Fermi Liquid Region Research Articles

Structural and physical properties of Ni 1−x V x alloys around and away from quantum critical point

We investigate the room temperature structure (global and local), temperature dependent magnetic and transport behaviour of Ni 1−x V x ( 0⩽x⩽0.13 ) alloys. Our Energy Dispersive Analysis of x-rays results show that the prepared compositions are stoichiometric. With increase in V doping, the compounds exhibit a quantum phase transition around x c = 0.12, where the ferromagnetic phase is suppressed. Our results show that all the compounds stabilize in face centred cubic structure at RT and the lattice parameter shows unusual behaviour close to x c . The magnetic and heat capacity studies show signature of Griffiths phase on either side of x c . From 25 K to the lowest collected temperature, we observe a linear T dependence of resistivity at x = 0.1 and around x c , which is separated by a Fermi-liquid region around x = 0.106. This suggests that the origin of the transport behaviour is different around the quantum critical point and away from it. Our Ni K-edge x-ray Absorption Spectroscopy results show that there is a significant reduction in the first coordination number around Ni central atom on doping. Further, with doping, there is distortion in the first coordination shell around Ni. This suggests, with V doping, the local structure around Ni is different from the global structure as obtained from the x-ray Diffraction results. Interestingly, with doping, we observe a direct connection between the extent of distortion at RT and the magnetic disorder obtained at 2 K. We believe our results will motivate the scientific community to further study the interplay between the structural disorder and quantum fluctuations with temperature at the local level.

Absence of a quantum limit to charge diffusion in bad metals

Good metals are characterised by diffusive transport of coherent quasi-particle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit, $\frac{ha}{e^{2}}$, where $a$ is the lattice constant. In bad metals, such as many strongly correlated electron materials, the resistivity exceeds the Mott-Ioffe-Regel limit and the transport is incoherent in nature. Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, recently proposed a lower bound to the charge diffusion constant, $D \gtrsim \hbar v_{F}^{2}/(k_{B}T)$, in the incoherent regime of transport, where $v_F$ is the Fermi velocity and $T$ the temperature. Using dynamical mean field theory (DMFT) we calculate the charge diffusion constant in a single band Hubbard model at half filling. We show that in the strongly correlated regime the Hartnoll's bound is violated in the crossover region between the coherent Fermi liquid region and the incoherent (bad metal) local moment region. The violation occurs even when the bare Fermi velocity $v_F$ is replaced by its low temperature renormalised value, $v_F^*$.The bound is satisfied at all temperatures in the weakly and moderately correlated systems as well as in strongly correlated systems in the high temperature region where the resistivity is close to linear in temperature. Our calculated charge diffusion constant, in the incoherent regime of transport, also strongly violates a proposed quantum limit of spin diffusion, $D_{s} \sim 1.3 \hbar/m$, where $m$ is the fermion mass, experimentally observed and theoretically calculated in a cold degenerate Fermi gas in the unitary limit of scattering.

Response to dynamical modulation of the optical lattice for fermions in the Hubbard model

Fermionic atoms in a periodic optical lattice provide a realization of the single-band Hubbard model. Using Quantum Monte Carlo simulations along with the Maximum Entropy Method, we evaluate the effect of a time-dependent perturbative modulation of the optical lattice amplitude on atomic correlations, revealed in the fraction of doubly-occupied sites. Our treatment extends previous approaches which neglected the time dependence of the on-site interaction, and shows that this term changes the results in a quantitatively significant way. The effect of modulation depends strongly on the filling-- the response of the double occupation is significantly different in the half-filled Mott insulator from the doped Fermi liquid region.

Canted antiferromagnetic order of imbalanced Fermi-Fermi mixtures in optical lattices by dynamical mean-field theory

We investigate antiferromagnetic order of repulsively interacting fermionic atoms in an optical lattice by means of dynamical mean-field theory (DMFT). Special attention is paid to the case of an imbalanced mixture. We take into account the presence of an underlying harmonic trap, both in a local-density approximation and by performing full real-space DMFT calculations. We consider the case in which the particle density in the trap center is at half-filling, leading to an antiferromagnetic region in the center, surrounded by a Fermi liquid region at the edge. In the case of an imbalanced mixture, the antiferromagnetism is directed perpendicular to the ferromagnetic polarization and canted. We pay special attention to the boundary structure between the antiferromagnetic and the Fermi liquid phase. For the moderately strong interactions considered here, no Stoner instability toward a ferromagnetic phase is found. Phase separation is only observed for strong imbalance and sufficiently large repulsion.

