Anderson impurity model in a semiconductor

2012

Abstract. A local moment approach is developed for single-particle excitations of a symmetric Anderson impurity model (AIM) with a soft-gap hybridization vanishing at the Fermi level: ∆I ∝ |ω | r, with r> 0. Local moments are introduced explicitly from the outset, and a two-self-energy description is employed in which single-particle excitations are coupled dynamically to low-energy transverse spin fluctuations. The resultant theory is applicable on all energy scales, and captures both the spinfluctuation regime of strong coupling (large-U), as well as the weak coupling regime where it is perturbatively exact for those r-domains in which perturbation theory in U is non-singular. While the primary emphasis is on single-particle dynamics, the quantum phase transition between strong coupling (SC) and local moment (LM) phases can also be addressed directly; for the spin-fluctuation regime in particular a number of asymptotically exact results are thereby obtained, notably for the beh...

Kondo Effect and Dephasing in Low-Dimensional Metallic Systems, 2001

We developed a self-consistent conserving pseudo particle approximation for the Anderson impurity model with finite Coulomb interaction, derivable from a Luttinger Ward functional. It contains an infinite series of skeleton diagrams built out of fully renormalized Green's functions. The choice of diagrams is motivated by the Schrieffer Wolff transformation which shows that singly and doubly occupied states should appear in all bare diagrams symmetrically. Our numerical results for TK are in excellent agreement with the exact values known from the Bethe ansatz solution. The low energy physics of non-Fermi liquid Anderson impurity systems is correctly described while the present approximation fails to describe Fermi liquid systems, since some important coherent spin flip and charge transfer processes are not yet included. It is believed that CTMA (Conserving T-matrix approximation) diagrams will recover also Fermi liquid behavior for Anderson models with finite Coulomb interaction as they do for infinite Coulomb interaction.

Physical Review B, 2004

The Anderson model of a twofold spin degenerate impurity level in the limit of infinite Coulomb repulsion, U → ∞, coupled to one and two degenerate conduction bands or channels, is considered in pseudo-particle representation. We extend the Conserving T-Matrix Approximation (CTMA), a general diagrammatic approximation scheme based on a fully renormalized computation of twoparticle vertex functions in the spin and in the charge channel, to the calculation of thermodynamic and spectral properties. In the single-channel case, the CTMA yields in the Kondo regime a temperature independent Pauli spin susceptibility for temperatures below the Kondo temperature TK and down to the lowest temperatures considered, reproducing the exact spin screening in the Fermi liquid state. The impurity spectral density appears to remain non-singular down to the lowest temperatures, in agreement with Fermi liquid behavior. However, the unitarity sum rule, which is crucial for an impurity solver like the CTMA to be applicable within Dynamical Mean Field Theories for strongly correlated lattice models, is overestimated at the lowest temperatures. We argue that this shortcoming may be due to numerical imprecision and discuss an appropriate scheme for its correction. In the two-channel case, the spectral density calculated within CTMA exhibits qualitatively the correct non-Fermi liquid behavior at low temperatures, i.e. a powerlaw singularity.

Physical Review B, 2005

We show that the traditional classification of quantum inpurity models based on thermodynamics is insufficient to probe the nature of their low-energy dynamics. We propose an analysis based on scattering theory, dividing Fermi liquids into regular Fermi liquids and singular Fermi liquids. In both cases electrons at the Fermi energy scatter elastically off the impurity, but in the case of regular Fermi liquids the scattering has analytical properties in the vicinity of the Fermi energy, while for singular Fermi liquids it does not, resulting in a breakdown of Nozières' Fermi-liquid picture and singular thermodynamic behavior. Using the Bethe ansatz and numerical renormalization group, we show that the ordinary Kondo model is a regular Fermi liquid whereas the underscreened Kondo model is a a singular Fermi liquid. Conventional regular Fermi liquid behavior is reestablished in an external magnetic field H, but with a density of states which diverges as 1 / H. Our results may be relevant for the recently observed field-tuned quantum criticality in heavy electron materials.

