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Register a new userRenormalizations in unconventional superconducting states born of normal and singular Fermi-liquids
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The density of low energy particle-hole excitations is non-analytic in a singular Fermi-liquid, but it is altered on entering a superconducting state in which, in the pure limit, it vanishes asymptotically at the chemical potential and in general is analytic. The single-particle excitations in the superconducting states are then quasi-particles so that a form of Landau theory may be constructed for thermodynamic and transport properties in the superconducting state. In this theory, the renormalization of measurable properties due to quasi-particle interactions, such as specific heat, compressibility, magnetic susceptibility, superfluid density, etc. changes in a temperature dependent fashion from the non-interacting theory. This is illustrated by showing the renormalization of these quantities and the relation between the parameters introduced to account for their temperature dependence. When the renormalizations in the normal state are large or singular, temperature dependence of properties in the superconducting states are then in general not useful for identifying the nodal character or symmetry of the superconducting state except for measurements at very low temperatures, upper limits of which are specified. The results obtained are expected to be useful in interpreting the experimental results for the temperature dependence of various properties in the superconducting state born of singular Fermi liquids.
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We have measured the superconducting penetration depth~$Lambda(T)$ in the heavy-fermion/intermediate-valent superconducting alloy series~Ce$_{1-x}$Yb$_x$CoIn$_5$ using transverse-field muon spin relaxation, to study the effect of intermediate-valent Yb doping on Fermi-liquid renormalization. From $Lambda(T)$ we determine the superfluid density $rho_s(T)$, and find that it decreases continuously with increasing nominal Yb concentration~$x$, i.e., with increasing intermediate valence. The temperature-dependent renormalization of the normal fluid density~$rho_N(T) = rho_s(0) - rho_s(T)$ in both the heavy-fermion and intermediate valence limits is proportional to the temperature-dependent renormalization of the specific heat. This indicates that the temperature-dependent Fermi-liquid Landau parameters of the superconducting quasiparticles entering the two different physical quantities are the same. These results represent an important advance in understanding of both intermediate valence and heavy-fermion phenomena in superconductors.
An introductory survey of the theoretical ideas and calculations and the experimental results which depart from Landau Fermi-liquids is presented. Common themes and possible routes to the singularities leading to the breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of Singular Fermi liquids (often called Non-Fermi liquids) include models of impurities in metals with special symmetries and one-dimensional interacting fermions. A review of these is followed by a discussion of Singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low-energy collective fluctuations, gauge fields due either to symmetries in the hamiltonian or possible dynamically generated symmetries, fluctuations around quantum critical points, the normal state of high temperature superconductors and the two-dimensional metallic state. For the last three systems, the principal experimental results are summarized and the outstanding theoretical issues highlighted.
The density correlations of some singular Fermi liquids with anomalous properties such as resistivity varying linearly with T at low temperatures, a $T log T$ contribution to the entropy and thermopower, etc., are expected to be quite different from that in Landau Fermi liquids. A possible statistical mechanical model for the quantum critical fluctuations in diverse systems with such properties is the 2D dissipative quantum XY model. Exact relations between the density correlations and singular irreducible vertices due to coupling of Fermions to the topological excitations of the 2D dissipative quantum XY model are used to derive results which were proposed phenomenologically long ago but are measurable only recently due to advances in experimental techniques. The density correlations are unusual at all momenta ${bf q}$ and energy $ u$, from the hydrodynamic limit to that for large momenta and energy. The hydrodynamic limit together with the continuity equation gives the linear in T resistivity. The density correlations are almost independent of frequency up to a high frequency cut-off for $q_{ZB} gtrsim q >> u/v_F$; $q_{ZB}$ is the Brillouin zone boundary and $v_F$ is the Fermi-velocity. The results should be applicable to loop-current quantum criticality in cuprates, and to 2D Fe based compounds near their antiferromagnetic quantum-criticality. The relation of the results to the temperature and frequency dependent conductivity and to Raman response is also discussed.
A system with charge conservation and lattice translation symmetry has a well-defined filling $ u$, which is a real number representing the average charge per unit cell. We show that if $ u$ is fractional (i.e. not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems. The most powerful constraint comes about if $ u$ is continuously tunable (i.e. the system is charge-compressible), in which case we show that the low-energy theory must have a very large emergent symmetry group -- larger than any compact Lie group. An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved. We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics. We call a system with this property an ersatz Fermi liquid. We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttingers theorem (which is thus extended to a large class of non-Fermi liquids) and periodic quantum oscillations in the response to an applied magnetic field. We also establis
Insulators occur in more than one guise, a recent finding was a class of topological insulators, which host a conducting surface juxtaposed with an insulating bulk. Here we report the observation of an unusual insulating state with an electrically insulating bulk that simultaneously yields bulk quantum oscillations with characteristics of an unconventional Fermi liquid. We present quantum oscillation measurements of magnetic torque in high purity single crystals of the Kondo insulator SmB6, which reveal quantum oscillation frequencies characteristic of a large three-dimensional conduction electron Fermi surface similar to the metallic rare earth hexaborides such as PrB6 and LaB6. The quantum oscillation amplitude strongly increases at low temperatures, appearing strikingly at variance with conventional metallic behaviour.
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