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V. A. Khodel

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

At least 19 recordsLinked to original sources
arXiv2024

A unified quasiparticle approach to the theory of strongly correlated electron liquids

Landau's quasiparticle formalism is generalized to describe a wide class of strongly correlated Fermi systems, in addition to conventional Fermi liquids. This class includes (i) so-called marginal exemplars and (ii) systems that harbor interaction-driven flat bands, in both of which manifestations of non-Fermi-liquid behavior are well documented. Specifically, the advent of such flat bands is attributed to a spontaneous topological rearrangement of the Landau state that supplements the conventional Landau quasiparticle picture with a different set of quasiparticles, the so-called fermion condensate, whose single-particle spectrum is dispersionless. The celebrated Landau-Luttinger theorem is extended to marginal Fermi liquids, in which the density of the augmented quasiparticle system is shown to coincide with the particle density. On the other hand, the total density of a system hosting an interaction-driven flat band turns out to be the sum of the densities of the two quasiparticle subsystems: the Landau-like component and the fermion condensate. We demonstrate that within the framework of the scenario proposed, a long-standing problem faced by theories of $D$-wave superconductivity in cuprates, namely a consistent explanation of the so-called Uemera plot, can be naturally resolved.

cond-mat.str-el↗
arXiv2021

Quasiparticle Pattern of Phenomena in Exotic Superconductors

The quasiparticle formalism invented by Lev Landau for description of conventional Fermi liquids is generalized to exotic superconductivity attributed to Cooper pairing, whose measured properties defy explanation within the standard BCS-Fermi Liquid description. We demonstrate that in such systems the quasiparticle number remains equal to particle number, just as in common Fermi liquids. We are then able to explain the puzzling relationship between the variation with doping $x$ of two key properties of the family La$_{2-x}$Sr$_x$Cu0$_4$ of exotic superconductors, namely the $T=0$ superfluid density $ρ_{s0}(x)$ and the coefficient $A_1(x)$ in the linear-in-$T$ component of the normal-state low-$T$ resistivity $ρ(T)=ρ_0+A_1T+A_2T^2$, in terms of the presence of interaction-induced flat bands in the ground states of these metals.

cond-mat.str-el↗
arXiv2020

Topological disorder triggered by interaction-induced flattening of electron spectra in solids

We address the intervention of classical-like behavior, well documented in experimental studies of strongly correlated electron systems of solids that emerges at temperatures $T$ far below the Debye temperature $T_D$. We attribute this unexpected phenomenon to spontaneous rearrangement of the conventional Landau state beyond a critical point at which the topological stability of this state breaks down, leading to the formation of an interaction-induced flat band adjacent to the nominal Fermi surface. We demonstrate that beyond the critical point, the quasiparticle picture of such correlated Fermi systems still holds, since the damping of single-particle excitations remains small compared with the Fermi energy $T_F=p^2_F/2m_e$. A Pitaevskii-style equation for determination of the rearranged quasiparticle momentum distribution $n_*({\bf p})$ is derived, which applies to explanation of the linear-in-$T$ behavior of the resistivity $ρ(T)$ found experimentally.

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arXiv2019

Impact of $e-e$ interactions on the superfluid density of dirty superconductors

Landau's theory of the Fermi liquid is adapted to analyze the impact of electron-electron ($e-e$) interactions on the deficit of the superfluid density $ρ_{s0}=ρ_s(T=0)$ in dirty superconducting electron systems in which the damping $γ$ of single-particle excitations exceeds the zero temperature BCS gap $Δ_0$. In the dirty strong-coupling limit $γ/Δ_0\gg 1,m^*/m_e\gg 1$, the formula derived for $ρ_{s0}$ is shown to coincide with the well-known empirical Uemura relation provided pair-breaking contributions are nonexistent. The roles of the crystal lattice and magnetic pair-breaking effects in the observed decline of the zero-temperature superfluid density $ρ_{s0}$ in overdoped LSCO compounds are also discussed. Our method is also applied to elucidation of results from the pioneering experimental studies performed recently by Bozovic and collaborators in overdoped LSCO compounds.

