The low temperature spectral weight transfer problem in Kondo insulators

In this paper we address the problem of the spectral weight transfer in Kondo insulators (KI). We employ the X-boson approach for the periodic Anderson model, in the U →∞ limit. We calculate the two energy gaps of the system analytically: the indirect gap, Δ_ind = E_g ≃ E_mir, present in the density of states, and the direct one Δ_dir, associated with the minimum energy necessary to produce inter-band transitions. We find that the optical behavior of the system is governed by two energy scales: one of low frequency, characterized by E_g ≃ E_mir, in the mid-infrared region (MIR), which is a reminiscent of the heavy fermion E_mir peak, that appears in Kondo insulators as a broad maximum in the MIR region and that controls the low temperature transport properties, the gap opening in optical conductivity and the formation of the Drude peak, at ω = 0, in the intermediate temperature range. The other energy scale appears at high frequencies, and is characterized by the direct gap Δ_dir. According to our results, this peak controls the anomalous redistribution of spectral weight in the optical conductivity. We apply the theory in order to study the Kondo insulator FeSi, and we calculate the optical conductivity of the system and the spectral weight transfer in the optical conductivity.     

Numerical study of the directed polymer in a 1 + 3 dimensional random medium

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length L, the high temperature phase is characterized by a diffusive behavior for the end-point displacement R² ∼L and by free-energy fluctuations of order ΔF(L) ∼O(1). The low-temperature phase is characterized by an anomalous wandering exponent R²/L ∼L^ω and by free-energy fluctuations of order ΔF(L) ∼L^ω where ω∼0.18. In this paper, we first study the scaling behavior of various properties to localize the critical temperature T_c. Our results concerning R²/L and ΔF(L) point towards 0.76 < T_c ≤T₂=0.79, so our conclusion is that T_c is equal or very close to the upper bound T₂ derived by Derrida and coworkers (T₂ corresponds to the temperature above which the ratio remains finite as L ↦ ∞). We then present histograms for the free-energy, energy and entropy over disorder samples. For T ≫T_c, the free-energy distribution is found to be Gaussian. For T ≪T_c, the free-energy distribution coincides with the ground state energy distribution, in agreement with the zero-temperature fixed point picture. Moreover the entropy fluctuations are of order ΔS ∼L^1/2 and follow a Gaussian distribution, in agreement with the droplet predictions, where the free-energy term ΔF ∼L^ω is a near cancellation of energy and entropy contributions of order L^1/2.     

A fractional-spin phase in the power-law Kondo model

We consider a Kondo impurity coupled to a fermionic host with a power-law density of states near the Fermi level, ρ(ε) ∼ |ε|^r, with exponent r < 0. Using both perturbative renormalization group (poor man's scaling) and numerical renormalization group methods, we analyze the phase diagram of this model for ferromagnetic and antiferromagnetic Kondo coupling. Both sectors display non-trivial behavior with several stable phases separated by continuous transitions. In particular, on the ferromagnetic side there is a stable intermediate-coupling fixed point with universal properties corresponding to a fractional ground-state spin. Received 18 February 2002 Published online 31 July 2002     

Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r>0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U>0case: it exhibits both strong coupling (SC) states (for r<1) and local moment states (for r>1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U>0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r>1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength. Received 26 August 1999     

Numerical renormalization group studies of SU(4) Kondo effect in quantum dots

We theoretically study an enhancement of the Kondo effect in quantum dots with two orbitals and spin . The Kondo temperature and conductance are evaluated as functions of energy difference Δ between the orbitals, using the numerical renormalization group method. The Kondo temperature is maximal around the degeneracy point (Δ=0) and decreases with increasing |Δ| following a power law, T_K(Δ)=T_K(0)(T_K(0)/|Δ|)^γ, which is consistent with the scaling analysis. The conductance at T=0 is almost constant 2e²/h. Both the orbitals contribute to the conductance around Δ=0, whereas the current through the upper orbital is negligibly small when |Δ|T_K(0). These are characteristics of SU(4) Kondo effect.     

Composite spin-triplet superconductivity in an symmetric lattice model

The two-channel Anderson lattice model which has SU (2) ⊗ SU (2) symmetry is of relevance to understanding of the magnetic, quadrupolar and superconducting phases in U_1-xTh_xBe₁₃ or Pr based skutterudite compounds such as PrFe₄P₁₂ or PrOs₄Sb₁₂. Possible unconventional superconducting phases of the model are explored. They are characterized by a composite order parameter comprising of a local magnetic or quadrupolar moment and a triplet conduction electron Cooper-pair. This binding of local degrees of freedom removes the entropy of the non Fermi-liquid normal state. We find superconducting transitions in the intermediate valence regime which are suppressed in the stable moment regime. The gap function is non analytic and odd in frequency: a pseudo-gap develops in the conduction electron density of states which vanishes as |ω| close to ω = 0. In the strong intermediate valent regime, the gap function acquires an additional -dependence. Received 28 February 2002 / Received in final form 18 April 2002 Published online 9 July 2002     

Parity law of the singlet-triplet gap in graphitic ribbons

This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number n_ω of benzene rings along the ribbon width is odd. A series of numerical calculations (quantitative mapping on spin 1/2 chains, renormalized excitonic treatments and Quantum Monte Carlo) confirms the parity law and the gapless character of the ribbon for even n_ω.     

