A model of Wigner liquid

A two-dimensional low-density system of charge carriers with strong Coulomb interaction, which can lead to the appearance of a short-wavelength soft mode (precursor of crystallization) is examined. This system provides elementary excitations of two types: Fermi excitations and Bose excitations with a gap in the spectrum. The latter excitations are similar to rotons in superfluid helium. A model involving the Fermi liquid and the soft mode is proposed, and interaction of different excitations with each other is described phenomenologically as in the Landau theory of Fermi liquid. By solving the derived equations, it was found that, as the temperature increases, the effective mass of Fermi excitations decreases and the gap in the Bose excitation spectrum increases.     

各向异性高压物质的电子能谱

本文以高压物质作为一种简单的各向异性金属模型,研究了静晶格场、电子间库仑相互作用和通过声子场的相互作用对单粒子元激发谱的影响。讨论了周期场中电子格林函数的微扰论级数,原则上解决了用微扰论求周期场中费米系统能谱的问题。具体计算了面心立方和体心立方高压物质的费米面和态密度,给出了数值结果。     

Properties of a two-dimensional semimetal in a strong magnetic field

A system of two-dimensional electrons and holes ha s been investigated in a strong magnetic field, when it is sufficient to take into account only the ground Landau level. It has been shown that the interaction of electrons and holes can lead to an ordered state. In this problem, the exchange interaction in electron and hole subsystems is significant. The following two cases have been considered: (a) there are one electron and one hole valleys, and at some magnetic field strength, there exists an ordered state, as in an excitonic insulator; and (b) there exist one electron and two equivalent hole valleys (as in the experiment performed by Kvon et al. [1]), and the hole system has an ordered state of the Stoner ferromagnetic type in a specific range of magnetic field strengths. The spectra of elementary excitations of the Bose and Fermi types have been obtained. The Fermi excitations have a gap in the energy spectrum, whereas the Bose excitations in the ordered states begin with zero (to these excitations there corresponds an electric dipole moment). The self-consistent field approximation has been used, which is exact when the numbers of electrons and holes are equal to each other.     

Excitation spectra of one-dimensional spin-1/2 Fermi gas with an attraction

Using an exact Bethe ansatz solution, we rigorously study excitation spectra of the spin-1/2 Fermi gas (called Yang–Gaudin model) with an attractive interaction. Elementary excitations of this model involve particle-hole excitation, hole excitation and adding particles in the Fermi seas of pairs and unpaired fermions. The gapped magnon excitations in the spin sector show a ferromagnetic coupling to the Fermi sea of the single fermions. By numerically and analytically solving the Bethe ansatz equations and the thermodynamic Bethe ansatz equations of this model, we obtain excitation energies for various polarizations in the phase of the Fulde–Ferrell–Larkin–Ovchinnikov-like state. For a small momentum (long-wavelength limit) and in the strong interaction regime, we analytically obtained their linear dispersions with curvature corrections, effective masses as well as velocities in particle-hole excitations of pairs and unpaired fermions. Such a type of particle-hole excitations display a novel separation of collective motions of bosonic modes within paired and unpaired fermions. Finally, we also discuss magnon excitations in the spin sector and the application of Bragg spectroscopy for testing such separated charge excitation modes of pairs and single fermions.     

Magnetic impurity interactions in a quantum well on the base of IV-VI semiconductors

We study the indirect exchange interaction of magnetic impurities via 2D excitations in a quantum well on the base of IV-VI narrow-gap semiconductors. The energy spectrum of 2D excitations takes into account the nonparabolicity of dispersion as well as the strong spin-orbit interaction. The calculations are performed for the case when the main mechanism is an exchange by virtual electron-hole pairs. It means that we assume the Fermi level to lie inside the energy gap, and the temperature to be small, T << ϵ₀. It is shown that at large distances. R >> ν/ϵ₀ (2ϵ₀ is the excitation energy for nearest size-quantized subbands, ϵ the interband interaction parameter), the antiferromagnetic interaction of pairs dominates, so that the impurity spins tend to be directed along the heterojunction plane perpendicular to the vector connecting the impurities. The interaction contains both the Heisenberg and pseudodipole terms.     