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arXiv2018

Toward a topological scenario for high-temperature superconductivity of copper oxides

The structure of the joint phase diagram demonstrating high-$T_c$ superconductivity of copper oxides is studied on the basis of the theory of interaction-induced flat bands. Prerequisites of an associated topological rearrangement of the Landau state are established, and related non-Fermi-liquid (NFL) behavior of the normal states of cuprates is investigated. We focus on manifestations of this behavior in the electrical resistivity $ρ(T)$, especially the observed gradual crossover from normal-state $T$-linear behavior $ρ(T,x)=A_1(x)T$ at doping $x$ below the critical value $x_c^h$ for termination of superconductivity, to $T$-quadratic behavior at $x>x_c^h$, which is incompatible with predictions of the conventional quantum-critical-point scenario. It is demonstrated that at $x<x^h_c$, in agreement with available experimental data, the coefficient $A_1( x)$ is decomposed into the product of two factors, one of which changes linearly with doping $x$, while the second is universal, being of the Planckian form.

cond-mat.str-el↗
arXiv2017

Interplay between BCS and Mott physics in the phenomenon of high-$T_c$ superconductivity

Superconducting electron systems of solids hosting flat bands are studied, with a view to improved understanding of the fundamental physics giving rise to high-temperature superconductivity. We present a modified form of the set of Gor'kov equations of BCS theory that incorporates a Mott-like gap in the single-particle spectrum. Such a quantity is emergent in systems with flat bands having interactions repulsive in the Cooper channel, provided particle-hole symmetry is broken. The equations so obtained are applied to the elucidation of features of the two-gap structure of single-particle spectra of underdoped high-$T_c$ superconductors, as revealed in angle-resolved photoemission spectrometry.

cond-mat.str-el↗
arXiv2016

Strongly correlated Fermi systems as a new state of matter

The aim of this review paper is to expose a new state of matter exhibited by strongly correlated Fermi systems represented by various heavy-fermion (HF) metals, two-dimensional liquids like $\rm ^3He$, compounds with quantum spin liquids, quasicrystals, and systems with one-dimensional quantum spin liquid. We name these various systems HF compounds, since they exhibit the behavior typical of HF metals. In HF compounds at zero temperature the unique phase transition, dubbed throughout as the fermion condensation quantum phase transition (FCQPT) can occur; this FCQPT creates flat bands which in turn lead to the specific state, known as the fermion condensate. Unlimited increase of the effective mass of quasiparticles signifies FCQPT; these quasiparticles determine the thermodynamic, transport and relaxation properties of HF compounds. Our discussion of numerous salient experimental data within the framework of FCQPT resolves the mystery of the new state of matter. Thus, FCQPT and the fermion condensation can be considered as the universal reason for the non-Fermi liquid behavior observed in various HF compounds. We show analytically and using arguments based completely on the experimental grounds that these systems exhibit universal scaling behavior of their thermodynamic, transport and relaxation properties. Therefore, the quantum physics of different HF compounds is universal, and emerges regardless of the microscopic structure of the compounds. This uniform behavior allows us to view it as the main characteristic of a new state of matter exhibited by HF compounds.

cond-mat.str-el↗
arXiv2016

Topological basis for understanding the behavior of the heavy-fermion metal $\rm {β-YbAlB_4}$ under application of magnetic field and pressure

