arXiv subjects

V. A. Khodel

Publications and source records attributed to V. A. Khodel.

At least 55 records · Page 3Linked to original sources

arXiv2010

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 four-fold rotational point-group symmetry ($C_4$) 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.

cond-mat.str-el↗

arXiv2009

Interplay of single-particle and collective degrees of freedom near 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 quasiparticle 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.

cond-mat.str-el↗

arXiv2008

Topology of the Fermi Surface Beyond the Quantum Critical Point

We examine the nature of phase transitions occurring in strongly correlated Fermi systems at the quantum critical point (QCP) associated with a divergent effective mass. Conventional scenarios for the QCP involving collective degrees of freedom are shown to have serious shortcomings. Working within the original Landau quasiparticle picture, we propose an alternative topological scenario for the QCP, in systems that obey standard Fermi liquid (FL) theory in advance of the QCP. Applying the technique of Poincaré mapping, we analyze the sequence of iterative maps generated by the Landau equation for the single-particle spectrum at zero temperature. It is demonstrated that the Fermi surface is subject to rearrangement beyond the QCP. If the sequence of maps converges, a multi-connected Fermi surface is formed. If it fails to converge, the Fermi surface swells into a volume that provides a measure of entropy associated with formation of an exceptional state of the system characterized by partial occupation of single-particle states and dispersion of their spectrum proportional to temperature. Based on this dual scenario, the thermodynamics of Fermi systems beyond the QCP exhibits striking departures from the predictions of standard FL theory. Mechanisms for the release of the entropy excess of the exceptional state are discussed.

cond-mat.str-el↗

arXiv2008

Non-Fermi-Liquid Behavior from the Fermi-Liquid Approach

Non-Fermi liquid behavior of strongly correlated Fermi systems is derived within the Landau approach. We attribute this behavior to a phase transition associated with a rearrangement of the Landau state that leads to flattening of a portion of the single-particle spectrum $ε({\bf p})$ in the vicinity of the Fermi surface. We demonstrate that the quasiparticle subsystem responsible for the flat spectrum possesses the same thermodynamic properties as a gas of localized spins. Theoretical results compare favorably with available experimental data. While departing radically from prevalent views on the origin of non-Fermi-liquid behavior, the theory advanced here is nevertheless a conservative one of in continuing to operate within the general framework of Landau theory.

cond-mat.str-el↗

arXiv2007

Flattening of Single-Particle Spectra in Strongly Correlated Electron Systems and the Violation of the Wiedemann-Franz Law

The renormalization of the Wiedemann-Franz (WF) ratio in strongly correlated electron systems is analyzed within the Landau quasiparticle picture. We demonstrate that the WF law is violated: (i) at the quantum critical point, where the effective mass diverges, and (ii) beyond a point of fermion condensation, where the single-particle spectrum $ε(p)$ becomes flat. Results of the analysis are compared with available experimental data.

cond-mat.str-el↗

arXiv2007

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 {\it topological} scenario of the QCP, associated with the emergence of bifurcation points in equation $ε(p)=μ$ 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.

cond-mat.str-el↗

arXiv2007

Properties of the Two-Dimensional Electron Gas Close to the Fermi-Liquid Quantum Critical Point

The rearrangement of single-particle degrees of freedom of a dilute two-dimensional electron gas in the vicinity of the quantum critical point is examined within a microscopic approach. It is shown that just beyond the critical point, the Landau state undergoes self-consistent rearrangement of the quasiparticle spectrum and momentum distribution. At very low temperatures, there emerges a multi-connected quasiparticle momentum distribution. With increasing temperature, two crossovers occur: a fermion condensate appears in the first and disappears in the second, giving way to universal non-Fermi-liquid behavior. Manifestations of these crossovers in thermodynamic properties of the electron gas are studied and characterized. The four quasiparticle phases predicted to exist in the vicinity of the critical point are collected in a schematic phase diagram.

cond-mat.str-el↗

arXiv2007

Merging of single-particle levels and non-Fermi-liquid behavior of finite Fermi systems