Low-temperature specific heat of [formula omitted

Low-temperature specific heat measurements on single crystalline YbRh 2 Si 2 in small magnetic fields are reported. The phase diagram around its quantum critical point is deduced which confirms the antiferromagnetic and the Fermi-liquid region as deduced from transport measurements. Furthermore, the specific heat reveals that the additional crossover line at T * which was recently observed in field-dependent transport and thermodynamic measurements is independent of the Fermi liquid regime.

Measurement of the Solubility of 4He in Liquid 3He in the Fermi-Liquid Region

The phase separation temperatures of dilute solutions of 4He in liquid 3He in the Fermi-liquid region have been measured by detecting the 4He film formation sensitively. From the obtained solubility curve, the effective mass of 4He atom and the difference in binding energy of 4He in liquid 4He and in liquid 3He are proposed.

The Effective Mass and Binding Energy of 4He in 3He in the Fermi Liquid Region

We have measured the solubility of4He in liquid3He down to about 40 mK and at pressures from zero up to ∼ 24 atm. The solubility was obtained from the thickness of the superfluid film in contact with unsaturated solutions of4He in3He as a function of temperature. By fitting the solubility data to Fermi liquid theory, we obtained the parameters m 4 * and Δ as a function of pressure. Here, m 4 * is the effective mass of4He in liquid3He and Δ the difference in binding energy between4He in pure4He and4He in liquid3He. This difference has a minimum near 10 atm. The average of the results for m 4 * , at different pressures, is (1.3 ± 0.2)m4. This agrees with the many body calculations of de Saavedra et al., and with the Stokes hydrodynamic mass using the partial volume of4He in3He, v 4 * . The partial volume was obtained by taking the derivative of Δ with respect to pressure.

Fermi-liquid quasi-particles and d x 2-y 2-superconductivity in the two-dimensional Hubbard model

A frequency- and momentum-renormalization-group acceleration together with an analytical approach is used to obtain the retarded Green's function in the self-consistent and conserving fluctuation-exchange (FLEX) approximation for the two-dimensional Hubbard model in the normal state and in the superconducting state. The analytical expressions for this approach are given. For band-fillings near half filling the self-energy in the normal state exhibits Fermi-liquid behaviour for, low temperatures and frequencies near the chemical potential, if the momentum is chosen near the Fermi-surface. However due to the presence of large many body effects the observed Fermi-liquid region near the chemical potential and near the Fermi-surface is very small. Results for the single particle density of states, the occupation number and the spectral function are presented. The superconducting state with symmetry is obtained for U = 2 to U = 6 and a (U, n)-phase diagram for the transition temperature Tc is presented. A maximum Tc/t of 0.0275 is obtained for U = 6 near half filling.

Characteristic of metamagnetic transition in CeRu2Si2 revealed with hall mobility

Field dependence of the Hall resistivity has been measured below and above a metamagnetic-like transition (MT) at 50 mK-2 K in a high quality single crystal CeRu 2Si2. The MT in the Fermi-liquid region is regarded as a continuous modification of resonance quasi-particle band near the Fermi level and no drastic change of carrier density is observed. In contrast, the MT in the incoherent region exhibits no clear change of effective mass or inelastic scattering time. The strong modification of the MT by the coherent effect is discussed.

An experiment to measure the diffusion of4He in4He in the Fermi liquid region

The diffusion coefficient D and the thermal diffusion factor γT, for4He in liquid3He at low temperatures T, have recently been calculated by solving the Boltzmann equation derived from Fermi-liquid theory. As T → 0, γT approaches a constant and D varies as 1/T. Both transport coefficients are determined solely by a 0 34 , the l = 0 forward scattering amplitude. Because a 0 34 can be found from thermodynamic data, e.g. the solubility of4He in liquid3He, X 4 sat , a strict test of the theory is possible. We have built an apparatus to measure D and X 4 sat as functions of pressure and temperature. The ratio of the capacitances of two parallel plate capacitors measures the number of4He atoms diffusing out of the liquid into the superfluid film. A bellows initiates the diffusion by changing the pressure in the liquid and thus the equilibrium concentration. A change of ∼ 10−8 in the4He concentration can be detected.

