Supersymmetric approach to heavy-fermion systems

We present a new supersymmetric approach to the Kondo lattice model in order to describe simultaneously the quasiparticle excitations and the low-energy magnetic fluctuations in heavy-Fermion systems. This approach mixes the fermionic and the bosonic representation of the spin following the standard rules of superalgebra. Our results show the formation of a bosonic band within the hybridization gap reflecting the spin collective modes. The density of states at the Fermi level is strongly renormalized while the Fermi surface sum rule includes n _c + 1 states. The dynamical susceptibility is made of a Fermi liquid superimposed on a localized magnetism contribution.     

Cluster perturbation theory in Hubbard model exactly taking into account the short-range magnetic order in 2 × 2 cluster

The cluster perturbation theory is presented in the 2D Hubbard model constructed using X operators in the Hubbard-I approximation. The short-range magnetic order is taken into account by dividing the entire lattice into individual 2 × 2 clusters and solving the eigenvalue problem in an individual cluster using exact diagonalization taking into account all excited levels. The case of half-filling taking into account jumps between nearest neighbors is considered. As a result of numerical solution, a shadow zone is discovered in the quasiparticle spectrum. It is also found that a gap in the density of states in the quasiparticle spectrum at zero temperature exists for indefinitely small values of Coulomb repulsion parameter U and increases with this parameter. It is found that the presence of this gap in the spectrum is due to the formation of a short-range antiferromagnetic order. An analysis of the temperature evolution of the density of states shows that the metal-insulator transition occurs continuously. The existence of two characteristic energy scales at finite temperatures is demonstrated, the larger scale is associated with the formation of a pseudogap in the vicinity of the Fermi level, and the smaller scale is associated with the metal-insulator transition temperature. A peak in the density of states at the Fermi level, which is predicted in the dynamic mean field theory in the vicinity of the metal-insulator transition, is not observed.     

Staggered flux fluctuations and the quasiparticle scattering rate in the SU(2) gauge theory of the t-J model

We study staggered flux fluctuations around the superconducting state of the SU(2) mean-field theory for the two-dimensional t-J model and their effect on the electron spectral function. The quasiparticle peaks near (pi,0),(0,pi) get strongly broadened and partially wiped out by these fluctuations while the quasiparticle peaks near the nodes of the d-wave gap are preserved over a wide parameter range. The strength of these effects is governed by an energy scale that decreases towards zero for doping x-->0 and that is related to the energy splitting between the SU(2)-related superconducting and staggered flux mean-field states.     

Exactly solvable toy model for the pseudogap state

We present an exactly solvable toy model which describes the emergence of a pseudogap in an electronic system due to a fluctuating off-diagonal order parameter. In one dimension our model reduces to the fluctuating gap model (FGM) with a gap that is constrained to be of the form , where A and Q are random variables. The FGM was introduced by Lee, Rice and Anderson [Phys. Rev. Lett. 31, 462 (1973)] to study fluctuation effects in Peierls chains. We show that their perturbative results for the average density of states are exact for our toy model if we assume a Lorentzian probability distribution for Q and ignore amplitude fluctuations. More generally, choosing the probability distributions of A and Q such that the average of vanishes and its covariance is , we study the combined effect of phase and amplitude fluctuations on the low-energy properties of Peierls chains. We explicitly calculate the average density of states, the localization length, the average single-particle Green's function, and the real part of the average conductivity. In our model phase fluctuations generate delocalized states at the Fermi energy, which give rise to a finite Drude peak in the conductivity. We also find that the interplay between phase and amplitude fluctuations leads to a weak logarithmic singularity in the single-particle spectral function at the bare quasi-particle energies. In higher dimensions our model might be relevant to describe the pseudogap state in the underdoped cuprate superconductors. Received 15 March 2000     

Density of states of narrow superconducting channels in the regime of quantum fluctuations of the order parameter

The current–voltage characteristics of superconductor–insulator–semiconductor (S1–I–S2) tunnel junctions, where superconducting electrode S2 is a thin nanowire, are studied experimentally. The observed blurring of the gap singularities is interpreted as a manifestation of the order parameter quantum fluctuations. We propose a model taking into account the broadening of the density of states due to the interaction of electrons with the Mooij–Schön plasmon mode emerging in a quasi-one-dimensional superconducting channel in the regime of quantum fluctuations of the order parameter. The model gives results that are in a reasonable qualitative agreement with the experimental data.     

Quasiparticle bandstructures of covalent semiconductors and their surfaces

The exchange-correlation self-energies and quasiparticle shifts are calculated for band states of covalent materials (diamond, silicon) and their (001) 2×1 surface in order to solve the bulk and surface band-gap problem of the LDA. The screening properties are described by a model dielectric function taking into account the spatial nonlocality in the surface case assuming specular electron reflection. The wave functions are expanded in terms of localized orbitals. The quasiparticle bandstructures obtained are in reasonable agreement with experimental results.     

