in the generating functional thus defining the ``Symmetrized finite-U NCA'' (SUNCA). We show that within SUNCA the low energy scale $T_K$ (Kondo temperatur…
The quantitative control of the dynamic correlations of single impurity Anderson models is essential in several very active fields. We analyze the one-particle Green function with a constant energy resolution by dynamic density-matrix renormalization. In contrast to other approaches, sharp dominant resonances at high energies are found. Their origin and importance are discussed.
We derive the polarizability of an electron system in (i) the superconducting phase, with d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Such a calculation is motivated by the recent proposals that imaging the effects of an isolated impurity may distinguish between precursor pairing and dDW order in the pseudogap regime of the high-Tc superconductors. In all three cases, the wave-vector dependence of the polarizability is characterized by an azymuthal …
We propose a realization of the two-impurity Anderson model in a double quantum-dot device. When charge transfer between the dots is suppressed the system exhibits a quantum phase transition, controlled by a surface of non-Fermi liquid fixed points parameterized by the charge valences of the dots. Employing conformal field theory techniques, we identify the scaling exponents that govern transport and thermodynamics close to criticality. We also determine the dynamical exponents that set the time scale for buildup of the non-Fermi liquid state after the system is suddenly shifted into the criti…
We discuss the two-channel Kondo problem with a pseudogap density of states, $ρ(\w)\propto|\w|^r$, of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi liquid behavior of the metallic $r=0$ case, is replaced by a stable particle-hole symmetric intermediate-coupling fixed point for $0<r<\rmax\approx0.23$. For $r>\rmax$, this non-Fermi liquid phase disappears, and instead a cr…
With the help of computer algebra, I devise an exact unitary transformation for the Anderson impurity model which allows to kill the hybridization term in the slightly simplified case of zero chemical potential. Then I compute explicitly the outcome of this transformation. This is a rigorous version of the well known Schrieffer-Wolff transformation. It should be possible to treat the general case at the price of increased computation time.
The Distributional Exact Diagonalization (DED) scheme is applied to the description of Kondo physics in the Anderson impurity model. DED maps Anderson's problem of an interacting impurity level coupled to an infinite bath onto an ensemble of finite Anderson models, each of which can be solved by exact diagonalization. An approximation to the self-energy of the original infinite model is then obtained from the ensemble averaged self-energy. Using Friedel's sum rule, we show that the particle number constraint, a central ingredient of the DED scheme, ultimately imposes Fermi liquid behavior on t…
We investigate the dynamical and steady-state spin response of the nonequilibrium Anderson model to magnetic fields, bias voltage, and temperature using a numerically exact method combining a bold-line quantum Monte Carlo technique with the memory function formalism. We obtain converged results in a range of previously inaccessible regimes, in particular the crossover to the Kondo domain. We provide detailed predictions for novel nonequilibrium phenomena, including non-monotonic temperature dependence of observables at high bias voltage and oscillatory quench dynamics at high magnetic fields.
We present a microscopic Fermi-liquid view on the low-energy transport through an Anderson impurity with $N$ discrete levels, at arbitrary electron filling $N_d$. It is applied to nonequilibrium current fluctuations, for which the two-quasiparticle collision integral and the three-body correlations that determine the quasiparticle energy shift play important roles. Using the numerical renormalization group up to $N=6$, we find that for strong interactions the three-body fluctuations are determined by a single parameter other than the Kondo energy scale in a wide filling range $1 \lesssim N_d \…
The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization group (NRG) calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the c…
We show how the density-matrix numerical renormalization group (DM-NRG) method can be used in combination with non-Abelian symmetries such as SU(N), where the decomposition of the direct product of two irreducible representations requires the use of a so-called outer multiplicity label. We apply this scheme to the SU(3) symmetrical Anderson model, for which we analyze the finite size spectrum, determine local fermionic, spin, superconducting, and trion spectral functions, and also compute the temperature dependence of the conductance. Our calculations reveal a rich Fermi liquid structure.
The twofold degenerate Anderson impurity model [1-4] is investigated and the strong electronic correlations of d-electrons of impurity ion are taken into account by elaborating suitable diagram technique. We discuss the properties of the Slater-Kanamori model [2-4] of d-impurity electrons. After finding the eigenfunctions and eigenvalues of all 16 local states, we determine the local one-particle propagator. Then we construct the perturbation theory around the atomic limit of the impurity ion and obtain the Dyson type equation for the renormalized one-particle propagator. Diagrammatic theory h…
We use the numerical renormalization group method to study an Anderson impurity in a conduction band with the density of states varying as rho(omega) \propto |omega|^r with r>0. We find two different fixed points: a local-moment fixed point with the impurity effectively decoupled from the band and a strong-coupling fixed point with a partially screened impurity spin. The specific heat and the spin-susceptibility show powerlaw behaviour with different exponents in strong-coupling and local-moment regime. We also calculate the impurity spectral function which diverges (vanishes) with |omega|^{-r…
A Josephson junction consisting of an Anderson impurity weakly coupled with two-band and single-band superconductors exposes a time reversal breaking ground state when the coupling between the two bands exceeds a certain threshold. The critical regime occurs around local moment formation. This indicates a fundamental and distinct role of strong correlations: Driving a system into a time reversal breaking ground state. One of the observable consequences is that the impurity magnetization in this phase is reduced.
