Schrieffer Model Research Articles

Superconducting state in Ba1−x Sr x Ni2As2 near the quantum critical point

In the phase diagram of the nickel-based superconductor Ba1−x Sr x Ni2As2, T c has been found to be enhanced sixfold near the quantum critical point (QCP) x = 0.71 compared with the parent compound. However, the mechanism is still under debate. Here, we report a detailed investigation of the superconducting properties near the QCP (x ≈ 0.7) by utilizing scanning tunneling microscopy and spectroscopy. The temperature-dependent superconducting gap and magnetic vortex state were obtained and analyzed in the framework of the Bardeen–Cooper–Schrieffer model. The ideal isotropic s-wave superconducting gap excludes the long-speculated nematic fluctuations while preferring strong electron–phonon coupling as the mechanism for T c enhancement near the QCP. The lower than expected gap ratio of Δ/(k B T c) is rooted in the fact that Ba1−x Sr x Ni2As2 falls into the dirty limit with a serious pair breaking effect similar to the parent compound.

Breakdown of the Meissner effect at the zero exceptional point in non-Hermitian two-band BCS model

The spontaneous symmetry breaking of a continuous symmetry in complex field theory at the exceptional point (EP) of the parameter space is known to exhibit interesting phenomena, such as the breakdown of a Higgs mechanism. In this work, we derive the complex Ginzburg–Landau model from a non-Hermitian two-band Bardeen–Cooper–Schrieffer model via path integral and investigate its spontaneous symmetry breaking. We find that analog to the Higgs mechanism, the Meissner effect of the complex Ginzburg–Landau model also breaks down at the EP while the gap parameters stay finite.

Bismuth antiphase domain wall: A three-dimensional manifestation of the Su-Schrieffer-Heeger model

The Su, Schrieffer and Heeger (SSH) model, describing the soliton excitations in polyacetylene due to the formation of antiphase domain walls (DW) from the alternating bond pattern, has served as a paradigmatic example of one-dimensional (1D) chiral topological insulators. While the SSH model has been realized in photonic and plasmonic systems, there have been limited analogues in three-dimensional (3D) electronic systems, especially regarding the formation of antiphase DWs. Here, we propose that pristine bulk Bi, in which the dimerization of $(111)$ atomic layers renders alternating covalent and van der Waals bonding within and between successive $(111)$ bilayers, respectively, serves as a 3D analogue of the SSH model. First, we confirm that the two dimerized Bi structures belong to different Zak phases of 0 and $\pi$ by considering the parity eigenvalues and Wannier charge centers, while the previously reported bulk topological phases of Bi remain invariant under the dimerization reversal. Next, we demonstrate the existence of topologically non-trivial $(111)$ and trivial $(11\bar{2})$ DWs in which the number of in-gap DW states (ignoring spin) is odd and even respectively, and show how this controls the interlinking of the Zak phases of the two adjacent domains. Finally, we derive general criteria specifying when a DW of arbitrary orientation exhibits a $\pi$ Zak phase based on the flip of parity eigenvalues. An experimental realization of dimerization in Bi and the formation of DWs may be achieved via intense femtosecond laser excitations that can alter the interatomic forces and bond lengths.

Pressure effect on magnetic susceptibility of intermediate-valence compound YbInAu2

The pressure dependence of the magnetic susceptibility of the intermediate-valence compound YbInAu2 has been measured in the temperature range of 78−300 K, showing a strong and temperature-dependent increase in susceptibility under pressure. The initial analysis of the experimental data within the framework of the integer valence Coqblin–Schrieffer model has given certain estimates of the Kondo temperature and its pressure derivative, but did not allow to describe quantitatively the specific temperature dependence of the susceptibility itself. The Anderson impurity model with infinite Coulomb repulsion U, the main parameters of which are the position of the f level relative to the Fermi energy and its hybridization width, turned out to be more suitable to describe the obtained experimental data for YbInAu2, indicating a strong dependence of the f-level position on the atomic volume.

