Topological crossovers near a quantum critical point

We study the temperature evolution of the single-particle spectrum ε-(p) and quasiparticle momentum distribution n(p) of homogeneous strongly correlated Fermi systems beyond a point where the necessary condition for stability of the Landau state is violated, and the Fermi surface becomes multi-connected by virtue of a topological crossover. Attention is focused on the different non-Fermi-liquid temperature regimes experienced by a phase exhibiting a single additional hole pocket compared with the conventional Landau state. A critical experiment is proposed to elucidate the origin of NFL behavior in dense films of liquid ³He.     

Contrasting different scenarios for the quantum critical point

Competing scenarios for quantum critical points (QCPs) of strongly interacting Fermi systems signaled by a divergent density of states at zero temperature are contrasted. The conventional scenario, which enlists critical fluctuations of a collective mode and attributes the divergence to a coincident vanishing of the quasi-particle strength z, is shown to be incompatible with identities arising from conservation laws prevailing in the fermionic medium. An alternative scenario, in which the topology of the Fermi surface is altered at the QCP, is found to explain the non-Fermi-liquid thermodynamic behavior observed experimentally in Yb-based compounds close to the QCP. It is suggested that combination of the topological scenario with the theory of quantum phase transitions will provide a proper foundation for analysis of the extended QCP region.     

Two scenarios of the quantum critical point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction.     

Two scenarios of the quantum critical point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction. The text was submitted by the author in English.     

Toward the theory of fermionic condensation

The diagrammatic technique elaborated by Belyaev for the theory of a Fermi liquid has been implemented to analyze the behavior of Fermi systems beyond the topological phase transition point, where the fermionic condensate appears. It has been shown that the inclusion of the interaction between the condensate and above-condensate particles leads to the emergence of a gap in the single-particle excitation spectrum of these particles even in the absence of Cooper pairing. Hence, the emergence of this gap in homogeneous electron systems of silicon field-effect structures leads to a metal–insulator phase transition rather than to superconductivity. It has been shown that the same interaction explains the nature of the Fermi arc structure in twodimensional electron systems of cuprates.     

Fermi surface reconstruction by dynamic magnetic fluctuations

We demonstrate that nearly critical quantum magnetic fluctuations in strongly correlated electron systems can change the Fermi surface topology and also lead to spin charge separation in two dimensions. To demonstrate these effects, we consider a small number of holes injected into the bilayer antiferromagnet. The system has a quantum critical point (QCP) which separates magnetically ordered and disordered phases. We demonstrate that in the physically interesting regime, there is a magnetically driven Lifshitz point (LP) inside the magnetically disordered phase. At the LP, the topology of the hole Fermi surface is changed. We also demonstrate that in this regime, the hole spin and charge necessarily separate when approaching the QCP. The considered model sheds light on generic problems concerning the physics of the cuprates.     

Evolution of spin susceptibility from the Pauli to Curie-Weiss type in strongly correlated Fermi systems

The magnetic properties of strongly correlated Fermi systems are studied within the framework of the fermioncondensation model—phase transition associated with the rearrangement of the Landau quasiparticle distribution, resulting in the appearance of a plateau at T=0 exactly in the Fermi surface of the single-particle excitation spectrum. It is shown that the Curie-Weiss term ～T^?1 appears in the expression for the spin susceptibility χ_ac(T) of the system after the transition point at finite temperatures. The behavior of χ_ac(T, H) as a function of temperature and static magnetic field H in the region where the critical fermion-condensation temperature T _f is close to zero is discussed. The results are compared with the available experimental data.     

Structure of the ground state of a nonsuperfluid dense quark-gluon plasma

The single-particle spectrum and momentum distribution of quasiparticles in a cold dense quark-gluon plasma are calculated within the Fermi liquid approach. It is shown that this system does not behave as a standard Fermi liquid: at zero temperature, the single-particle spectrum has a plateau at the Fermi surface, while the Fermi surface itself has a nonzero volume in momentum space.     

Some consequences of electronic topological transition in 2D system on a square lattice: Excitonic ordered states

We study in a mean-field approximation the ordered “excitonic” states which develop around the quantum critical point (QCP) associated with the electronic topological transition (ETT) in a 2D electron system on a square lattice. We consider the case of hopping beyond nearest neighbors when ETT has an unusual character. We show that the amplitude of the order parameter (OP) and of the gap in the electron spectrum increase with increasing the distance from the QCP, , where and n is an electron concentration. Such a behavior is different from the ordinary case when OP and the gap decrease when going away from the point which is a motor for instability. We show that the chemical potential lies always inside the gap for wavevectors in a proximity of whatever is the doping concentration. The spectrum gets a characteristic flat shape as a result of hybridization effect in the vicinity of two different SP's. The shape of the spectrum as a function of and the angle dependence of the gap have a striking similarity with the features observed in the normal state of the underdoped high- cuprates. We discuss also details about the phase diagram and the behaviour of the density of states. Received 9 June 1999     

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-T<Subscript>c</Subscript> superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d _xz and 3d _yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d _{(x + iy)z} and d ? = 3d _{(x ? iy)z} orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.     

Dynamical nature of chaos in electron systems of high-T c superconductors

A model of the fermion-condensation phase transition forming a plateau in the spectrum of single-particle excitations near the Fermi surface at T=0 is used to analyze those features of the spectral functions of normal states of high-T _c superconductors which are inherent in a marginal Fermi liquid contaminated by impurities. With this model, such a behavior is shown to be due to the fermion condensate, which acts as an impurity subsystem because its energy spectrum at T=0 is dispersionless. The influence of the anisotropy of condensate distribution in the Brillouin zone on the spectral functions is discussed.     