Quantum adiabatic polarons by translationally invariant perturbation theory

The translationally invariant diagrammatic quantum perturbation theory (TPT) is applied to the polaron problem on the 1D lattice, modeled through the Holstein Hamiltonian with the phonon frequency ω₀, the electron hopping t and the electron-phonon coupling constant g. The self-energy diagrams of the fourth-order in g are calculated exactly for an intermittently added electron, in addition to the previously known second-order term. The corresponding quadratic and quartic corrections to the polaron ground state energy become comparable at t/ω₀>1 for g/ω₀∼(t/ω₀) ^1/4 when the electron self-trapping and translation become adiabatic. The corresponding non adiabatic/adiabatic crossover occurs while the polaron width is large, i.e. the lattice coarsening negligible. This result is extended to the range (t/ω₀)^1/2>g/ω₀>(t/ω₀)^1/4>1 by considering the scaling properties of the high-order self-energy diagrams. It is shown that the polaron ground state energy, its width and the effective mass agree with the results found traditionally from the broken symmetry side, kinematic corrections included. The Landau self-trapping of the electron in the classic self-consistent, localized displacement potential, the restoration of the translational symmetry by the classic translational Goldstone mode and the quantization of the polaronic translational coordinate are thus all encompassed by a quantum theory which is translationally invariant from the outset. This represents the first example, open to various generalizations, of the capability of TPT to hold through the adiabatic symmetry breaking crossover. Plausible arguments are also given that TPT can describe the g/ω₀>(t/ω₀)^1/2 regime of the small polaron with adiabatic or non-adiabatic translation, i.e., that TPT can cover the whole g/ω₀, t/ω₀ parameter space of the Holstein Hamiltonian.     

Temperature dependent properties of metallic clusters containing magnetic impurities

The properties of magnetic impurities in small metallic clusters are investigated in the framework of the Anderson model by using exact diagonalization methods. Parameters representative of the Kondo limit are considered. The spin gap ΔE = E(S=1, 3/2) - E(S=0, 1/2) shows a remarkable band-filling dependence that can be interpreted in terms of the cluster-specific conduction-electron spectrum. Finite-temperature properties such as the magnetic susceptibility and specific heat are calculated exactly in the canonical and grand canonical ensembles. The structural dependence is illustrated. Received 30 November 2000     

Influence of local spin polarization to the Kondo effect

We use the spin non-degenerate single impurity Anderson model to investigate the influence of the local spin polarization to the Kondo effect. By using the Schrieffer-Wolff transformation, we obtain a generalized s-d exchange Hamiltonian, which describes the interaction between a polarized local spin and conduction electrons. In this case, the singlet is no longer an eigenstate as shown by variational calculations where the splitting of the local energy Δ = ɛ _d↑ − ɛ _d↓ can be arbitrarily small. The local spin polarization generates the instability of the singlet ground state of the S = 1/2 s-d exchange model.      

Nuclear matter properties in relativistic mean-field model with σ- ω coupling

The σ-ω coupling is introduced phenomenologically in the linear σ-ω model to study the nuclear matter properties. It is shown that not only the effective nucleon mass M^* but also the effective σ meson mass m _σ ^* and the effective ω meson mass m _ω ^* are nucleon-density-dependent. When the model parameters are fitted to the nuclear saturation point, with the nuclear radius constant r ₀ = 1.14 fm and volume energy a ₁ = 16.0 MeV, as well as to the effective nucleon mass M ^* = 0.85M, the model yields m _σ ^* = 1.09m _σ and m _ω ^* = 0.90m _ω at the saturation point, and the nuclear incompressibility K ₀ = 501 MeV. The lowest value of K₀ given by this model by adjusting the model parameters is around 227 MeV. Received: 23 March 2001 / Accepted: 8 June 2001     

Spin glass and ferromagnetism in Kondo lattice compounds

The Kondo lattice model has been analyzed in the presence of a random inter-site interaction among localized spins with non zero mean J₀ and standard deviation J. Following the same framework previously introduced by us, the problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields. The static approximation and the replica symmetry ansatz have allowed us to solve the problem at a mean field level. The resulting phase diagram displays several phase transitions among a ferromagnetically ordered region,a spin glass one, a mixed phase and a Kondo state depending on J₀, J and its relation with the Kondo interaction coupling J_K. These results could be used to address part of the experimental data for the CeNi _{1 - x} Cu _x compound, when x ⩽ 0.8. Received 24 June 2002 Published online 31 December 2002     

Low temperature properties of the Kondo insulator FeSi

In this paper we study the low temperature (T) properties of the Kondo insulator FeSi within the X-boson approach. We show that the ground state of the FeSi is metallic and highly correlated with a large effective mass; the low temperature contributions to the specific heat and the resistivity are of the Fermi-liquid type. The low temperature properties are governed by a reentrant transition into a metallic state, that occurs when the chemical potential crosses the gap and enters the conduction band, generating a metallic ground state. The movement of the chemical potential is due to the strong correlations present in the system. We consider the low temperature regime of the Kondo insulator FeSi, where the hybridization gap is completely open. In this situation we identify the two characteristic temperatures: the coherence temperature T₀ and the Kondo temperature T_KL. In the range T < T₀, we identify a regime characterized by the formation of coherent states and Fermi-liquid behavior of the low temperature properties; in the range T_KL > T > T₀, we identify a regime characterized by an activation energy. Within the X-boson approach we study those low temperature regimes although we do not try to adjust parameters to recover the experimental energy scales.     