We review a systematic many-body method capable of describing Fermi liquid and Non-Fermi liquid behavior of quantum impurity models at low temperatures on the same footing. The crossover to the high temperature local moment regime is covered as well. The approach makes use of a pseudo-particle representation of the impurity Hilbert space in the limit of infinite Coulomb repulsion $U$ as well as for finite $U$. Approximations are derived from a generating Luttinger-Ward functional, in terms of renormalized perturbation theory in the hybridization $V$. Within a ``conserving T-matrix approximation'' (CTMA), including all two-particle vertex functions, an infinite series of leading infrared singular skeleton diagrams is included. The local constraint is strictly enforced. Applied to the SU(N) $\times$ SU(M) multichannel Anderson model the method allows to recover the Fermi liquid behavior of the single channel case, as well as the non-Fermi liquid behavior in the multi-channel c...

Journal of Physics-condensed Matter, 2000

A local moment approach is developed for single-particle excitations of a symmetric Anderson impurity model (AIM) with a soft-gap hybridization vanishing at the Fermi level: I | |r , with r >0. Local moments are introduced explicitly from the outset, and a two-self-energy description is employed in which single-particle excitations are coupled dynamically to low-energy transverse spin fluctuations. The resultant

Journal of Physics: Condensed Matter, 2017

We study Gutzwiller-correlated wave functions as variational ground states for the two-impurity Anderson model (TIAM) at particle-hole symmetry as a function of the impurity separation R. Our variational state is obtained by applying the Gutzwiller many-particle correlator to a single-particle product state. We determine the optimal single-particle product state fully variationally from an effective non-interacting TIAM that contains a direct electron transfer between the impurities as variational degree of freedom. For a large Hubbard interaction U between the electrons on the impurities, the impurity spins experience a Heisenberg coupling proportional to V 2 /U where V parameterizes the strength of the on-site hybridization. For small Hubbard interactions we observe weakly coupled impurities. In general, for a three-dimensional simple cubic lattice we find discontinuous quantum phase transitions that separate weakly interacting impurities for small interactions from singlet pairs for large interactions.

Physical Review B, 1998

The M-channel Anderson impurity model (M = 1, 2) is studied in the Kondo limit with a finite voltage bias applied to the conduction electron reservoirs. Using the Non-Crossing Approximation (NCA), we calculate the local spectral functions, the differential conductance, and susceptibility at non-zero bias for symmetric as well as asymmetric coupling of the impurity to the leads. We describe an effective procedure to solve the NCA integral equations which enables us to reach temperatures far below the Kondo scale. This allows us to study the scaling regime where the conductance depends on the bias only via a scaling function. Our results are applicable to both tunnel junctions and to point contacts. We present a general formula which allows one to go between the two cases of tunnel junctions and point contacts. Comparison is also made between the conformal field theory and the NCA conduction electron self-energies in the two channel case.

Physical Review B, 2011

We analyze the spectral function of the single-impurity two-terminal Anderson model at finite voltage using the recently developed diagrammatic quantum Monte Carlo technique as well as perturbation theory. In the (particle-hole-)symmetric case we find an excellent agreement of the numerical data with the perturbative results of second order up to interaction strengths U/Γ ≈ 2, where Γ is the transparency of the impurity-electrode interface. The analytical results are obtained in form of the nonequilibrium self-energy for which we present explicit formulas in the closed form at arbitrary bias voltage. We observe an increase of the spectral density around zero energy brought about by the Kondo effect. Our analysis suggests that a finite applied voltage V acts as an effective temperature of the system. We conclude that at voltages significantly larger than the equilibrium Kondo temperature there is a complete suppression of the Kondo effect and no resonance splitting can be observed. We confirm this scenario by comparison of the numerical data with the perturbative results.

Physical Review B, 2005

We present the solution of the SU (N)⊗SU (M) Anderson impurity model using the Bethe-Ansatz. We first explain what extensions to the formalism were required for the solution. Subsequently we determine the ground state and derive the thermodynamics over the full range of temperature and fields. We identify the different regimes of valence fluctuation at high temperatures, followed by moment formation or intrinsic mixed valence at intermediate temperatures and a low temperature non-Fermi liquid phase. Among other things we obtain the impurity entropy, charge valence, and specific heat over the full range of temperature. We show that the low-energy physics is governed by a line of fixed points. This describes non-Fermi-liquid behavior in the integral valence regime, associated with moment formation, as well as in the mixed valence regime where no moment forms.