Informative recent measurements on the heavy-fermion metal $\rm β-YbAlB_4$ performed with applied magnetic field and pressure as control parameters are analyzed with the goal of establishing a sound theoretical explanation for the inferred scaling laws and non-Fermi-liquid (NFL) behavior, which demonstrate some unexpected features. Most notably, the robustness of the NFL behavior of the thermodynamic properties and of the anomalous $T^{3/2}$ temperature dependence of the electrical resistivity under applied pressure $P$ in zero magnetic field $B$ is at variance with the fragility of the NFL phase under application of a field. We show that a consistent topological basis for this combination of observations, as well as the empirical scaling laws, may be found within fermion-condensation theory in the emergence and destruction of a flat band, and explain that the paramagnetic NFL phase takes place without magnetic criticality, thus not from quantum critical fluctuations. Schematic $T-B$ and $T-P$ phase diagrams are presented to illuminate this scenario.

cond-mat.str-el↗
arXiv2016

The occurrence of a Mott-like gap in single-particle spectra of electron systems possessing flat bands

An unconventional type of the Mott's insulators where the gap in the spectrum of single-particle excitations is associated with repulsive effective interactions between quasiparticles is shown to exist in strongly correlated electron systems of solids that possess flat bands. The occurrence of this gap is demonstrated to be the consequence of violation of particle-hole symmetry, inherent in such systems. The results obtained are applied to elucidate the Fermi arc structure observed at temperatures up to $100\,$ K in angle-resolved photoemission spectra of the compound Sr$_2$IrO$_4$, not showing superconductivity down to low $T$.

cond-mat.str-el↗
arXiv2016

Scaling behavior of the thermopower of the archetypical heavy-fermion metal $\rm{YbRh_2Si_2}$

We reveal and explain a scaling behavior of the thermopower $S/T$ exhibiting by the archetypical heavy-fermion (HF) metal $\rm{YbRh_2Si_2}$ under the application of magnetic field $B$ at temperatures $T$. We show that the same scaling is demonstrated by such different HF compounds as $β$-${\rm YbAlB_4}$ and the strongly correlated layered cobalt oxide $\rm [BiBa_{0.66}K_{0.36}O_{2}]CoO_{2}$. Using $\rm{YbRh_2Si_2}$ as an example, we demonstrate that the scaling behavior of $S/T$ is violated at the antiferromagnetic phase transition, while both the residual resistivity $ρ_0$ and the density of states $N$ experience jumps at the phase transition, making the thermopower experience two jumps and change its sign. Our elucidation is based on flattening of the single-particle spectrum that profoundly affects $ρ_0$ and $N$. To depict the main features of the $S/T$ behavior, we construct the $T-B$ schematic phase diagram of $\rm{YbRh_2Si_2}$. Our calculated $S/T$ for the HF compounds are in good agreement with experimental facts and support our observations.

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arXiv2015

Fate of the Wiedemann-Franz law near quantum critical points of electron systems in solids

We introduce and analyze two different scenarios for violation of the Wiedemann-Franz law in strongly correlated electron systems of solids, close to a topological quantum critical point (TQCP) where the density of states $N(0)$ diverges. The first, applicable to the Fermi-liquid (FL) side of the TQCP, involves a transverse zero-sound collective mode that opens a new channel for the thermal conductivity, thereby enhancing the Lorenz number $L(0)$ relative to the value $L_0=π^2k^2_B/3e^2$ dictated by conventional FL theory. The second mechanism for violation of the WF law, relevant to the non-Fermi-liquid (NFL) side of the TQCP, involves the formation of a flat band and leads instead to a reduction of the Lorenz number.

cond-mat.str-el↗
arXiv2015

Interaction-induced merging of Landau levels in an electron system of double quantum wells

We show that the disappearance of the chemical potential jumps over the range of perpendicular magnetic fields at fixed integer filling factor in a double quantum well with a tunnel barrier is caused by the interaction-induced level merging. The distribution function in the merging regime is special in that the probability to find an electron with energy equal to the chemical potential is different for the two merged levels.

cond-mat.str-el↗
arXiv2015

Occurrence of flat bands in strongly correlated Fermi systems and high-$T_c$ superconductivity of electron-doped compounds