Density of prelocalized states in mesoscopic NS systems

The semiclassical theory of the proximity effect predicts the formation of a gap E _g ～?D/L ² in the excitation spectrum of a diffusive contact between a normal metal and a superconductor (NS). Mesoscopic fluctuations lead to the emergence of states localized anomalously in the normal metal and weakly linked with the superconducting bank, creating a nonzero density of states for energies lower than E _g . In this review, the behavior of the density of quasiparticle states below a quasi-classical gap is considered for various geometries of the NS system (special attention is paid to SNS junctions) and for the problem of a superconductor with a low concentration of magnetic impurities, in which a similar effect is observed. Analysis is mainly carried out on the basis of a fully microscopic method of the supermatrix σ model; in this method, a nonzero density of states emerges due to instanton configurations with broken supersymmetry. In addition, the results of an alternative approach proceeding from the idea of universality of the spectra of random Hamiltonians with the given symmetry are reviewed. In situations studied using both methods, the results are identical. They include the exact expression for the mean density of states of an NS system in the vicinity of E _g . In the framework of 1D and 2D σ models, the subgap density of states is determined with an exponential accuracy. The contacts with a poor transparency of the NS interface are also considered. It is shown that the number of subgap states in the case of low transparency is much greater than unity.

     

Energy scales and quasiparticle properties in an extended Hubbard model for HTC

By means of a strong-coupling approach, developed in previous works, we study the quasiparticle properties in an extended Hubbard model in presence of critical charge fluctuations near a stripe-quantum critical-point. We show that the quasiparticle dispersion has a kink along the diagonal Brillouin zone at the energy of the order 50 meV, for realistic values of the parameters. The energy and momentum distribution curves (EDC, MDC) along the diagonal are also analyzed. The results for the EDC derived quasiparticle width reveals an anomalous drop in the low-energy scattering rate at the same energy of the kink. This drop corresponds to a new energy scale in the system that reflects the interaction between the quasiparticles and the critical charge fluctuations. The results offer a possible interpretation of the ARPES and photoemission experiments on Bi2212.Received: 17 November 2003, Published online: 19 February 2004PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems     

Slave-boson phase diagram of the two-dimensional extended Hubbard model: Influence of electron-phonon coupling

We present a detailed study of the extended Hubbard-Peierls model on a square lattice using the slave-boson method proposed by Kotliar and Ruckenstein. The emphasis is on the investigation of the ground state phase diagram. To compare the relative stability of several homogenous phases, the effective bosonized action was evaluated by means of a two-sublattice saddlepoint approximation which allows for the symmetry broken states compatible with the underlying bipartite lattice structure. Paying particular attention to the interplay of electron-electron and electron-phonon interaction, we take into account various types of magnetic ordered phases, i.e. para-, ferro-, ferri-, and antiferromagnetic states, as well as charge ordered phases, e.g. a static (, ) Peierls distorted state. Furthermore the approach has been applied to the following special cases: the Hubbard model, the extended Hubbard model, and the Hubbard-Peierls model. A careful numerical solution of the corresponding self-consistency equations enables us to map out the ground-state phase diagrams of the various models at arbitrary band filling over the whole range of interaction strength. In the phase diagram of the Hubbard model we found a large region with ferrimagnetic order away from half-filling. The phase diagram of the halffilled band extended Hubbard model shows a first-order transition from a spin-density-wave to a charge-density-wave state which is displaced from the mean-field lineU=4V towards largerV. At large negativeU andV we obtain a domain with charge separation. The phase compares favorably with earlier quantum Monte-Carlo results. Including the local electron-phonon coupling the charge-density-wave region is considerably enlarged. Away from half-filling the phase diagram becomes more complex: besides the pure magnetic phases we obtain ferri- and paramagnetic states which show additional charge-density order. Aspects of phase separation are discussed. Finally we investigate the variation of the different gap and order parameters along characteristic lines in the parameter space and determine the renormalized quasiparticle bands.     

Study of non-Fermi-liquid-like state and pairing symmetry in iron pnictides based on the multiorbital Hubbard-Holstein model

We study the five-orbital Hubbard-Holstein model, taking account of the electron–phonon (e-ph) interaction due to the Fe-ion oscillation. In order to include the self-energy correction, we employ the fluctuation exchange (FLEX) approximation. It is revealed that the orbital fluctuations are enhanced by the e-ph interaction, which causes a strong attractive pairing interaction. The orbital fluctuations give rise to highly anisotropic quasiparticle lifetime (hot/cold spot structure) and non-Fermi-liquid-like transport phenomena. From the phase diagram obtained by the FLEX approximation, we find that (i) s-wave state without sign reversal is stable for the moderate e-ph coupling in the broad parameter region, which is consistent with the experimental non-magnetic impurity effect, (ii) the renormalization induced by the orbital fluctuation is not so strong, and (iii) superconducting (SC) state with node can appear in the broad parameter region in the presence of impurities.     