Fermi surface reconstruction in strongly correlated Fermi systems as a first-order phase transition

A quantum phase transition in strongly correlated Fermi systems beyond the topological quantum critical point has been studied using the Fermi liquid approach. The transition takes place between topologically equivalent states with three Fermi surface sheets, but one of them is characterized by a quasiparticle halo in the quasiparticle momentum distribution n(p), and the other one is characterized by a hole pocket. It has been found that the transition between these states is a first-order phase transition for the interaction constant g and temperature T. The phase diagram in the vicinity of this transition has been constructed.     

Asymmetric Tunneling Conductance and the Non-Fermi Liquid Behavior of Strongly Correlated Fermi Systems

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the non-Fermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau–Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V. This is because the particle–hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle–hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V. This asymmetry can be observed when a strongly correlated metal is in its normal, superconducting or pseudogap states. We show that the asymmetric part of the dynamic conductance does not depend on temperature provided that the metal is in its superconducting or pseudogap states. In normal state, the asymmetric part diminishes at rising temperatures. Under the application of magnetic field the metal transits to the Landau–Fermi liquid state and the differential tunneling conductivity becomes a symmetric function of V. These findings are in good agreement with recent experimental observations.     

Superfluid phase transition in trapped atomic Fermi gas

Superfluid phase transition in an atomic Fermi gas confined to a harmonic trap is studied. The critical transition temperature and the temperature dependence and spatial shape of the order parameter are determined. The spectrum and wave functions of single-particle and collective excitations are obtained for a gas in the superfluid phase. The excitation eigenfrequencies exhibit a pronounced temperature dependence, allowing, e.g., identification of the superfluid phase.     

Distribution of single-particle strengths in the nuclei 207Tl, 207Pb, 209Bi and 209Pb

Within the theory of finite Fermi systems we calculate the distribution of single-particle strengths in the odd mass nuclei surrounding ²⁰⁸Pb. The Dyson equation with an energy dependent mass operator is solved and the resulting single-particle propagator is analysed. It turns out that the concept of quasiparticles used in this theory is very well justified for nearly all the states in the first and the second shells below and above the Fermi surface.     

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.     

Superconducting instability of a non-centrosymmetric system

The Fermi gas approach to the weak-coupling superconductivity in the non-centrosymmetric systems lead to a conclusion of an approximately spin-orbit coupling independent critical temperature of the singlet states as well as the triplet states defined by the order parameter aligned with the antisymmetric spin-orbit coupling vector. We indicate that the above results follow from a simplified approximation of a density of states by a constant Fermi surface value. Such a scenario does not properly account for the spin-split quasiparticle energy spectrum and reduces the spin-orbit coupling influence on superconductivity to the bare pair-breaking effect of a lifted spin degeneracy. Applying the tight-binding model, which captures the primary features of the spin-split energy band, i.e., its enhanced width and the spin-orbit coupling induced redistribution of the spectral weights in the density of states, we calculate the critical temperature of a non-centrosymmetric superconductor. We report a general tendency of the critical temperature to be suppressed by the antisymmetric spin-orbit coupling. We indicate that, the monotonic decrease of the critical temperature may be altered by the spin-orbit coupling induced van Hove singularities which, when driven to the Fermi level, generate maxima in the phase diagram. Extending our considerations to the intermediate-coupling superconductivity we point out that the spin-orbit coupling induced change of the critical temperature depends on the structure of the electronic energy band and both – the strength and symmetry of the pair potential. Finally, we discuss the mixed singlet-triplet state superconducting instability and establish conditions concerning the symmetry of the singlet and triplet counterparts as well as the range of the spin-orbit coupling energy which make such a phase transition possible.     

Single-particle excitation spectrum of the Hubbard model with magnetic frustration at finite temperature

The single-particle excitation spectrum of the Hubbard model with magnetic frustration at finite temperature is examined using numerical exact diagonalization techniques. The magnetic frustration is introduced by a proper choice of the Hamiltonian parameters, which lead to rich low-energy spin excitation behavior, resembling those observed in heavy fermion systems. At finite temperature, the low-lying excited states become thermally populated with significant weight. As a result, the calculated spectrum shows interesting temperature dependent evolution. The calculated results are presented and discussed in a many-body picture to gain insight into the photoelectron spectroscopy of strongly correlated electron systems.     

Interplay of Quantum and Classical Fluctuations Near Quantum Critical Points

For a system near a quantum critical point (QCP), above its lower critical dimension d _L , there is in general a critical line of second-order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, d _eff?=?d?+?z (d is the Euclidean dimension of the system and z the dynamic quantum critical exponent) is above its upper critical dimension $d_{_{C}}$ there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation ψ?=?νz between the shift exponent ψ of the critical line and the crossover exponent νz, for $d+z>d_{_{C}}$ by a dangerous irrelevant interaction. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP.     

Field-induced quantum critical point in CeCoIn5

The resistivity of the heavy-fermion superconductor CeCoIn5 was measured as a function of temperature, down to 25 mK and in magnetic fields of up to 16 T applied perpendicular to the basal plane. With increasing field, we observe a suppression of the non-Fermi liquid behavior, rho approximately T, and the development of a Fermi liquid state, with its characteristic rho=rho(0)+AT2 dependence. The field dependence of the T2 coefficient shows critical behavior with an exponent of 1.37. This is evidence for a field-induced quantum critical point (QCP), occurring at a critical field which coincides, within experimental accuracy, with the superconducting critical field H(c2). We discuss the relation of this field-tuned QCP to a change in the magnetic state, seen as a change in magnetoresistance from positive to negative, at a crossover line that has a common border with the superconducting region below approximately 1 K.