We study the growth of entanglement entropy in density matrix renormalization group calculations of the real-time quench dynamics of the Anderson impurity model. We find that with appropriate choice of basis, the entropy growth is logarithmic in both the interacting and noninteracting single-impurity models. The logarithmic entropy growth is understood from a noninteracting chain model as a critical behavior separating regimes of linear growth and saturation of entropy, corresponding respectively to an overlapping and gapped energy spectra of the set of bath states. We find that with an approp…
The pseudogap Kondo problem, describing quantum impurities coupled to fermionic quasiparticles with a pseudogap density of states, rho(omega) ~ |omega|^r, shows a rich zero-temperature phase diagram, with different screened and free moment phases and associated transitions. We analyze both the particle-hole symmetric and asymmetric cases using renormalization group techniques. In the vicinity of r=0, which plays the role of a lower-critical dimension, an expansion in the Kondo coupling is appropriate. In contrast, r=1 is the upper-critical dimension in the absence of particle-hole symmetry, an…
We show that a generic single-orbital Anderson impurity model, lacking for instance any kind of particle-hole symmetry, can be exactly mapped without any constraint onto a resonant level model coupled to two Ising variables, which reduce to one if the hybridisation is particle-hole symmetric. The mean-field solution of this model is found to be stable to unphysical spontaneous magnetisation of the impurity, unlike the saddle-point solution in the standard slave-boson representation. Remarkably, the mean-field estimate of the Wilson ratio approaches the exact value $R_\text{W}=2$ in the Kondo r…
We investigate static and dynamical ground-state properties of the two-impurity Anderson model at half filling in the limit of vanishing impurity separation using the dynamical density-matrix renormalization group method. In the weak-coupling regime, we find a quantum phase transition as function of inter-impurity hopping driven by the charge degrees of freedom. For large values of the local Coulomb repulsion, the transition is driven instead by a competition between local and non-local magnetic correlations. We find evidence that, in contrast to the usual phenomenological picture, it seems to…
An exact relation between the conductance maximum $G_0$ at zero temperature and a ratio of lead densities is derived within the framework of the single impurity Anderson model: $G_0={\mathfrak R}[n] \frac{2e^2}{h}$, where ${\mathfrak R}[n]=4ΔN_{{\cal L},x} ΔN_{{\cal R},x}/(ΔN_{{\cal L},x}+ΔN_{{\cal R},x})^2$ and $ΔN_{{\cal L},x}$, $ΔN_{{\cal R},x}$ denote the excess density in the left/right lead at distance $x$ due to the presence of the impurity at the origin, $x=0$. The relation constitutes a parameter-free expression of the conductance of the model in terms of the ground state density that…
We develop a continuous-time quantum Monte Carlo method based on a strong-coupling expansion for Anderson impurity models with phonon-assisted hybridizations for arbitrary number of phonon modes. As a benchmark, we investigate the two-channel Anderson model with a single phonon, and numerically demonstrate that an SO(5) susceptibility composed of localized-electron charge and phonon-parity operators diverges logarithmically at the non-Fermi liquid critical point in the model, which verifies the predictions by the boundary conformal field theory[K. Hattori: Phys. Rev. B {\bf 85} (2012) 214411].
We find by Wilson numerical renormalization group and conformal field theory that a three-orbital Anderson impurity model for a C$_{60}^{n-}$ molecule has a very rich phase diagram which includes non-Fermi-liquid stable and unstable fixed points with interesting properties, most notably high sensitivity to doping $n$. We discuss the implications of our results to the conductance behavior of C$_{60}$-based single-molecule transistor devices.
Josephson current for a system consisting of an Anderson impurity weakly coupled to two unconventional superconductors is studied and shown to be driven by a surface zero energy (mid-gap) bound-state. The repulsive Coulomb interaction in the dot can turn a $π$ junction into a 0-junction. This effect is more pronounced in p-wave superconductors while in high-temperature superconductors with $d_{x^2-y^2}$ symmetry it can exit for rather large artificial centers at which tunneling occurs within a finite region.
We study a generalization of the Kondo model in which the impurity spin is represented by Abrikosov fermions in a rotation group SU(P) larger than the SU(N) group associated to the spin of the conduction electrons, thereby forcing the single electronic bath to underscreen the localized moment. We demonstrate how to formulate a controlled large N limit preserving the property of underscreening, and which can be seen as a ``dual'' theory of the multichannel large N equations usually associated to overscreening. Due to the anomalous scattering on the uncompensated degrees of freedom, the Fermi li…
We investigate a modified Anderson model at the large-$N$ limit, where Coulomb interaction is replaced by Sachdev-Ye-Kitaev random interaction. The resistivity of conduction electron $ρ_{c}$ has a minimum value around temperature $\widetilde{T}_{K}$, which is similar to the Kondo system, but the impurity electron's density of state $A_{d}(ω)$ elucidates no sharp-peak like Kondo resonance around the Fermi surface. The impurity electron's entropy $S_{d}$ and specific heat capacity $C_{\textrm{v}}$ illustrate a crossover from Fermi liquid to the non-Fermi liquid. The system is a non-Fermi liquid …
The cyclic sudden switching of a magnetic impurity from Kondo to a non-Kondo state and back was recently shown to involve an important dissipation of the order of several $k_BT_K$ per cycle. The possibility to reveal this and other electronic processes through nanomechanical dissipation by e.g., ultrasensitive Atomic Force Microscope (AFM) tools currently represents an unusual and interesting form of spectroscopy. Here we explore the dependence on the switching time of the expected dissipation, a quantity whose magnitude is physically expected to drop from maximum to zero between sudden and sl…
A theory is developed to study shot noise in superconducting (SAS) and hybrid (SAN) junctions with singly occupied Anderson impurity (A) as a weak link. The zero-frequency DC component of the shot noise spectral density is calculated at zero temperature as a function of the bias at different Coulomb repulsion strengths U, and show a remarkable structure resulting from combination of electron-electron interaction and Andreev reflections.
