Viable phenomenologies of the normal state of cuprates

We revisit the problem of constructing an elusive scaling theory of the strange metal phase of the cuprates. By using the four robust experimentally established temperature dependencies as the constitutive relations we then predict the scaling behaviors of a number of other observables, all those for which the reliable data are available being in agreement with experiment. Such predictions are also contrasted against the recent proposal inspired by the holographic approach, thus allowing one to critically assess the status of the latter.Comment: Latex, 4+ pages, no figure

Non-Fermi-Liquid Behavior of Compressible States of Electrons on the Lowest Landau Level

Experiments show that at even denominator fractions (EDFs) ($\nu=1/2, 3/4, 3/2$,...) the two-dimensional electron gas in a strong magnetic field becomes compressible, has no energy gap, and demonstrates the presence of an ostensible Fermi surface. Since this phenomenon results from a minimization of the interaction, rather than the kinetic energy, the EDF states might well exhibit deviations from a conventional Fermi liquid. We show that impurity scattering at EDFs and its interference with electron-electron and electron-phonon interactions provide examples of intrinsically non-Fermi-liquid transport.Comment: 5 pages, Latex. To appear in the Proceedings of the Euroconference on "Correlations in Unconventional Quantum Liquids" in Z.Phys.

Simulating holographic correspondence in flexible graphene

In the spirit of the generalized holographic conjecture, we explore a relationship between the bulk and boundary properties of non-interacting massive Dirac fermions living on a flexible surface, such as a sheet of graphene. We demonstrate that the boundary correlations can mimic those normally found in the system of one-dimensional interacting fermions, a specific form of such phantom interaction being determined by the bulk geometry. This geometrical interpretation of the boundary interaction effects offers a new insight into the possible origin of the more sophisticated types of holographic correspondence and suggests potential ways of visualizing 'analogue holography' in the experimentally viable environments.Comment: Latex, 4+ pages, no figure

Composite Dirac fermions in graphene

Generalizing the notion of composite fermions to the "pseudo-relativistic" Quantum Hall phenomena in graphene, we discuss a possible emergence of compressible states at the filling factors -3/2, -1/2, 1/2, 3/2. This analysis is further extended to the nearby incompressible states viewed as the Integer Quantum Hall Effect of the composite Dirac fermions, as well as those that might occur at the filling factors -1, 0, 1 as a result of the (pseudo)spin-singlet pairing between them.Comment: Latex, 4+ page

Logarithmic Temperature Dependence of Conductivity at Half Filled Landau Level

We study temperature dependence of diagonal conductivity at half filled Landau level by means of the theory of composite fermions in the weakly disordered regime $(k_{F}l>>1)$. At low temperatures we find the leading $\log T$ correction resulting from interference between impurity scattering and gauge interactions of composite fermions. The prefactor appears to be strongly enhanced as compared to the standard Altshuler-Aronov term in agreement with recent experimental observations.Comment: Nordita report, 9 pages, late

True SYK or (con)sequences

Some generalizations of the Sachdev-Ye-Kitaev (SYK) model and different patterns of their reparametrization symmetry breaking are discussed. The analysis of such (pseudo)holographic systems relates their generalized one-dimensional Schwarzian dynamics to (quasi) two-dimensional Liouvillian quantum mechanics. As compared to the original SYK case, the latter might be dissipative or have discrete states in its spectrum, either of which properties alters thermodynamics and correlations while preserving the underlying $SL(2,R)$ symmetry.Comment: Latex, no figure