We examine the problem of finite Fermi systems having a degenerate single-particle spectrum and show that the Landau approach, applied to such a system, admits the possibility of merging single-particle levels. It is demonstrated that the opportunity for this behavior is widespread in quantum many-body systems. The salient feature of the phenomenon is the occurrence of nonintegral quasiparticle occupation numbers, leading to a radical alteration of the standard quasiparticle picture. Implications of this alteration are considered for nuclear, atomic, and solid-state systems.

cond-mat.str-el↗

arXiv2006

Merging of single-particle levels in finite Fermi systems

Properties of the distribution of single-particle levels adjacent to the Fermi surface in finite Fermi systems are studied, focusing on the case in which these levels are degenerate. The interaction of the quasiparticles occupying these levels lifts the degeneracy and affects the distance between the closest levels on opposite sides of the Fermi surface, as the number of particles in the system is varied. In addition to the familiar scenario of level crossing, a new phenomenon is uncovered, in which the merging of single-particle levels results in the disappearance of well-defined single-particle excitations. Implications of this finding are discussed for nuclear, solid-state, and atomic systems.

cond-mat.str-el↗

arXiv2006

Nodes of the Gap Function and Anomalies in Thermodynamic Properties of Superfluid $^3$He

Departures of thermodynamic properties of three-dimensional superfluid $^3$He from the predictions of BCS theory are analyzed. Attention is focused on deviations of the ratios $Δ(T=0)/T_c$ and $[C_s(T_c)-C_n(T_c)]/C_n(T_c)$ from their BCS values, where $Δ(T=0)$ is the pairing gap at zero temperature, $T_c$ is the critical temperature, and $C_s$ and $C_n$ are the superfluid and normal specific heats. We attribute these deviations to the momentum dependence of the gap function $Δ(p)$, which becomes well pronounced when this function has a pair of nodes lying on either side of the Fermi surface. We demonstrate that such a situation arises if the P-wave pairing interaction $V(p_1,p_2)$, evaluated at the Fermi surface, has a sign opposite to that anticipated in BCS theory. Taking account of the momentum structure of the gap function, we derive a closed relation between the two ratios that contains no adjustable parameters and agrees with the experimental data. Some important features of the effective pairing interaction are inferred from the analysis.

cond-mat.supr-con↗

arXiv2005

Curie law, entropy excess, and superconductivity in heavy fermion metals and other strongly interacting Fermi liquids

Low-temperature thermodynamic properties of strongly interacting Fermi liquids with fermion condensate are investigated. We demonstrate that the spin susceptibility of these systems exhibits the Curie-Weiss law, and the entropy contains a temperature-independent term. The excessive entropy is released at the superconducting transition, enhancing the specific heat jump Delta C and rendering it proportional to the effective Curie constant. The theoretical results are favorably compared with the experimental data on the heavy fermion metal CeCoIn5, as well as He-3 films.

cond-mat.str-el↗

arXiv2005

Damping effects and the metal-insulator transition in the two-dimensional electron gas

The damping of single-particle degrees of freedom in strongly correlated two-dimensional Fermi systems is analyzed. Suppression of the scattering amplitude due to the damping effects is shown to play a key role in preserving the validity of the Landau-Migdal quasiparticle picture in a region of a phase transition, associated with the divergence of the quasiparticle effective mass. The results of the analysis are applied to elucidate the behavior of the conductivity $σ(T)$ of the two-dimensional dilute electron gas in the density region where it undergoes a metal-insulator transition.

cond-mat.str-el↗

arXiv2005

Thermodynamic properties of Fermi systems with flat single-particle spectra

The behavior of strongly correlated Fermi systems is investigated beyond the onset of a phase transition where the single-particle spectrum $ξ({\bf p})$ becomes flat. The Landau-Migdal quasiparticle picture is shown to remain applicable on the ordered side of this transition. Nevertheless, low-temperature properties evaluated within this picture show profound changes relative to results of Landau theory, as a direct consequence of the flattening of $ξ({\bf p})$. Stability conditions for this class of systems are examined, and the nature of antiferromagnetic quantum phase transitions is elucidated.

