Theory Of Fermion Condensation Research Articles

General Properties of Conventional and High-Temperature Superconductors

In our review, we analyze the scaling of the condensation energy EΔ divided by γ, EΔ/γ≃N(0)Δ12/γ, and quasiparticles of both conventional and unconventional superconductors, where N(0) is the density of states at zero temperature T=0, Δ1 is the maximum value of the superconducting gap, and γ is the Sommerfeld coefficient. It is shown that Bogoliubov quasiparticles act in superconducting states of unconventional and conventional superconductors. At the same time, quasiparticles are also present in the normal state of unconventional superconductors. We briefly describe the difference between unconventional superconductors and conventional ones, such as the resistivity in normal states and the difference in superfluid density in superconducting states. For the first time, we theoretically show that the universal scaling of EΔ/γ∝Tc2 applies equally to both conventional and unconventional superconductors. Our consideration is based on two experimental facts: Bogoliubov quasiparticles act in conventional and non-conventional superconductors and the corresponding flat band is deformed by the non-conventional superconducting state. As a result, our theoretical observations based on the theory of fermion condensation agree well with the experimental facts.

Magnetic Field as an Important Tool in Exploring the Strongly Correlated Fermi Systems and Their Particle–Hole and Time-Reversal Asymmetries

In this review, we consider the impact of magnetic field on the properties of strongly correlated heavy-fermion compounds such as heavy-fermion metals and frustrated insulators with quantum spin liquid. Magnetic field B can be considered a universal tool, allowing the exploration of the physics controlling the remarkable properties of heavy-fermion compounds. These vivid properties are T/B scaling, exhibited under the application of magnetic field B and at fixed temperature T, and the emergence of Landau Fermi liquid behavior under the application of magnetic field. We analyze the influence of quasiparticle–hole asymmetry on the properties of heavy-fermion (HF) compounds such as the universal scaling behavior of the thermopower S/T exhibited under the application of magnetic field B. We show that universal scaling is demonstrated by different HF compounds such as β-YbAlB4, YbRh2Si2, and strongly correlated layered cobalt oxide [BiBa0.66K0.36O2]CoO2. Analyzing YbRh2Si2, we show that the T/B scaling behavior of S/T is violated at the antiferromagnetic phase (AF) transition. The residual resistivity ρ0 and the density of states N0 experience jumps at the AF transition, causing two jumps in the thermopower and its sign reversal. Our consideration is based on the flattening of the single-particle spectrum that strongly affects ρ0 and N0 and leads to the violation of particle–hole symmetry. The particle–hole asymmetry generates the asymmetrical part Δσd(V) of tunneling differential conductivity σd(V), Δσd(V)=σd(V)−σd(−V), where V is the voltage bias. We demonstrate that in the presence of magnetic field, the quasiparticle–hole asymmetry vanishes, the LFL behavior is restored, and the asymmetry disappears. Our calculations of the mentioned properties of HF compounds, based on the fermion condensation theory, are in good agreement with the experiment and support our conclusion that the fermion condensation theory is capable of describing the properties of HF compounds, including those exhibited under the application of magnetic field.

Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal T/B scaling behavior; (2) the linear dependence of the resistivity on T, ρ(T)∝A1T (with A1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature Tc∝g with g being the coupling constant, while the M* becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with ρ(T)∝T is defined by the presence of flat bands.

Strongly Correlated Quantum Spin Liquids versus Heavy Fermion Metals: A Review.

This review considers the topological fermion condensation quantum phase transition (FCQPT) that explains the complex behavior of strongly correlated Fermi systems, such as frustrated insulators with quantum spin liquid and heavy fermion metals. The review contrasts theoretical consideration with recent experimental data collected on both heavy fermion metals (HF) and frustrated insulators. Such a method allows to understand experimental data. We also consider experimental data collected on quantum spin liquid in and quasi-one dimensional (1D) quantum spin liquid in both and with the aim to establish a sound theoretical explanation for the observed scaling laws, Landau Fermi liquid (LFL) and non-Fermi-liquid (NFL) behavior exhibited by these frustrated insulators. The recent experimental data on the heavy-fermion metal , with , and on its sister compounds and , carried out under the application of magnetic field as a control parameter are analyzed. We show that the thermodynamic and transport properties as well as the empirical scaling laws follow from the fermion condensation theory. We explain how both the similarity and the difference in the thermodynamic and transport properties of and in its sister compounds and emerge, as well as establish connection of these (HF) metals with insulators , and . We demonstrate that the universal LFL and NFL behavior emerge because the HF compounds and the frustrated insulators are located near the topological FCQPT or are driven by the application of magnetic fields.

