Quantum critical phase and Lifshitz transition in an extended periodic Anderson model

We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of 'strange' metal phases in quantum matter.     

Avoided antiferromagnetic order and quantum critical point in CeCoIn5

We measured the specific heat and resistivity of heavy fermion CeCoIn5 between the superconducting critical field H(c2)=5 T and 9 T, with the field in the [001] direction, and at temperatures down to 50 mK. At 5 T the data show a non-Fermi liquid (NFL) behavior down to the lowest temperatures. At the field above 8 T the data exhibit a crossover from the Fermi liquid to a non-Fermi liquid behavior. We analyzed the scaling properties of the specific heat and compared both the resistivity and the specific heat with the predictions of a spin-fluctuation theory. Our analysis leads us to suggest that the NFL behavior is due to incipient antiferromagnetism (AFM) in CeCoIn5 with the quantum critical point in the vicinity of H(c2). Below H(c2) the AFM phase which competes with the paramagnetic ground state is superseded by the superconducting transition.     

Mott Transition and Superconductivity in Quantum Spin Liquid Candidate NaYbSe_2

The Mott transition is one of the fundamental issues in condensed matter physics,especially in the system with antiferromagnetic long-range order.However,such a transition is rare in quantum spin liquid(QSL) systems without long-range order.Here we report the experimental pressure-induced insulator to metal transition followed by the emergence of superconductivity in the QSL candidate NaYbSe_2 with a triangular lattice of 4 f Yb~(3+) ions.Detail analysis of transport properties in metallic state shows an evolution from non-Fermi liquid to Fermi liquid behavior when approaching the vicinity of superconductivity.An irreversible structure phase transition occurs around 11 GPa,which is revealed by the x-ray diffraction.These results shed light on the Mott transition in the QSL systems.     

Universal behavior of heavy-fermion metals near a quantum critical point

The behavior of the electronic system of heavy-fermion metals is considered. We show that there exist at least two main types of the behavior when the system is near quantum critical point, which can be identified as the fermion condensation quantum phase transition (FCQPT). We show that the first type is represented by the behavior of a highly correlated Fermi liquid, while the second type is depicted by the behavior of a strongly correlated Fermi liquid. If the system approaches FCQPT from the disordered phase, it can be viewed as a highly correlated Fermi liquid which at low temperatures exhibits the behavior of Landau Fermi liquid (LFL). At higher temperatures T, it demonstrates the non-Fermi liquid (NFL) behavior which can be converted into the LFL behavior by the application of magnetic fields B. If the system has undergone FCQPT, it can be considered as a strongly correlated Fermi liquid which demonstrates the NFL behavior even at low temperatures. It can be turned into LFL by applying magnetic fields B. We show that the effective mass M* diverges at the very point that the Neél temperature goes to zero. The B-T phase diagrams of both liquids are studied. We demonstrate that these B-T phase diagrams have a strong impact on the main properties of heavy-fermion metals, such as the magnetoresistance, resistivity, specific heat, magnetization, and volume thermal expansion.     

Two types of the effective mass divergence and the Grüneisen ratio in heavy-fermion metals

The behavior of the specific heat c_p, effective mass M^*, and the thermal expansion coefficient of a Fermi system located near the fermion condensation quantum phase transition (FCQPT) is considered. We observe the first type behavior if the system is close to FCQPT: the specific heat , , while the thermal expansion coefficient . Thus, the Grüneisen ratio Γ(T)=/c_p does not diverges. At the transition region, where the system passes over from the non-Fermi liquid to the Landau Fermi liquid, the ratio diverges as . When the system becomes the Landau Fermi liquid, Γ(T,r)∝1/r, with r being a distance from the quantum critical point. Provided the system has undergone FCQPT, the second type takes place: the specific heat behaves as , M^*∝1/T, and =a+bT with a,b being constants. Again, the Grüneisen ratio diverges as .     

Quantum phase transition for the BEC-BCS crossover in condensed matter physics and CPT violation in elementary particle physics

We discuss the quantum phase transition that separates a vacuum state with fully gapped fermion spectrum from a vacuum state with topologically protected Fermi points (gap nodes). In the context of condensed-matter physics, such a quantum phase transition with Fermi point splitting may occur for a system of ultracold fermionic atoms in the region of BEC-BCS crossover, provided Cooper pairing occurs in the non-s-wave channel. For elementary particle physics, the splitting of Fermi points may lead to CPT violation, neutrino oscillations, and other phenomena.     

Phase fluctuations and pseudogap phenomena

This article reviews the current status of precursor superconducting phase fluctuations as a possible mechanism for pseudogap formation in high-temperature superconductors. In particular we compare this approach which relies on the two-dimensional nature of the superconductivity to the often used T-matrix approach. Starting from simple pairing Hamiltonians we present a broad pedagogical introduction to the BCS–Bose crossover problem. The finite temperature extension of these models naturally leads to a discussion of the Berezinskii–Kosterlitz–Thouless superconducting transition and the related phase diagram including the effects of quantum phase fluctuations and impurities. We stress the differences between simple Bose–BCS crossover theories and the current approach where one can have a large pseudogap region even at high carrier density where the Fermi surface is well-defined. Green's function and its associated spectral function, which explicitly show non-Fermi liquid behavior, is constructed in the presence of vortices. Finally different mechanisms including quasi-particle–vortex and vortex–vortex interactions for the filling of the gap above T_c are considered.     