We consider a class of strongly correlated Fermi systems that exhibit an interaction-induced flat band pinned to the Fermi surface, and generalize the Landau strategy to accommodate a flat band and apply the more comprehensive theory to electron systems of solids. The non-Fermi-liquid behavior that emerges is compared with relevant experimental data on heavy-fermion metals and electron-doped high-$T_c$ compounds. We elucidate how heavy-fermion metals have extremely low superconducting transition temperature $T_c$, its maximum reached in the heavy-fermion metal CeCoIn$_5$ does not exceed 2.3 K, and explain the enhancement of $T_c$ observed in high-$T_c$ superconductors. We show that the coefficient $A_1$ of the $T$-linear resistivity scales with $T_c$, in agreement with the experimental behavior uncovered in the electron-doped materials. We have also constructed schematic temperature-doping phase diagram of the copper oxide superconductor $\rm La_{2-x}Ce_xCuO_4$ and explained the doping dependence of its resistivity.

cond-mat.supr-con↗
arXiv2015

High-$T_c$ superconductivity of electron systems with flat bands pinned to the Fermi surface

The phenomenon of flat bands pinned to the Fermi surface is analyzed on the basis of the Landau-Pitaevskii relation, which is applicable to electron systems of solids. It is shown that the gross properties of normal states of high-$T_c$ superconductors, frequently called strange metals, are adequately explained within the flat-band scenario. Most notably, we demonstrate that in electron systems moving in a two-dimensional Brillouin zone, superconductivity may exist in domains of the Lifshitz phase diagram lying far from lines of critical antiferromagnetic fluctuations, even if the effective electron-electron interaction in the Cooper channel is repulsive.

cond-mat.supr-con↗
arXiv2014

Comment on "Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice" (Punk, M., Chowdhury, D. & Sachdev, S. Nature Physics 10, 289-293 (2014))

The authors of a recent paper evidently take the view that the whole of progress made toward a theoretical understanding of the physics of quantum spin liquids (QSL) is associated with models of the kind proposed and applied in their present work. As motivation for this work, they observe that in contrast to existing theoretical models of both gapped and gapless spin liquids, which give rise to sharp dispersive features in the dynamic structure factor, the measured dynamic structure factor reveals an excitation continuum that is remarkably flat as a function of frequency. They go on to assert that "so far, the only theoretical model for a spin liquid state on the kagome lattice which naturally gives rise to a flat excitation band at low energies consists of the $Z_2$ spin liquids". Here we point out that there already exists a different and demonstrably successful approach to the QSL problem that does naturally feature a flat band.

cond-mat.str-el↗
arXiv2014

Theory of fermion condensation as an analog of the liquid-drop theory of atomic nuclei

Employing the duality between the momentum distribution $n(p)$ and density distribution $ρ(r)$, problems of theory of systems with flat bands, pinned to the Fermi surface, are discussed. We propose that the Lifshitz topological phase transition associated with the formation of additional pockets of the Fermi surface is the precursor of fermion condensation.

cond-mat.str-el↗
arXiv2014

General properties of phase diagrams of heavy-fermion metals

We study the temperature-magnetic field T-B phase diagrams of heavy fermion (HF) metals, and show that at sufficiently high temperatures outside the ordered phase the crossover temperature T*(B), regarded as the energy scale, follows a linear B-dependence, crossing the origin of the T-B phase diagram. This behavior of T*(B) constitutes the general property, and is formed by the presence of fermion condensation quantum phase transition hidden within the ordered phase. Our result is in good agreement with the experimental T-B phase diagram of the HF metals YbRh2Si2, Yb(Rh{0.93}Co{0.07})2Si2, and Yb(Rh{0.94}Ir{0.06})2Si2. To support our observations, we analyze the isothermal magnetization M, and demonstrate that dM/dT exhibits a universal temperature behavior over magnetic field scaling. The obtained results are in good agreement with the corresponding data collected on YbRh2Si2 as a function of magnetic field at different temperatures under hydrostatic pressure.

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