Superfluid bose liquid with a suppressed BEC and an intensive pair coherent condensate as a model of 4He

One introduces a model of the superfluid state of a Bose liquid with repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate, there exists an intensive pair coherent condensate, analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is solved numerically, and a quasiparticle spectrum is obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid 4He. It is shown that the roton minimum in the spectrum is associated with the negative minimum of the Fourier component of the pair interaction potential.     

Functional Integrals and Collective Excitations in Boson-Fermion Model

In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.     

Functional Integrals and Collective Excitations in Boson-Fermion Model

In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.     

Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities

The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction U_c remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.     

Adaptation of the Landau-Migdal quasiparticle pattern to strongly correlated Fermi systems

A quasiparticle pattern advanced in Landau’s first article on Fermi-liquid theory is adapted to elucidate the properties of a class of strongly correlated Fermi systems characterized by a Lifshitz phase diagram featuring a quantum critical point (QCP) where the density of states diverges. The necessary condition for stability of the Landau Fermi-Liquid state is shown to break down in such systems, triggering a cascade of topological phase transitions that lead, without symmetry violation, to states with multi-connected Fermi surfaces. The end point of this evolution is found to be an exceptional state whose spectrum of single-particle excitations exhibits a completely flat portion at zero temperature. Analysis of the evolution of the temperature dependence of the single-particle spectrum yields results that provide a natural explanation of classical behavior of this class of Fermi systems in the QCP region.     

Selective spectroscopy of tunneling transitions between the Landau levels in vertical double-gate graphene–boron nitride–graphene heterostructures

The spectral and total electron densities of states in two-dimensional FeAs clusters, which simulate iron-based superconductors, have been calculated using the generalized quantum Monte Carlo algorithm within the full two-orbital model. Spectra have been reconstructed by solving the integral equation relating the Matsubara Green’s function and spectral density by the method combining the gradient descent and Monte Carlo algorithms. The calculations have been performed for clusters with dimensions up to 10 × 10 FeAs cells. The profiles of the Fermi surface for the entire Brillouin zone have been presented in the quasiparticle approximation. Data for the total density of states near the Fermi level have been obtained. The effect of the interaction parameter, size of the cluster, and temperature on the spectrum of excitations has been studied.     

Structure of the superfluid ground state of an atomic Fermi gas near the Feshbach resonance

The ground state of an atomic Fermi gas near the Feshbach resonance for a negative scattering length is investigated using the variational method. The structure of the superfluid state is formed by two coherently coupled subsystems, viz., the quasimolecular subsystem in a closed channel and the subsystem of atomic pairs in an open channel. The derived system of equations makes it possible to describe the properties of the ground state for arbitrary values of the parameters (in particular, to find the gap in the single-particle Fermi excitation spectrum and the speed of sound characterizing the branch of collective Bose excitations).     

The exact spectrum of Fermi quasiparticles in Kondo-Anderson ferromagnetic lattice

The spectrum of Fermi excitations of a nondegenerate ferromagnetic semiconductor at T=0 with one electron present is investigated in order to describe the electronic structure of manganites with inclusion of strong electron correlations within the Anderson periodic model with s-d exchange interaction. Exact dispersion relations and the Green functions for different spin projections are found. The density-of-states function is calculated for different positions of the d level relative to the band bottom.     

A calculation of the odd parity spectrum of16O and40Ca from the interaction between nucleons: Method and first results

In the framework of an exact many-body theory based on the formalism of Green's functions, we rederive an eigenvalue equation capable of describing single particle excitations of a Fermi system. The effective two-particle interaction entering this equation is extracted free of all adjustable parameters from a very simple nucleon-nucleon interaction by solving the corresponding integral equation for nuclear matter and using a local density approximation. We apply our method for describing those states of the doubly magic nuclei¹⁶O and⁴⁰Ca which probably can be understood as one-particle-one-hole excitations from the ground state, i.e. low-lying negative parity levels, and — in view of the simplicity of the interaction assumed — find reasonably good aggreement with experimental evidence.     