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.     

Roles of zeros of the Green function in Fermi arc and non-Fermi liquid in the two-dimensional Hubbard model

We clarify effects of zeros of the Green function on a Fermi arc and on a non-Fermi liquid behavior in the two-dimensional Hubbard model by means of the cellular dynamical mean-field theory (CDMFT). We study in detail the state with a hole-pocket Fermi surface and zeros of the Green function, which was found for a slightly doped Mott insulator in an earlier CDMFT calculation [T.D. Stanescu, G. Kotliar, Phys. Rev. B 74 (2006) 125110; T.D. Stanescu, M. Civelli, K. Haule, G. Kotliar, Ann. Phys. (N.Y.) 321 (2006) 1682]. As thermal or other extrinsic scatterings of electrons broaden the zeros, regions around the zero surface gain an imaginary part of the self-energy, which strongly suppresses the spectral intensity, especially on the closer side of the hole pocket to the zero surface. Then the rest emerges as a Fermi arc. Quasiparticle weight becomes ill defined on the closer side of the Fermi pocket while it is well defined on the opposite side, which means that a differentiation of electrons occurs in the momentum space, indicating an emergence of a non-Fermi liquid phase.     

Quantum liquids of particles with generalized statistics

We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We discuss both equilibrium (specific heat, compressibility, and Pauli spin susceptibility) and nonequilibrium (current and thermal conductivities, thermopower) properties. Low-temperature quantities have the same temperature dependences as for the Fermi liquid, with the coefficients depending on the statistics parameter. The novel quantum liquids provide an explicit realization of systems with a non-Fermi liquid Lorentz ratio in two and more dimensions. Consistency of the theory is verified by deriving the compressibility and f-sum rules.     

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.     

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 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.     

Charge-density-wave partial gap opening in quasi-2D KMo6O17 purple bronze studied by angle resolved photoemission spectroscopy

Low dimensional (LD) metallic oxides have been a subject of continuous interest in the last two decades, mainly due to the electronic instabilities that they present at low temperatures. In particular, charge density waves (CDW) instabilities associated with a strong electron-phonon interaction have been found in Molybdenum metallic oxides such as KMo₆O₁₇ purple bronze. We report an angle resolved photoemission (ARPES) study from room temperature (RT) to T ∼40 K well below the Peierls transition temperature for this material, with CDW transition temperature T_CDW ∼120 K. We have focused on photoemission spectra along ΓM high symmetry direction as well as photoemission measurements were taken as a function of temperature at one representative k_F point in the Brillouin zone in order to look for the characteristic gap opening after the phase transition. We found out a pseudogap opening and a decrease in the density of states near the Fermi energy, E_F, consistent with the partial removal of the nested portions of the Fermi surface (FS) at temperature below the CDW transition. In order to elucidate possible Fermi liquid (FL) or non-Fermi liquid (NFL) behaviour we have compared the ARPES data with that one reported on quasi-1D K_0.3MoO₃ blue bronze.     

The holographic fermions dual to massive gravity

We investigate the properties of the spectral function of the fermionic operator in the field theory which is dual to a 4-dimensional massive gravity. We first study the Fermi surface and the dispersion relation in the dual boundary theory. We find that as the massive parameters is decreased, the Fermi momentum becomes lower and the low energy excitation near Fermi surface behaves more like non-Fermi liquid. Then, we introduce a dipole coupling in the bulk theory and explore the emergence of a gap in the fermionic spectral function. It is found that larger critical dipole coupling is needed to open the gap than that in Einstein gravity. Accordingly, in the field theory dual to massive gravity, it requires stronger negative dipole coupling to generate the marginal Fermi liquid.     

Magnetic instability of a two-dimensional Anderson non-Fermi liquid

We show that in the Anderson model for a two-dimensional non-Fermi liquid a magnetic instability can lead to the itinerant electron ferromagnetism. The critical temperature and the susceptibility of the paramagnetic phase have been analytically calculated. The usual Fermi behavior is re-obtained by taking the anomalous exponent to be zero.     

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.     

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.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Universal scaling and a novel quantum critical behavior of CeRhSb1-xSnx

We observe and explain a universal scaling rhochi = const for the electrical resistivity rho with the inverse magnetic susceptibility chi(-1) for the Kondo insulator CeRhSb(1-x)Snx. In the regime where the Kondo gap disappears (x > 0.12), the system forms a non-Fermi liquid (NFL), which transforms into a Fermi liquid at higher temperature. The NFL behavior is associated with the presence of a novel quantum critical point (QCP) at the Kondo insulator-correlated metal boundary. The divergent behavior of the resistivity, the susceptibility, and the specific heat has been observed when approaching the QCP from the metallic side and is interpreted as due to the competition between the Kondo and the intersite magnetic correlations.