Theory of the diffusion of 4He in liquid 3He in the Fermi liquid region.

The diffusion coefficient $D$ and the thermal diffusion ratio ${k}_{T}$ for $^{4}\mathrm{He}$ in liquid $^{3}\mathrm{He}$ at low $T$ have been calculated by solving the Boltzmann equation derived from Fermi liquid theory. As $T\ensuremath{\rightarrow}0, {k}_{T}$ approaches a constant and $D$ varies as $\frac{1}{T}$; both are determined solely by ${a}_{0}^{34}$, the $l=0$ forward scattering amplitude. Since ${a}_{0}^{34}$ can be found from thermodynamics, a strict test of the theory can be made without any assumptions about the dependence of the scattering amplitude on the momentum transfer, making $^{4}\mathrm{He}$ in $^{3}\mathrm{He}$ unique among applications of Fermi liquid theory.

Microwave reflectivity of CeRu2Si2: Collective excitations in the electronic Fermi liquid.

We present microwave reflectivity data (35--134 GHz) on the magnetically nonordering heavy fermion compound ${\mathrm{CeRu}}_{2}$${\mathrm{Si}}_{2}$. In the Fermi liquid region at fields near to the metamagnetic transition (${\mathit{B}}_{\mathit{c}}$\ensuremath{\simeq}8 T) we observe pronounced effects with a reflectivity change of several percent. The experimental features can be explained within an oscillator model in \ensuremath{\epsilon}\ifmmode \tilde{}\else \~{}\fi{}(\ensuremath{\omega}) and \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{}(\ensuremath{\omega}). The oscillator frequencies become soft at ${\mathit{B}}_{\mathit{c}}$. The relaxation frequencies ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{\ensuremath{\epsilon}},\mathrm{\ensuremath{\mu}}}^{\mathrm{osc}}$() are extremely small and point to long lived collective excitations. They are supposed to represent the propagation of a zero sound mode and spin waves.

A “Leggett-Rice” effect in solid 3He — spin rotation induced by exchange

In solid 3He the internuclear exchange interaction may be interpreted as a molecular field, as in the Weiss theory of magnetism. In an applied magnetic field the magnetic moment precesses about the total magnetic field, to which the molecular field contributes. As Leggett showed for liquid helium in the Fermi liquid region, this leads to a modification of the time evolution of the magnetisation; it is no longer purely diffusive. In solid 3He at low polarisation there is conventional spin diffusion; at high polarisations the evolution is in the form of spin waves. We show that the intermediate behaviour may be expressed in terms of a complex diffusion coefficient of constant magnitude, whose phase angle depends on the polarisation.

The viscosity and some related properties of liquid3He at the melting curve between 1 and 100 mK

The viscosity η of liquid 3 He has been measured along the melting curve from 1 to 100 mK by means of a vibrating wire viscometer. In the normal Fermiliquid region we find 1/ηT2 = 1.17−3.10T, where η is in ΜP and T in K. At the transition temperature T A = 2.6 mK a rapid decrease occurs in η n , the viscosity of the normal component. Within 0.3 mK below T A , η n decreases to about 25% of ηA, but then becomes essentially constant. In the B phase η n first decreases to 20% of ηA and then seems to increase below 1.4 mK. Data on ϱ n , the density of the normal component, are also presented in the A and B phases. The results show that viscous flow is accompanied by a flow of zero dissipation, thus proving superfluidity in the A and B phases. The viscosity data at magnetic fields up to 0.9T have been related to theoretical calculations of the energy gap of superfluid 3 He near T A . The splitting of the A transition and the suppression of the B phase in an external field were also measured.

The low temperature viscosity of normal liquid3He

Measurements between 35 and 110 mK along the melting curve indicate that in the normal Fermi liquid region the viscosity of 3 He is given by (ηT 2 )−1 =a−bT n withn=1.0. The measured constants area=0.816 andb=4.43 for η in micropoise andT in Kelvin. Very little solid could be formed in this particular apparatus without immobilizing the vibrating wire viscometer. Patterns were observed in the solidification, however, which suggest that such a device could be operated at much lower temperatures in a compressional cooling cell of appropriate design. A systematic study was made of the excitation of different vibrational modes of the viscometer by varying the magnetic field orientation and the nature of the driving current. The use of tone burst and dc, as well as CW, excitation currents allows the same viscometer to be used over a wide range of viscosities.