The temperature (T) dependence of the muon and $^{63}$Cu nuclear spin-lattice relaxation rates $1/T_1$ in YbCu4.4Au0.6 is reported over nearly four decades. It is shown that for $T\to 0$ $1/T_1$ diverges following the behaviour predicted by the self-consistent renormalization (SCR) theory developed by Moriya for a ferromagnetic quantum critical point. On the other hand, the static uniform susceptibility $χ_s$ is observed to diverge as $T^{-2/3}$ and $1/T_1T\propto χ_s^2$, a behaviour which is not accounted for by SCR theory. The application of a magnetic field $H$ is observed to induce a crossover to a Fermi liquid behaviour and for $T\to 0$ $1/T_1$ is found to obey the scaling law $1/T_1(H)= 1/T_1(0)[1+(μ_BH/k_BT)^2]^{-1}$.
The non-Fermi liquid system (NFL) YbCu_(5-x)Al_(x) (x = 1.3 - 1.75) has been investigated in hetero- as well as homo-contact arrangement in magnetic fields up to 22.5 T. The observed dV/dI(V) characteristics reveal asymmetry in hetero-contact arrangement and do not agree with the model of thermal contact heating, at least close to zero-bias voltage. In the case of a hetero-contact arrangement we have observed a maximum at only one voltage polarity at about 1.3 mV (for x = 1.5), which asymmetry is suppressed in an applied magnetic field. This behavior is connected with NFL properties of studied…
A strong departure from Landau-Fermi liquid (LFL) behavior have been recently revealed in observed anomalies in both the magnetic susceptibility $χ$ and the muon and $\rm ^{63}Cu$ nuclear spin-lattice relaxation rates $1/T_1$ of ${\rm {YbCu_{5-x}Au_x}}$ ($x=0.6$). We show that the above anomalies along with magnetic-field-induced reentrance of LFL properties are indeed determined by the scaling behavior of the quasiparticle effective mass. We obtain the scaling behavior theoretically utilizing our approach based on fermion condensation quantum phase transition (FCQPT) notion. Our theoretical a…
The physical properties of the very heavy fermion YbCu$_4$Ni were characterized through structural, magnetic, thermal and transport studies along nearly four decades of temperature ranging between 50 milikelvin and 300 K. At high temperature, the crystal electric field levels splitting was determined with $Δ_1 (Γ_6)= 85$ K and $Δ_2 (Γ_8) \approx 200$ K, the latter being a quartet in this cubic symmetry. An effective magnetic moment $μ_{eff} \approx 3μ_B$ is evaluated for the $Γ_7$ ground state, while at high temperature the value for a Yb$^{3+}$ ion is observed. At low temperature this compoun…
We investigate the pressure-temperature phase diagram of YbIr$_2$Si$_2$ by measuring the electrical resistivity $ρ(T)$. In contrast to the widely investigated YbRh$_2$Si$_2$, YbIr$_2$Si$_2$ is a paramagnetic metal below $p_c\simeq 8$ GPa. Interestingly, a first-order, presumably ferromagnetic, transition develops at $p_c$. Similar magnetic properties were also observed in YbRh$_2$Si$_2$ and YbCu$_2$Si$_2$ at sufficiently high pressures, suggesting a uniform picture for these Yb compounds. The ground state of YbIr$_2$Si$_2$ under pressure can be described by Landau Fermi-liquid (LFL) theory, in…
Self-energy at zero temperature is investigated up to the third-order of interaction using one-patch model in two dimensions, whose interaction process corresponds to $g_4$-process of $g$-ology model in one dimension. The self-energy $Σ^R({\mib k},ε)$ diverges at $ε=ξ_k$, and the contribution from the particle-hole process in third-order self-energy diagrams has a stronger divergence compared to the one from the particle-particle process. This implies that the loop-cancellation in the forward scattering is insufficient due to the effect of the warping of the Fermi surface. The strong energy de…
Using the field-theoretical methods we studied the evolution from BCS description of a non-Fermi superconductor to that of Bose-Einstein condensation (BEC) in one loop approximation. We showed that the repulsive interaction between composite bosons is determined by the exponent $α$ of the Anderson propagator in a two dimensional model. For $\a\neq 0$ the crossover is also continous and for $\a=0$ we obtain the case of the Fermi liquid.