cond-mat.str-el↗

arXiv2004

Anomalous Behavior of Thermodynamic Properties of Strongly Correlated Fermi Systems

Thermodynamic characteristics of Fermi systems are investigated in the vicinity of a phase transition where the effective mass diverges and the single-particle spectrum becomes flat. It is demonstrated that at extremely low temperatures $T$, the flattening of the spectrum is reflected in non-Fermi-liquid behavior of the inverse susceptibility $χ^{-1}(T) \sim T^α$ and the specific heat $C(T)/T\sim T^{-α}$, with the critical index $α=2/3$. In the presence of an external static magnetic field $H$, both these quantities are found to exhibit a scaling behavior, e.g. $χ^{-1}(T,H)=χ^{-1}(T,0)+ T^{2/3}F(H/T)$, in agreement with available experimental data.

cond-mat.str-el↗

arXiv2004

Phase Transitions in Nucleonic Matter and Neutron-Star Cooling

A new scenario for neutron-star cooling is proposed, based on the correspondence between pion condensation, occurring in neutron matter due to critical spin-isospin fluctuations, and the metal-insulator phase transition in a two-dimensional electron gas. Beyond the threshold density for pion condensation, where neutron-star matter loses its spatial homogeneity, the neutron single-particle spectrum acquires an insulating gap that quenches neutron contributions to neutrino-production reactions and to the star's specific heat. In the liquid phase at densities below the transition point, spin-isospin fluctuations are found to play dual roles. On the one hand, they lead to a multi-sheeted neutron Fermi surface that extends to low momenta, thereby activating the normally forbidden direct-Urca cooling mechanism; on the other, they amplify the nodeless $P$-wave neutron superfluid gap while suppressing $S$-wave pairing. In this picture, lighter stars without a pion-condensed core experience slow cooling, while enhanced cooling occurs in heavier stars through direct-Urca emission from a narrow shell of the interior.

astro-ph↗

arXiv2004

Anomalous Behavior of the Spin Susceptibility of Strongly Correlated Fermi Systems

The spin susceptibility $χ(T)$ of strongly correlated Fermi systems is investigated in the density region where Fermi-liquid theory fails. We attribute this failure to a specific quantum phase transition associated with a rearrangement of the Landau state at low temperatures $T$, retaining the assumption that the Landau quasiparticle picture survives in a generic sense. Taking into account the resulting modification of the quasiparticle istribution function, the spin susceptibility $χ(T)$ is shown to contain a Curie-Weiss component $χ_{\rm CW}(T)\sim (T-Θ_{\rm W})^{-1}$, with the Weiss temperature $Θ_{\rm W}$ vanishing at the critical density for the transition.

cond-mat.str-el↗

arXiv2004

Hot Spots and Transition from d-Wave to Another Pairing Symmetry in the Electron-Doped Cuprate Superconductors

We present a simple theoretical explanation for a transition from d-wave to another superconducting pairing observed in the electron-doped cuprates. The d_{x^2-y^2} pairing potential Delta, which has the maximal magnitude and opposite signs at the hot spots on the Fermi surface, becomes suppressed with the increase of electron doping, because the hot spots approach the Brillouin zone diagonals, where Delta vanishes. Then, the d_{x^2-y^2} pairing is replaced by either singlet s-wave or triplet p-wave pairing. We argue in favor of the latter and discuss experiments to uncover it.

cond-mat.supr-con↗

arXiv2004

Mechanisms driving alteration of the Landau state in the vicinity of a second-order phase transition

The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation $ε(p)=μ$, a condition that ordinarily has the Fermi momentum $p_F$ as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative alteration of the Landau state, well before the collapse of the collective degree of freedom that is responsible for the second-order transition. The competition between mechanisms that drive rearrangement of the Landau quasiparticle distribution is explored, taking into account the feedback of the rearrangement on the spectrum of critical fluctuations. It is demonstrated that the transformation of the Landau state to a new ground state may be viewed as a first-order phase transition.

cond-mat.str-el↗