Universal T/B Scaling Behavior of Heavy Fermion Compounds (Brief Review)

In our mini-review, we address manifestations of $T/B$ scaling behavior of heavy-fermion (HF) compounds, where $T$ and $B$ are respectively temperature and magnetic field. Using experimental data and the fermion condensation theory, we show that this scaling behavior is typical of HF compounds including HF metals, quasicrystals, and quantum spin liquids. We demonstrate that such scaling behavior holds down to the lowest temperature and field values, so that $T/B$ varies in a wide range, provided the HF compound is located near the topological fermion condensation quantum phase transition (FCQPT). Due to the topological properties of FCQPT, the effective mass $M^*$ exhibits a universal behavior, and diverges as $T$ goes to zero. Such a behavior of $M^*$ has important technological applications. We also explain how to extract the universal scaling behavior from experimental data collected on different heavy-fermion compounds. As an example, we consider the HF metal $\rm YbCo_2Ge_4$, and show that its scaling behavior is violated at low temperatures. Our results obtained show good agreement with experimental facts.

Flat Bands and Salient Experimental Features Supportingthe Fermion Condensation Theory of Strongly Correlated Fermi Systems

The physics of strongly correlated Fermi systems, being the mainstream topic for more than half a century, still remains elusive. Recent advancements in experimental techniques permit to collect important data, which, in turn, allow us to make the conclusive statements about the underlying physics of strongly correlated Fermi systems. Such systems are close to a special quantum critical point represented by topological fermion-condensation quantum phase transition which separates normal Fermi liquid and that with a fermion condensate, forming flat bands. Our review paper considers recent exciting experimental observations of universal scattering rate related to linear temperature dependence of resistivity in a large number of strongly correlated Fermi systems as well as normal metals. We show that the observed scattering rate is explained by the emergence of flat bands, while the so-called Planckian limit occurs accidentally since the normal metals exhibit the same scattering rate behavior. We also analyze recent challenging experimental data on tunneling differential conductivity collected under the application of magnetic field on the twisted graphene and the archetypical heavy fermion metal YbRh $${}_{2}$$ Si $${}_{2}$$ . Also we describe recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that these observations support the fermion condensation theory. Our theoretical results are in good agreement with corps of different and seemingly unrelated experimental facts. They show that the fermion-condensation quantum phase transition is an intrinsic property of strongly correlated Fermi systems and can be viewed as the universal agent explaining their core physics.

Fermion Condensation: Theory and Experiment

Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum $$\epsilon({\mathbf{p}})=0$$ in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature $$T_{c}$$ and, with allowance for $$C_{4}$$ crystal-lattice symmetry, the $$D$$ -wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap $$\Delta$$ , the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap $$\Upsilon$$ that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.

Thermodynamic, Dynamic, and Transport Properties of Quantum Spin Liquid in Herbertsmithite from an Experimental and Theoretical Point of View

In our review, we focus on the quantum spin liquid (QSL), defining the thermodynamic, transport, and relaxation properties of geometrically frustrated magnet (insulators) represented by herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 . The review mostly deals with an historical perspective of our theoretical contributions on this subject, based on the theory of fermion condensation closely related to the emergence (due to geometrical frustration) of dispersionless parts in the fermionic quasiparticle spectrum, so-called flat bands. QSL is a quantum state of matter having neither magnetic order nor gapped excitations even at zero temperature. QSL along with heavy fermion metals can form a new state of matter induced by the topological fermion condensation quantum phase transition. The observation of QSL in actual materials such as herbertsmithite is of fundamental significance both theoretically and technologically, as it could open a path to the creation of topologically protected states for quantum information processing and quantum computation. It is therefore of great importance to establish the presence of a gapless QSL state in one of the most prospective materials, herbertsmithite. In this respect, the interpretation of current theoretical and experimental studies of herbertsmithite are controversial in their implications. Based on published experimental data augmented by our theoretical analysis, we present evidence for the the existence of a QSL in the geometrically frustrated insulator herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 , providing a strategy for unambiguous identification of such a state in other materials. To clarify the nature of QSL in herbertsmithite, we recommend measurements of heat transport, low-energy inelastic neutron scattering, and optical conductivity σ ¯ in ZnCu 3 ( OH ) 6 Cl 2 crystals subject to an external magnetic field at low temperatures. Our analysis of the behavior of σ ¯ in herbertsmithite justifies this set of measurements, which can provide a conclusive experimental demonstration of the nature of its spinon-composed quantum spin liquid. Theoretical study of the optical conductivity of herbertsmithite allows us to expose the physical mechanisms responsible for its temperature and magnetic field dependence. We also suggest that artificially or spontaneously introducing inhomogeneity at nanoscale into ZnCu 3 ( OH ) 6 Cl 2 can both stabilize its QSL and simplify its chemical preparation, and can provide for tests that elucidate the role of impurities. We make predictions of the results of specified measurements related to the dynamical, thermodynamic, and transport properties in the case of a gapless QSL.