We investigate a system of one dimensional Hubbard chains of interacting fermions coupled by inter-chain hopping. Using a generalization of the Dynamical Mean Field Theory we study the deconfinement transition from a Mott insulator to a metal and the crossover between Luttinger and Fermi liquid phases. One-particle properties, local spin response and inter-chain optical conductivity are calculated. Possible applications to organic conductors are discussed.
We theoretically investigate the interlayer magnetoresistance in quasi-two-dimensional Dirac fermion systems, where the Fermi energy is at the Dirac point. If there is an intermediate insulating layer that has an overlap with the wave functions in the Dirac fermion layers, there appears a positive magnetoresistance regime due to the intervalley tunneling. We show that the interlayer magnetoresistance can be used to find whether Dirac fermions are massive or not from the minimum in the interlayer magnetoresistance. As a specific system, we consider \alphaI under high pressure. We also discuss t…
A crossover from a non-Fermi liquid to a Fermi liquid phase in Yb$_2$Ni$_{12}$P$_7$ is observed by analyzing electrical resistivity $ρ(T)$, magnetic susceptibility $χ(T)$, specific heat $C(T)$, and thermoelectric power $S(T)$ measurements. The electronic contribution to specific heat, $C_{e}(T)$, behaves as $C_{e}(T)/T \sim -\ln(T)$ for 5 K $< T <$ 15 K, which is consistent with non-Fermi liquid behavior. Below $T \sim$ 4 K, the upturn in $C_{e}(T)/T$ begins to saturate, suggesting that the system crosses over into a Fermi-liquid ground state. This is consistent with robust $ρ(T) - ρ_0 = AT^2$…
The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover fro…
The antiferromagnetic spin correlation function $S_{\bf Q}$, the staggered spin susceptibility $χ_{\bf Q}$ and the energy scale $ω_{FL}=S_{\bf Q}/χ_{\bf Q}$ are studied numerically within the t-J model and the Hubbard model, as relevant to cuprates. It is shown that $ω_{FL}$, related to the onset of the non-Fermi-liquid spin response at $T>ω_{FL}$, is very low in the regime below the 'optimum' hole doping $c_h < c_h^* \sim 0.16$, while it shows a steep increase in the overdoped regime. A quantitative analysis of NMR spin-spin relaxation-rate $1/T_{2G}$ for various cuprates reveals a similar be…
By means of a specific heat ($C$) and electrical resistivity ($\varrho$) study, we give evidence of a pronounced Fermi liquid (FL) behavior with sizable mass renormalization, $m^{\ast}/m = 30$, up to unusually high temperatures $\sim$70 K in the layered system Cu$_{2/3}$V$_{1/3}$V$_2$S$_4$. At low temperature, a marked upturn of both $C$ and $\varrho$ is suppressed by magnetic field, which suggests a picture of Kondo coupling between conduction electrons in the VS$_2$ layers and impurity spins of the V$^{3+}$ ions located between layers. This picture opens the possibility of controlling electr…
We explore the effect of inhomogeneity on electronic properties of the two-dimensional Hubbard model on a square lattice using dynamical mean-field theory (DMFT). The inhomogeneity is introduced via modulated lattice hopping such that in the extreme inhomogeneous limit the resulting geometry is a Lieb lattice, which exhibits a flat-band dispersion. The crossover can be observed in the uniform sublattice magnetization which is zero in the homogeneous case and increases with the inhomogeneity. Studying the spatially resolved frequency-dependent local self-energy, we find a crossover from Fermi-l…
K(BEDT-TTF)2Cu(NCS)2 has been investigated by Raman scattering in both bulk and nanoparticle compounds. Phonon modes from 20 to 1600 cm-1 have been assigned. Focusing on the unexplored low frequency phonons, a plateau in frequencies is observed in the bulk phonons between 50 and 100 K and assigned to the signature of the bad metal phase. Nanoparticles of K(BEDT-TTF)2Cu(NCS)2 exhibit anomalies at 50 K associated to the crossover from a bad metal to a Fermi liquid whose origins are discussed.