Poor man’s scaling: XYZ Coqblin–Schrieffer model revisited

We derive the third-order poor man’s scaling equation for a generic Hamiltonian describing a quantum impurity embedded into an itinerant electron gas. We show that the XYZ Coqblin–Schrieffer model introduced by one of us earlier is algebraically renormalizable in the sense that the form of the Hamiltonian is preserved along the scaling trajectory, write down the scaling equations for the model, and analyze the renormalization group flows in the cases of both constant and pseudogap densities of states.

Energetics and magnetism of topological graphene nanoribbons

The topological properties of graphene nanoribbons (GNRs) have received a significant amount of attention in emerging fields such as spintronics and quantum computing. This study is focused on the energetics and magnetism of symmetry-protected junction state arrays, which are realized in the alternating periodic structures of two topologically different armchair GNRs. We found that the antiferromagnetic states require at least eight unit cells for each segment of the periodic armchair GNRs, where the armchair GNRs whose numbers of carbon atoms in a row are seven and nine are connected with a junction structure. We also found the junction structure that provides more stable antiferromagnetic states. Furthermore, we propose an end (armchair GNRs/vacuum interface) structure to avoid disturbing the global topological properties of the junction state array. This means that if the topological end states (non-trivial phases of the Su, Schrieffer, and Heeger model or Majorana fermions) exist, they are properly formed at the endmost junctions without the requirement for extra effort such as long end extension. We believe that this study can add new guidelines and challenges for realizing graphene-based quantum computing.

Direct observation of defect modes in molecular aggregate analogs

In this work we investigate defect modes localized at the ends and within the bulk of 1D metamaterial analogs of molecular aggregates. The study is undertaken in the microwave regime, where the cm scale of the metamaterial analog provides an opportunity to directly probe the modes deep within their near fields in ways not easily achieved in molecular systems. To demonstrate the power of this approach we compare our observations to predictions from a simple Su, Schrieffer, and Heeger (SSH) model and find good qualitative agreement.

Ratios of negative-to-positive parity level densities in Mo isotopes

The ratios of negative-to-positive parity level densities in 94,96,98Mo isotopes are calculated using a microscopic formalism based on the Bardeen–Cooper–Schrieffer (BCS) model. In this calculation, the single-particle energies are obtained with the Nilsson model. Mass number, shell, and deformation effects on the parity equilibration phenomenon in these isotopes are discussed in this work.

Poor man's scaling: anisotropic Kondo and Coqblin–Schrieffer models

We discuss Kondo effect for a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, and derive scaling equation to the second order for such a model. We show how the scaling equation for the spin-anisotropic Kondo model with the power law density of states (DOS) for itinerant electrons follows from the general scaling equation. We introduce the anisotropic Coqblin–Schrieffer model, apply the general method to derive scaling equation for that model for the power law DOS, and integrate the derived equation analytically.

Interplay of antiferromagnetism and Kondo effect in [formula omitted

The interplay of antiferromagnetic (AFM) and Kondo effect in Ce8Pd24Al with the dilution of Ce with La is investigated by means of electrical and thermal transport and magnetic properties measurements. X - ray diffraction studies confirm a cubic AuCu3 - type crystal structure with space group Pm3¯m for all compositions in the alloy series (Ce1−xLax)8Pd24Al(0≤x≤1). Electrical resistivity, ρ(T) results show evolution from coherent Kondo lattice scattering with a well defined Kondo peak at Tmax to incoherent single-ion Kondo scattering with increasing La content x. Magnetoresistivity MR measurements on Ce dilute alloys are negative and analyzed based on the calculations by Schlottmann for the Bethe - ansatz in the framework of the Coqblin - Schrieffer model and yield values of the Kondo temperature TK and the effective moment of the Kondo ion μK. The decrease of Tmax and TK is described by the compressible Kondo lattice model. The thermoelectric power, S(T) measurements are interpreted within the phenomenological resonance model. The Lorentz number, L/L0 increases rapidly on cooling the samples and reaches a maximum value around 6K. The magnetic susceptibility, χ(T) data at high temperature follow the Curie - Weiss behaviour and yield effective magnetic moments, μeff values across the series close to the value of 2.54μB expected for the free Ce3+ - ion. The low temperature χ(T) shows an AFM anomaly associated with a Néel temperature TN for alloys in the range 0≤x≤0.2. No metamagnetic transition was observed from the magnetization results, M(μ0H).

