Spontaneous breaking of four-fold rotational symmetry in two-dimensional electronic systems explained as a continuous topological transition

The Fermi liquid approach is applied to the problem of spontaneous violation of the C ₄ symmetry in strongly correlated two-dimensional electronic systems on a square lattice. The symmetry breaking is traced to the existence of a topological phase transition. This continuous transition is triggered when the Fermi line, driven by the quasiparticle interactions, reaches the van Hove saddle points, where the group velocity vanishes and the density of states becomes singular. An unconventional Fermi liquid emerges beyond the implicated quantum critical point.     

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.     

Microscopic theory of a strongly correlated two-dimensional electron gas

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T _⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T _*, appears through a crossover at temperatures T ∼ T _* > T _⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T ^−α with the exponent α }~ 2/3.     

Finite Fermi systems theory and self-consistency relations

The self-consistent theory of the finite Fermi systems is outlined. This approach is based on the same Fermi liquid theory principles as the familiar theory for finite Fermi systems (FFS) by Migdal. We show that the basic Fermi system properties can be evaluated in terms of the quasiparticle Lagrangian L_q which incorporates the energy dependency effects. This Lagrangian is defined so that the corresponding Lagrange equations should coincide with the FFS theory equations of motion of the quasiparticles. The quasiparticle energy E_q defined in the terms of t he quasiparticle Lagrangian L_q according to the usual canonical rules is shown to be equal to the binding energy E_o of the system. For a given Lagrangian L_q the particle densities in nuclei, the nuclear single-particle spectra, the low-lying collective states (LCS) properties, and the amplitude of the interquasiparticle interaction are also evaluated. The suggested approach is compared with the Hartree-Fock theory with effective forces.     

Quasiparticles of strongly correlated Fermi liquids at high temperatures and in high magnetic fields

Strongly correlated Fermi systems are among the most intriguing, best experimentally studied and fundamental systems in physics. There is, however, lack of theoretical understanding in this field of physics. The ideas based on the concepts like Kondo lattice and involving quantum and thermal fluctuations at a quantum critical point have been used to explain the unusual physics. Alas, being suggested to describe one property, these approaches fail to explain the others. This means a real crisis in theory suggesting that there is a hidden fundamental law of nature. It turns out that the hidden fundamental law is well forgotten old one directly related to the Landau-Migdal quasiparticles, while the basic properties and the scaling behavior of the strongly correlated systems can be described within the framework of the fermion condensation quantum phase transition (FCQPT). The phase transition comprises the extended quasiparticle paradigm that allows us to explain the non-Fermi liquid (NFL) behavior observed in these systems. In contrast to the Landau paradigm stating that the quasiparticle effective mass is a constant, the effective mass of new quasiparticles strongly depends on temperature, magnetic field, pressure, and other parameters. Our observations are in good agreement with experimental facts and show that FCQPT is responsible for the observed NFL behavior and quasiparticles survive both high temperatures and high magnetic fields.     

Quantum criticality of a Fermi gas with a spherical dispersion minimum

We describe the quantum phase transition of a Fermi gas occurring when the quasiparticle excitation energy has a minimum in momentum space which crosses zero on a sphere of radius k(0) not equal 0. The quasiparticles have a universal interaction which controls the physical properties in the vicinity of the quantum-critical point. We discuss possible applications to fermionic superfluids formed by pairing two fermion species, near the point where the densities of the two species become unequal.     

Phase diagram of strongly correlated Fermi systems

Phase transitions caused by the redistribution of quasiparticle occupation numbers n(p) in homogeneous Fermi systems with particle repulsion are analyzed. The phase diagram of a strongly correlated Fermi system, when drawn in the coordinates “density ρ-dimensionless coupling constant η,” resembles a Washington pie for a rather broad class of interactions. Its upper part is “filled” with Fermi condensate, and the bottom part is filled with normal Fermi liquid. Both parts are separated by a narrow interlayer of Lifshitz phase with a multiply connected Fermi surface.     

Instabilities of a Fermi Gas with Nested Fermi Surfaces

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a vector Q commensurate with the lattice in conjunction with the interaction between the quasiparticles can give rise to a rich phase diagram. Of particular importance is itinerant antiferromagnetic order in the context of pnictides and heavy fermion compounds. By mismatching the nesting the order can gradually be suppressed and as the Néel temperature tends to zero a quantum critical point is obtained. A superconducting dome above the quantum critical point can be induced by the transfer of pairs of electrons between the pockets. The conditions under which such a dome arises are studied. In addition numerous other phases may arise, e.g. charge density waves, non‐Fermi liquid behavior, non‐s‐wave superconductivity, Pomeranchuk instabilities of the Fermi surface, nematic order, and phases with persistent orbital currents.     

费米超流气体的非线性Landau-Zener 隧穿

在平均场近似下,通过对相平面和不动点的分析, 研究了非线性两能级系统中费米超流气体的Landau-Zener 隧穿现象. 研究发现,费米子间的相互作用能够显著地影响量子隧穿. 当相互作用参数c小于临界值c^*时,在绝热极限下隧穿仍然满足量子绝热定理, 而大于这一临界值时,量子绝热定理不再满足. 最后通过和线性情况比较,得到了c*时隧穿率与扫描速率间满足的指数关系.     