We consider a theoretical problem of electron-electron scattering time in a quasi-one-dimensional (Q1D) conductor in a magnetic field, perpendicular to its conducting axis. We show that inverse electron-electron scattering time becomes of the order of characteristic electron energy, $1/τ\sim ε\sim T$, in a high magnetic field, directed far from the main crystallographic axes, which indicates breakdown of the Fermi liquid theory. In a magnetic field, directed close to one of the main crystallographic axis, inverse electron-electron scattering time becomes much smaller than characteristic electr…
We report a systematic nuclear magnetic resonance investigation of the $^{23}$Na spin-lattice relaxation rate, $1/T_1$, in sodium loaded low-silica X (LSX) zeolite, Na$_n$/Na$_{12}$-LSX, for various loading levels of sodium atoms $n$ across the metal-to-insulator crossover. For high loading levels of $n \geq 14.2$, $1/T_1T$ shows nearly temperature-independent behavior between 10 K and 25 K consistent with the Korringa relaxation mechanism and metallic ground state. As the loading levels decrease below $n \leq 11.6$, the extracted density of states (DOS) at the Fermi level sharply decreases, a…
The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover only governed by the density parameter $r_s$. For $r_s>r_c$, the data are consistent with a Wigner molecule description, while for $r_s<r_c$, Fermi liquid behavior is recovered. The crossover value $r_c \approx 4$ is surprisingly small.
By using a Path Integral formalism, we study the fluctuating fields in the order parameter for a 3D uniform Fermi gas at T<Tc. The BCS-BEC crossover condition is included into the analysis in the framework of the usual s-wave scattering approximation. The general expressions for the temperature dependence of the partition function and the quadratic average in the fluctuations fields are explicitly established in terms of the BCS-Gor'kov correlation propagators.
We consider the low-energy region of an array of Luttinger liquids coupled by a weak interchain hopping. The leading logarithmic divergences can be re-summed to all orders within a self-consistent perturbative expansion in the hopping, in the large-dimension limit. The anomalous exponent scales to zero below the one-particle crossover temperature. As a consequence, coherent quasiparticles with finite weight appear along the whole Fermi surface. Extending the expansion self-consistently to all orders turns out to be crucial in order to restore the correct Fermi-liquid behavior.