Topologically protected localised states in spin chains

We consider spin chain families inspired by the Su, Schrieffer and Hegger (SSH) model. We demonstrate explicitly the topologically induced spatial localisation of quantum states in our systems. We present detailed investigations of the effects of random noise, showing that these topologically protected states are very robust against this type of perturbation. Systems with such topological robustness are clearly good candidates for quantum information tasks and we discuss some potential applications. Thus, we present interesting spin chain models which show promising applications for quantum devices.

The effect of shell closure on the thermodynamic properties of 207Pb and 89Y

Nuclear level densities of [Formula: see text]Pb and [Formula: see text]Y are calculated using the Lipkin–Nogami (LN) method and Bradeen–Cooper–Schrieffer (BCS) model. It is revealed that the calculated nuclear level densities are highly matched with the experimental data of Oslo group. The excitation energy and entropy are calculated for mentioned nuclei. In the case of two studied nuclei the characteristic of being magic for the number of neutrons or protons causes the decrease of the excitation energy and entropy contribution of magic system at low temperatures.

Particle-number fluctuation of pairing correlations for Dy isotopes**Supported by Fundamental Research Funds for the Central Universities (JUSRP1035), National Natural Science Foundation of China (11305077)

Within the relativistic mean field (RMF) theory, the ground state properties of dysprosium isotopes are studied using the shell-model-like approach (SLAP), in which pairing correlations are treated with particle-number conservation, and the Pauli blocking effects are taken into account exactly. For comparison, calculations of the Bardeen–Cooper–Schrieffer (BCS) model with the RMF are also performed. It is found that the RMF+SLAP calculation results, as well as the RMF+BCS ones, reproduce the experimental binding energies and one- and two-neutron separation energies quite well. However, the RMF+BCS calculations give larger pairing energies than those obtained by the RMF+SLAP calculations, in particular for nuclei near the proton and neutron drip lines. This deviation is discussed in terms of the BCS particle-number fluctuation, which leads to the sizable deviation of pairing energies between the RMF+BCS and RMF+SLAP models, where the fluctuation of the particle number is eliminated automatically.

Crystal fields and Kondo effect: New results for the magnetic susceptibility

The thermodynamic Bethe ansatz equations for the Coqblin–Schrieffer model have been solved for the first time to obtain the magnetic susceptibility in the presence of crystal fields for non-zero temperatures. For the case of N=4 effective ionic states an analytic expression for the limiting values of the pseudo-energies has been found facilitating the numerical solution for various crystal and magnetic field configurations. The single-impurity model applies to a wide range of dense Kondo systems and has been used before to explain apparent non-Fermi-liquid behavior. The flattening off of the susceptibility curves at a substantially higher temperature than the specific heat is shown to be a general feature of the Coqblin–Schrieffer thermodynamics.

Analysis of the superconductivity in perovskite oxides using three-square-well BCS formalism

Superconductivity in perovskite, BaKBiO, is studied in the Bardeen–Cooper–Schrieffer (BCS) model, with three-square-well potentials. Components of the new coupling are: the attractive acoustic phonon–electron, optical phonon–electron and repulsive Coulomb interactions. With these in the BCS pairing Hamiltonian, expressions for the superconducting transition temperature and isotope effect exponent are obtained. Results of our analysis are consistent with experiments. Contributions of interactions to system properties are exhibited and analysed. Acoustic phonon–electron and optical phonon–electron interactions have near-identical elevation of transition temperature, holding out possible explanations for high- Tc. Contrastingly, optical phonon–electron and Coulomb couplings cause debilitation of isotope exponent, a possible explanation for low isotope exponent in the cuprates and other high- Tc systems. It is found that BCS electron–phonon coupling appears synonymous with acoustic phonon–electron coupling.