Space-time dispersion of graphene conductivity

We present an analytic calculation of the conductivity of pure graphene as a function of frequency ω, wave-vector k, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter γ≃3 eV, but much larger than the collision rate τ^-1. The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for kv₀≪ T≪ω is equal to σ(ω,k)=e²/4ħ and independent of the band structure parameters γ and v₀. Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure.     

Submillimetric cyclotron resonance linewidths and electron relaxation time in copper

For the first time submillimetric microwaves (λ<1 mm) are used to observe Azbel' Kaner cyclotron resonance in metals. The very high frequency used (typicallyF≅400 GHz) gives a large value ofωτ (typically 500) and therefore very sharp peaks. The fundamental resonance fieldH _c=m ^* cω/e is rather high (typically 200 KG), so subharmonicsH _c/n can be observed at many values ofH in the field region 0–27 KG. If relatively few electrons participate in the resonance and ifω _cτ≧50 (ω _c=eH/m ^* c,τ relaxation time) thenChambers has shown that the line shapes are independent of relaxation time while the fractional linewidthΔH/H varies as l/ωτ. For the belly orbit in pure copper the conditions of Chambers' theory are satisfied forH≧20 KG parallel to [111] axis.m ^* is a minimum andτ=1.8×10⁻¹⁰ s.     

Collective electronic excitations in a semiconductor superlattice in the Landau and Wannier-Stark ladder regime

Using a mean-field approximation, we have developed a systematic treatment of collective electronic modes in a semiconductor superlattice (SL) in the presence of strong electric and magnetic fields parallel to the SL axis. The spectrum of collective modes with zero wavevector along the SL axis is shown to consist of a principle magnetoplasmon mode and an infinite set of Bernstein-like modes. For non-zero wavevector along the SL axis, in addition to the cyclotron modes, extra collective modes are found at the frequencies |Nω _c±Mω _s|, which we call cyclotron-Stark modes (ω _c and ω _s are respectively the cyclotron and Stark frequencies, N and M are integer numbers). The frequencies of the modes propagating in “oblique” direction with respect to the SL axis show oscillatory behavior as a function of electric field strength. All the modes considered have very weak spatial dispersion and they are not Landau damped. The specific predictions made for the dispersion relations of the collective excitations should be observable in resonant Raman scattering experiments. Received 29 August 2002 / Received in final form 25 February 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: 612033@inbox.ru     

Transport theory of multiterminal hybrid structures

We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact. The maximal conductance of a two-channel contact is proportional to (e ²/h)(a ₀/D)²exp[-D/ξ(ω^*)], where D is the distance between the contacts, a₀ the lattice spacing, ξ(ω) is the superconducting coherence length, and ω^* is the cross-over frequency between a perturbative regime ( ω < ω^*) and a non perturbative regime ( ω^* < ω < Δ). Received 18 June 2001 and Received in final form 17 January 2002     

Statistical mechanics and Vlasov equation allow for a simplified Hamiltonian description of Single-Pass Free Electron Laser saturated dynamics

A reduced Hamiltonian formulation which reproduces the saturated regime of a Single Pass Free Electron Laser, around perfect tuning, is here discussed. Asymptotically, N_m particles are found to organize in a dense cluster, that evolves as an individual massive unit. The remaining particles fill the surrounding uniform sea, spanning a finite portion of phase space, approximately delimited by the average momenta ω₊ and ω_-. We propose a theoretical framework in which the external parameters N_m, ω₊ and ω_- are self-consistently determined. To this aim, we make use of a statistical mechanics treatment of the Vlasov equation, that governs the initial field amplification process. Simulations of the reduced dynamics are shown to successfully capture the oscillating regime observed within the original N-body picture.     

The Scaling Limit Geometry of Near-Critical 2D Percolation

We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for p = p _c+λδ^1/ν, with ν = 4/3, as the lattice spacing δ → 0. Our proposed framework extends previous analyses for p = p _c, based on SLE ₆. It combines the continuum nonsimple loop process describing the full scaling limit at criticality with a Poissonian process for marking double (touching) points of that (critical) loop process. The double points are exactly the continuum limits of “macroscopically pivotal” lattice sites and the marked ones are those that actually change state as λ varies. This structure is rich enough to yield a one-parameter family of near-critical loop processes and their associated connectivity probabilities as well as related processes describing, e.g., the scaling limit of 2D minimal spanning trees.