We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single bar…
Quantum critical systems derive their finite temperature properties from the influence of a zero temperature quantum phase transition. The paradigm is essential for understanding unconventional high-Tc superconductors and the non-Fermi liquid properties of heavy fermion compounds. However, the microscopic origins of quantum phase transitions in complex materials are often debated. Here we demonstrate experimentally, with support from numerical renormalization group calculations, a universal crossover from quantum critical non-Fermi liquid behavior to distinct Fermi liquid ground states in a hi…
A unified theory is outlined for the cuprates, Fe-based, and related superconductors. Their low-energy excitations are approached in terms of auxiliary particles representing combinations of atomic-like electron configurations, and the introduction of a Lagrange Bose field enables their treatment as bosons or fermions. This theory correctly describes the observed phase diagram of the cuprates, including the non-Fermi-liquid to FL crossover in the normal state, the existence of Fermi arcs below T^* and of "marginal-FL" behavior above it. The anomalous behavior of numerous physical quantities is…
We study the crossover of a quasi-two-dimensional Fermi gas trapped in the radial plane from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime by crossing a wide Feshbach resonance. We consider two effective two-dimensional Hamiltonians within the mean-field level, and calculate the zero-temperature cloud size and number density distribution. For a model 1 Hamiltonian with renormalized atom-atom interaction, we observe a constant cloud size for arbitrary detunings. For a model 2 Hamiltonian with renormalized interactions between atoms and dressed molecul…
We study graphene-based electron systems with long-range Coulomb interaction by performing an analytic continuation in the number of dimensions. We characterize in this way the crossover between the marginal Fermi liquid behavior of a graphite layer and the Luttinger liquid behavior at $D = 1$. The former persists for any dimension above $D = 1$. However, the proximity to the $D = 1$ fixed-point strongly influences the phenomenology of quasi-onedimensional systems, giving rise to an effective power-law behavior of observables like the density of states. This applies to nanotubes of large radiu…
We consider the density response of a trapped two-component Fermi gas. Combining the Bogoliubov-deGennes method with the random phase approximation allows the study of both collective and single particle excitations. Calculating the density response across a wide range of interactions, we observe a crossover from a weakly interacting pair vibration mode to a strongly interacting Goldstone mode. The crossover is associated with a depressed collective mode frequency and an increased damping rate, in agreement with density response experiments performed in strongly interacting atomic gases.
We determine the effects on the BCS-BEC crossover of the energy dependence of the effective two-body interaction, which at low energies is determined by the effective range. To describe interactions with an effective range of either sign, we consider a single-channel model with a two-body interaction having an attractive square well and a repulsive square barrier. We investigate the two-body scattering properties of the model, and then solve the Eagles-Leggett equations for the zero temperature crossover, determining the momentum dependent gap and the chemical potential self-consistently. From…
We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature to predictions for both fermions and bosons from Quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for inves…
We investigate the Gorkov--Melik-Barkhudarov (GM) correction to superfluid transition temperature in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC) across the SOC-driven BCS-BEC crossover. In the calculation of the induced interaction, we find that the spin-component mixing due to SOC can induce both of the conventional screening and additional antiscreening contributions that interplay significantly in the strong SOC regime. While the GM correction generally lowers the estimate of transition temperature, it turns out that at a fixed weak interaction, the correction effect e…
We present a systematic investigation of the effects of "nonmagnetic" impurities on the $s$-wave BCS-BEC crossover in atomic Fermi gases within a pairing fluctuation theory. Both pairing and impurity scattering $T$-matrices are treated self-consistently at the same time. While the system is less sensitive to impurity scattering in the Born limit, for strong impurity scatterers, both the frequency and the gap function are highly renormalized, leading to significant suppression of the superfluid $T_c$, the order parameter and the superfluid density. We also find the formation of impurity bands a…
We study the Hall conductivity in single layer gapped Dirac fermion materials including coupling to a phonon field, which not only modifies the quasi-particle dynamics through the usual self-energy term but also renormalizes directly the gap. Consequently the Berry curvature is modified. As the temperature is increased the sign of the renormalized gap can change and the material can cross over from a band insulator to a topological insulator at higher temperature (T). The effective Chern numbers defined for valley and spin Hall conductivity show a rich phase diagram with increasing temperature…
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 the 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.
BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains: entanglement and correlation signatures from DMRG and effective-pairing theory
Charles University（查理大学）；São Paulo State University (UNESP)（圣保罗州立大学）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）
This report adresses topics and questions of common interest in the fields of ultra-cold gases and nuclear physics in the context of the BCS-BEC crossover. The BCS-BEC crossover has recently been realized experimentally, and essentially in all of its aspects, with ultra-cold Fermi gases. This realization, in turn, has raised the interest of the nuclear physics community in the crossover problem, since it represents an unprecedented tool to test fundamental and unanswered questions of nuclear many-body theory. Here, we focus on the several aspects of the BCS-BEC crossover, which are of broad jo…
We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the 2D mean-field theory indicates that the quantum fluctuations are much more pronounced than those in 3D. In this work, we show that the …