Multiply connected Fermi sphere and fermion condensation

We examine the structure of the ground state of a homogeneous Fermi liquid beyond the instability point of the Fermi-like quasiparticle momentum distribution in the effective-functional method with a strong repulsive effective interaction. A numerical study of the initial stage of rearrangement of the ground state, based on a simple effective functional, showed that there exists a temperature T ₀, above which the behavior of the system is the same as in the theory of fermion condensation, and for T<T ₀ the scenario of rearrangement of the ground state is different. At low temperatures an intermediate structure arises, with a multiply connected quasiparticle momentum distribution. The transition of this structure with growth of the coupling constant to a state with a fermion condensate is discussed. Zh. éksp. Teor. Fiz. 114, 2078–2088 (December 1998)     

Self-consistent random phase approximation within the O(5) model and Fermi transitions

Self-consistent quasiparticle random phase approximation (SCQRPA) is considered in application to the Fermi transitions within the O(5) model. It is demonstrated that SCQRPA improves on renormalized QRPA (RQRPA), a method that has recently become rather popular in this context. The analytical form of the SCQRPA vacuum is used to evaluate all the matrix elements. The SCQRPA results show a general trend similar to the exact solutions. The necessity to change the single particle basis beyond the transition point, and to include the proton-proton and neutron-neutron channels in the QRPA operator, in addition to the proton-neutron one, is pointed out.     

Intervortex quasiparticle tunneling and the electronic structure of multivortex configurations in type-II superconductors

The electronic spectrum of multivortex configurations in type-II superconductors is studied taking into account the effect of quasiparticle tunneling between the vortex cores. The tunneling is responsible for the formation of strongly coupled quasiparticle states for intervortex distances a < a _cc , where the critical distance a _c is of the order of several coherence lengths ξ. When analyzing the resulting spectra of vortex clusters bonded by quasiparticle tunneling, we find a transition from a set of degenerate Caroli-de Gennes-Matricon branches to anomalous branches similar to the ones in multiquantum giant vortices. This spectrum transformation results in the oscillatory behavior of the density of states at the Fermi level as a function of a and could be observed in mesoscopic superconductors and disordered flux line arrays in bulk systems. The text was submitted by the authors in English.     

BCS-BEC crossover and topological phase transition in 3D spin-orbit coupled degenerate Fermi gases

We investigate the BCS-BEC crossover in three-dimensional degenerate Fermi gases in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that the superfluid order parameter destroyed by a large Zeeman field can be restored by the SOC. With increasing strengths of the Zeeman field, there is a series of topological quantum phase transitions from a nontopological superfluid state with fully gapped fermionic spectrum to a topological superfluid state with four topologically protected Fermi points (i.e., nodes in the quasiparticle excitation gap) and then to a second topological superfluid state with only two Fermi points. The quasiparticle excitations near the Fermi points realize the long-sought low-temperature analog of Weyl fermions of particle physics. We show that the topological phase transitions can be probed using the experimentally realized momentum-resolved photoemission spectroscopy.     

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.     

Polarons in alkaline-earth-like atoms with multiple background Fermi surfaces

We study the impurity problem in a Fermi gas of ¹⁷³Yb atoms near an orbital Feshbach resonance (OFR), where a single moving particle in the ³P₀ state interacts with two background Fermi seas of particles in different nuclear states of the ground ¹S₀ manifold. By employing wave function ansatz to molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. In comparison to the case where only one Fermi sea is populated, we find that the presence of an additional Fermi sea acts as an energy shift between the two channels of the OFR. In addition, quantum fluctuations near the Fermi level can also induce sizable effects to various properties of the attractive and repulsive polarons.     

The tunneling phenomena of the Fermi superfluid gases in a double-well potential by manipulating the s-wave scattering length

In the present work, we have investigated tunneling dynamics of superfluid Fermi gas in a double-well potential in deep BEC regime and in the unitarity regime by adjusting the scattering length or the interaction parameter y. The scattering length a _sc or y could affect the quantum transition dramatically. At certain regime, the complete population transfer between two modes can be obtained. However, at some other regimes, the quantum transition can be completely blocked.     

Fermi surface and quasiparticle dynamics of Na0.7CoO2 investigated by angle-resolved photoemission spectroscopy

We present the first angle-resolved photoemission study of Na0.7CoO2, the host material of the superconducting NaxCoO2.nH(2)O series. Our results show a hole-type Fermi surface, a strongly renormalized quasiparticle band, a small Fermi velocity, and a large Hubbard U. The quasiparticle band crosses the Fermi level from M toward Gamma suggesting a negative sign of effective single-particle hopping t(eff) (about 10 meV) which is on the order of magnetic exchange coupling J in this system. Quasiparticles are well defined only in the T-linear resistivity (non-Fermi-liquid) regime. Unusually small single-particle hopping and unconventional quasiparticle dynamics may have implications for understanding the phase of matter realized in this new class of a strongly interacting quantum system.     

Fermion condensation and non Fermi liquid behavior in a model with long range forces

The phenomenon of the so called Fermion condensation, a phase transition analogous to Bose condensation but for Fermions, postulated in the past to occur in systems with strong momentum dependent forces, is reanalyzed in a model with infinite range interactions. The strongly non Fermi Liquid behavior of this system is demonstrated analytically at T = 0 and at T ≠ 0 in the superconducting and normal phases. The validity of the quasiparticle picture is investigated and seen to hold true for temperatures less than the characteristic temperature T _f of the Fermion condensation.