Zeros of the order parameter in the superconducting phase of the UGe2 band ferromagnet

Under the assumption of a strong spin-orbital interaction, two forms of the order parameter are obtained for two superconducting phases of the ferromagnetic UGe₂ that are allowed by the crystal symmetry. For each of the two phases, symmetry nodes in the gap of Fermi excitations are found, and the consequences of the existence of nodes, which can be used for experimental phase identification, are discussed.     

Charge order driven by Fermi-arc instability and its connection with pseudogap in cuprate superconductors

The recently discovered charge order is a generic feature of cuprate superconductors, however, its microscopic origin remains debated. Within the framework of the fermion-spin theory, the nature of charge order in the pseudogap phase and its evolution with doping are studied by taking into account the electron self-energy (then the pseudogap) effect. It is shown that the antinodal region of the electron Fermi surface is suppressed by the electron self-energy, and then the low-energy electron excitations occupy the disconnected Fermi arcs located around the nodal region. In particular, the charge order state is driven by the Fermi-arc instability, with a characteristic wave vector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Moreover, although the Fermi arc increases its length as a function of doping, the charge order wave vector reduces almost linearity with the increase of doping. The theory also indicates that the Fermi arc, charge order and pseudogap in cuprate superconductors are intimately related to each other, and all of them emanates from the electron self-energy due to the interaction between electrons by the exchange of spin excitations.     

Momentum dependence of the spin and charge excitations in the two dimensional Hubbard model

The low energy spin and charge excitations in the 2D Hubbard model near half filling are analyzed. The RPA spectra derived from inhomoheneous mean field textures are analyzed. Spin excitations show a commensurate peak at half filling, incommensurate peaks near half filling, and a broad background typical of a dilute Fermi liquid away from half filling. Charge excitations, near half filling, are localized near (0,0), and they occupy a small portion of the Brillouin Zone, in a way consistent with the existence of a small density of carriers, and a small Fermi surface. At higher hole densities, they fill the entire BZ, and can be understood in terms of a conventional Fermi liquid picture. The results are consistent with the observed features of the high-T_c superconductors.     

Low-energy monopole modes of a trapped atomic Fermi gas

We consider the low energy collective monopole modes of a trapped weakly interacting atomic Fermi gas in the collisionless regime. The spectrum is calculated for varying coupling strength and chemical potential. Using an effective Hamiltonian, we derive analytical results that agree well with numerical calculations in various regimes. The onset of superfluidity is shown to lead to effects such as the vanishing of the energy required to create a Cooper molecule at a critical coupling strength and to the emergence of pair vibration excitations. Our analysis suggests ways to experimentally detect the presence of the superfluid phase in trapped atomic Fermi gases.     

四氯化碳费米共振的拉曼光谱研究

费米共振现象是一种广泛存在于分子振动光谱中的现象,特别是结构比较复杂的多原子分子.在多原子分子中当振动倍频或组合频位于某一基频附近,由于发生振动耦合,会出现两个新峰,峰的位置向两侧发生移动,二者谱线强度发生变化,把这种现象称为费米共振.费米共振现象不仅存在于红外光谱中,也存在于拉曼光谱中.文章中测量了CCl4的拉曼光谱,利用所得到的谱线峰位和用Originpro7.5软件程序获得积分强度,用费米共振的相关理论计算了C-Cl的a1对称伸缩振动频率v1与C-Cl2的f对称弯曲振动频率v4的组合频(v1 v4)与(某一未知基频)C-Cl的f对称伸缩振动频率v03的费米共振特征参数,进而计算出了耦合系数W和这一未知基频v03.该文对理解费米共振,了解分子振动频率,研究分子结构有很重要的参考价值.