Electrical and thermal transport properties of the alloy system (Ce1-xLax)Cu4In

The studies of electrical resistivity, ρ(T), magnetoresistivity, MR, thermoelectric power, S(T) and thermal conductivity, λ(T), of the alloy system (Ce1-xLax)Cu4In (0 ≤ x ≤ 1) are reported. The room temperature powder X-ray diffraction studies confirm the orthorhombic CeCu4.38ln1.62 – type crystal structure with space group Pnnm (No. 58) for all investigated compositions across the series. ρ(T) results indicate an evolution from coherent Kondo scattering to incoherent single – ion Kondo scattering, with increased La content x. ρ(T) for each composition at high temperature is described by a -ln(T) behaviour. MR measurements on Ce dilute alloys are interpreted within the single – ion Bethe ansatz description of the Coqblin – Schrieffer model. S(T) results are described by the phenomenological resonance model. λ(T) data increase linearly with temperature from low T and shows a tendency toward saturation above 300 K for dilute Ce alloys. The Lorentz number, L/L0 and the dimensionless figure of merit, ZT = S2T/λρ increase upon cooling and exhibit maxima at low temperatures.

The atomic approach for the Coqblin–Schrieffer model

In this work we consider the Coqblin–Schrieffer model when the spin is S=1/2. The atomic solution has eight states: four conduction and two localized states, and we can then calculate the eigenenergies and eigenstates analytically. From this solution, employing the cumulant Green׳s functions results of the Anderson model, we build a “seed”, that works as the input of the atomic approach, developed earlier by some of us. We obtain the T-matrix as well as the conduction Green׳s function of the model, both for the impurity and the lattice cases. The generalization for other moments within N states follows the same steps. We present results both for the impurity as well as for the lattice case and we indicate possible applications of the method to study ultra cold atoms confined in optical superlattices and Kondo insulators. In this last case, our results support an insulator–metal transition as a function of the temperature.

A study of self-consistent Hartree–Fock plus Bardeen–Cooper–Schrieffer calculations with finite-range interactions

In this work we test the validity of a Hartree–Fock plus Bardeen–Cooper–Schrieffer model in which a finite-range interaction is used in the two steps of the calculation by comparing the results obtained to those found in fully self-consistent Hartree–Fock–Bogoliubov calculations using the same interaction. Specifically, we consider the Gogny-type D1S and D1M forces. We study a wide range of spherical nuclei, far from the stability line, in various regions of the nuclear chart, from oxygen to tin isotopes. We calculate various quantities related to the ground state properties of these nuclei, such as binding energies, radii, charge and density distributions, and elastic electron scattering cross sections. The pairing effects are studied by direct comparison with the Hartree–Fock results. Despite its relative simplicity, in most cases, our model provides results very close to those of the Hartree–Fock–Bogoliubov calculations, and it reproduces the empirical evidence of pairing effects rather well in the nuclei investigated.

CaLi2 superconductor under the pressure of 100 GPa: the thermodynamic critical field and the specific heat

In this paper the thermodynamic properties of the CaLi2 superconductor have been studied at a pressure of 100 GPa. The thermodynamic critical field (HC) and the specific heats for the superconducting and normal states (CS and CN) have been obtained. The calculations have been made within the framework of the Eliashberg approach for a wide range of the Coulomb pseudopotential: μ⋆∈〈0.1,0.3〉. It has been shown that the low-temperature critical field and the specific heat jump at TC strongly decrease if μ⋆ increases. The value of the dimensionless ratio RC ≡ (CS − CN)/CN at the critical temperature differs significantly from the value predicted by the Bardeen–Cooper–Schrieffer (BCS) model. In particular, the parameter RC decreases from 1.83 to 1.73 with the increase of the Coulomb pseudopotential value. In the paper, the interpolation formulas for the functions TC(μ⋆) and RC(μ⋆) have also been given.

Evidence for two-gap superconductivity in the non-centrosymmetric compound LaNiC2

We study the superconducting properties of the non-centrosymmetric compound LaNiC2 by measuring the London penetration depth Δλ(T), the specific heat C(T,B) and the electrical resistivity ρ(T,B). Both Δλ(T) and the electronic specific heat Ce(T) exhibit behavior at low temperatures that can be described in terms of a phenomenological two-gap Bardeen–Cooper–Schrieffer (BCS) model. The residual Sommerfeld coefficient in the superconducting state, γ0(B), shows a rapid increase at low fields and then an eventual saturation with increasing magnetic field. A pronounced upturn curvature is observed in the upper critical field Bc2(T) near Tc. All these experimental observations support the existence of two-gap superconductivity in LaNiC2.