Effects of competing orders and quantum phase fluctuations on the low-energy excitations and pseudogap phenomena of cuprate superconductors

We investigate the low-energy quasiparticle excitation spectra of cuprate superconductors by incorporating both superconductivity (SC) and competing orders (CO) in the bare Green’s function and quantum phase fluctuations in the proper self-energy. Our approach provides consistent explanations for various empirical observations, including the excess subgap quasiparticle density of states, “dichotomy” in the momentum-dependent quasiparticle coherence and the temperature-dependent gap evolution, and the presence (absence) of the low-energy pseudogap in hole- (electron-) type cuprates depending on the relative scale of the CO and SC energy gaps.     

Self-Consistent Consideration of Fluctuations in Singlet Superconducting Phases with s and d Symmetry

We analyze the behavior of thermal fluctuations of the superconducting order parameter with extended s-wave and $${{d}_{{{{x}^{2}} - {{y}^{2}}}}}$$-wave symmetry. For this purpose, we develop a method of self-consistent consideration of the order parameter fluctuations and charge carrier scatterers by fluctuations of coupled electron pairs using the theory of functional integration. The study is performed based on the quasi-two-dimensional one-band model with attraction between electrons located at neighboring sites. We obtain the distribution functions of the phase fluctuation probabilities depending on temperature, charge carrier concentrations, and model parameters. It is shown that the phase of the order parameter in the superconducting region is coherent, and the density of states has a dip at the Fermi level. In approaching the incoherent region of the phase diagram, the dip in the density of states disappears simultaneously with the loss of phase coherence. At the same time, the order parameter amplitude averaged over fluctuations remains finite at any temperature and concentration of charge carriers. Our results show that the pseudogap state cannot be explained in the frames of this scenario.     

Fluctuation effects in disordered Peierls systems

We review the density of states (DOS) and related quantities of quasi one‐dimensional disordered Peierls systems in which fluctuation effects of a backscattering potential play a crucial role. The low‐energy behavior of non‐interacting fermions which are subject to a static random backscattering potential will be described by the strictly one‐dimensional fluctuating gap model (FGM). Recently, the FGM has also been used to explain the pseudogap phenomenon in high‐T_c superconductors. We develop a non‐perturbative method which allows for a simultaneous calculation of the DOS and inverse localization length for an arbitrary given disorder potential by solving a simple initial value problem. In the white noise limit, we recover all known results by solving a Fokker‐Planck equation. For the physically interesting case of finite correlation lengths, we use analytical and numerical methods to show that a complex order parameter leads to a suppression of the DOS, i.e. a pseudogap, and that for a real order parameter this pseudogap is overshadowed by a singularity in the DOS. We will also consider the case of classical phase fluctuations which applies to low temperatures where amplitude fluctuations are frozen out. For this regime we present analytic results for the DOS, the inverse localization length, the specific heat, and the Pauli susceptibility.     

Bound and Scattering States of Extended Calogero Model with an Additional PT Invariant Interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameters differ from each other in the presence of PT invariant interaction.     

Density of localized states and linear specific heat for anderson model of amorphous semiconductors

The Anderson model is used to describe the role of electron correlation in localized states in amorphous semiconductors. We adopt a quasiparticle approach and discuss both the Fermi level pinning and the linear specific heat in terms of temperature and concentration changes of the one-particle density of states.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.     

Probing the unconventional superconducting state of LiFeAs by quasiparticle interference

A crucial step in revealing the nature of unconventional superconductivity is to investigate the symmetry of the superconducting order parameter. Scanning tunneling spectroscopy has proven a powerful technique to probe this symmetry by measuring the quasiparticle interference (QPI) which sensitively depends on the superconducting pairing mechanism. A particularly well-suited material to apply this technique is the stoichiometric superconductor LiFeAs as it features clean, charge neutral cleaved surfaces without surface states and a relatively high T(c)～18 K. Our data reveal that in LiFeAs the quasiparticle scattering is governed by a van Hove singularity at the center of the Brillouin zone which is in stark contrast to other pnictide superconductors where nesting is crucial for both scattering and s(±) superconductivity. Indeed, within a minimal model and using the most elementary order parameters, calculations of the QPI suggest a dominating role of the holelike bands for the quasiparticle scattering. Our theoretical findings do not support the elementary singlet pairing symmetries s(++), s(±), and d wave. This brings to mind that the superconducting pairing mechanism in LiFeAs is based on an unusual pairing symmetry such as an elementary p wave (which provides optimal agreement between the experimental data and QPI simulations) or a more complex order parameter (e.g., s+id wave symmetry).     

Influence of disorder on the local density of states in high- T(c) superconducting thin films

Using a low temperature scanning tunneling microscope in the spectroscopic mode, we find that the disorder in a Bi(2)Sr(2)CaCu(2)O(8+delta) thin film modifies dramatically the quasiparticle local density of states. Small, but well-defined superconducting regions, coexisting with dominating semiconducting areas, show well-pronounced gap structures, similar to those observed previously in high-quality single crystals. Surprisingly, between these two regions, the detailed shape of the quasiparticle spectrum is virtually identical to the pseudogap previously observed at temperatures T>T(c), or in the vortex core, at 4.2 K. Thus, the role of the disorder in destroying the superconducting phase is comparable to that of the magnetic field or thermal fluctuations.