Topological Scenario for High-Temperature Superconductivity in Cuprates

The structure of the joint phase diagram of high-temperature superconducting cuprates has been studied within the theory of fermion condensation. Prerequisites of the topological rearrangement of the Landau state with the formation of a flat band adjacent to the nominal Fermi surface have been established. The related non-Fermi-liquid behavior of cuprates in the normal phase has been studied with focus on the non-Fermi-liquid behavior of the resistivity ρ(T), including the observed crossover from the linear temperature behavior ρ(T, x) = A1(x)T at doping levels x below the critical value x c h corresponding to the boundary of the superconducting region to the quadratic temperature behavior at x > x c h , which is incompatible with predictions of the conventional quantum-critical-point scenario. It has been demonstrated that the slope of the coefficient A1(x) is universal and is the same on both boundaries of the joint phase diagram of cuprates in agreement with available experimental data. It has also been shown that the fermion condensate is responsible for pairing in the D-wave state in cuprates. The effective Coulomb repulsion in the Cooper channel, which prevents the existence of superconductivity in normal metals in the S channel, leads to high-temperature superconductivity in the D channel.

Topological basis for understanding the behavior of the heavy-fermion metalβ−YbAlB4under application of magnetic field and pressure

Informative recent measurements on the heavy-fermion metal $\rm \beta-YbAlB_4$ 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.

Theory of Fermion Condensation as an Analog of the Liquid-Drop Theory of Atomic Nuclei

Theory of Fermion Condensation as an Analog of the Liquid-Drop Theory of Atomic Nuclei

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

We discuss problems of theory of systems with a fermion condensate or, in different words, systems with flat bands pinned to the Fermi surface, employing the duality of the momentum distribution n(p) and the density distribution ρ(r). 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.

Fermion condensate generates a new state of matter by making flat bands

This short review paper is devoted to 90th anniversary of S.T. Belyaev birthday. Belyaev’s ideas associated with the condensate state in Bose interacting systems have stimulated intensive studies of the possible manifestation of such a condensation in Fermi systems. In many Fermi systems and compounds at zero temperature a phase transition happens that leads to a quite specific state called fermion condensation. As a signal of such a fermion condensation quantum phase transition (FCQPT) serves unlimited increase of the effective mass of quasiparticles that determines the excitation spectrum and creates flat bands. We show that the class of Fermi liquids with the fermion condensate forms a new state of matter. We discuss the phase diagrams and the physical properties of systems located near that phase transition. A common and essential feature of such systems is quasiparticles different from those suggested by L.D. Landau by crucial dependence of their effective mass on temperature, external magnetic field, pressure, etc. It is demonstrated that a huge amount of experimental data collected on different compounds suggest that they, starting from some temperature and down, form the new state of matter, and are governed by the fermion condensation. Our discussion shows that the theory of fermion condensation develops completely good description of the NFL behavior of strongly correlated Fermi systems. Moreover, the fermion condensation can be considered as the universal reason for the NFL behavior observed in various HF metals, liquids, compounds with quantum spin liquids, and quasicrystals. We show that these systems exhibit universal scaling behavior of their thermodynamic properties. Therefore, the quantum critical physics of different strongly correlated compounds is universal, and emerges regardless of the underlying microscopic details of the compounds. This uniform behavior, governed by the universal quantum critical physics, allows us to view it as the main characteristic of the new state of matter.

Strongly correlated Fermi-systems: Non-Fermi liquid behavior, quasiparticle effective mass and their interplay

Basing on the density functional theory of fermion condensation, we analyze the non-Fermi liquid behavior of strongly correlated Fermi-systems such as heavy-fermion metals. When deriving equations for the effective mass of quasiparticles, we consider solids with a lattice and homogeneous systems. We show that the low-temperature thermodynamic and transport properties are formed by quasiparticles, while the dependence of the effective mass on temperature, number density, magnetic fields, etc., gives rise to the non-Fermi liquid behavior. Our theoretical study of the heat capacity, magnetization, energy scales, the longitudinal magnetoresistance and magnetic entropy are in good agreement with the remarkable recent facts collected on the heavy-fermion metal YbRh 2 Si 2 .

Low-temperature phase transitions in systems with fermion condensate

Phase transitions observed in electronic systems of solids in the vicinity of the quantum critical point where the effective mass diverges are analyzed within the framework of the theory of fermion condensation. It is shown that the disordered phase contains a fermion condensate. Its entropy is finite at T → 0 and initiates a chain of transitions occurring at extremely low temperatures. The results are in agreement with experiment.

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 T0, above which the behavior of the system is the same as in the theory of fermion condensation, and for T<T0 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.