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Register a new userA variational method in the problem of screening an external charge in strongly correlated metals
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Gian Guzman-Verri G
Publication date
2012
fields
Physics
and research's language is
English
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We describe a variational calculation for the problem of screening of a point charge in a layered correlated metal for dopings close to the Mott transition where the screening is non-linear due to the proximity to the incompressible insulating state. We find that external charge can induce locally incompressible regions and that the non-linear dependence of the screening on density can induce overscreening in the nearest nearby layers while preserving overall charge neutrality.
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A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids are not amenable to the perturbative methods of Fermi liquid theory, but can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene, which possesses Dirac dispersions at low energies as well as significant Coulomb interactions between the electrons. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes of their band structure provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in stoichiometric Scandium (Sc) Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction and hence reflects the strength of the correlations, is enhanced by a factor of about 3.2 as compared to graphene, due to orbital hybridization. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put, for the first time, the turbulent flow regime described by holography within the reach of experiments.
An exact formula for the temperature dependent Hall number of metals is derived. It is valid for non-relativistic fermions or bosons, with arbitrary potential and interaction. This DC transport coefficient is proven to (remarkably) depend solely on equilibrium susceptibilities, which are more amenable to numerical algorithms than the conductivity. An application to strongly correlated phases is demonstrated by calculating the Hall sign in the vicinity of Mott phases of lattice bosons.
We report a theoretical analysis of variational wave functions for the BCS pairing problem. Starting with a Jastrow-Feenberg (or, in a more recent language fixed-node) wave function for the superfluid state, we develop the full optimized Fermi-Hypernetted Chain (FHNC-EL) equations which sum a local approximation of the parquet-diagrams. Close examination of the procedure reveals that it is essential to go beyond the usual Jastrow-Feenberg approximation to guarantee the correct stability range.
Correlations between electrons and the effective dimensionality are crucial factors that shape the properties of an interacting electron system. For example, the onsite Coulomb repulsion, U, may inhibit, or completely block the intersite electron hopping, t, and depending on the ratio U/t, a material may be a metal or an insulator. The correlation effects increase as the number of allowed dimensions decreases. In 3D systems, the low energy electronic states behave as quasiparticles (QP), while in 1D systems, even weak interactions break the quasiparticles into collective excitations. Dimensionality is particularly important for a class of new exotic low-dimensional materials where 1D or 2D building blocks are loosely connected into a 3D whole. Small interactions between the blocks may induce a whole variety of unusual transitions. Here, we examine layered systems that in the direction perpendicular to the layers display a crossover from insulating-like, at high temperatures, to metallic-like character at low temperatures, while being metallic over the whole temperature range within the layers. We show that this change in effective dimensionality correlates with the existence or non-existence of coherent quasiparticles within the layers.
We review recent advances in the field of full counting statistics (FCS) of charge transfer through impurities imbedded into strongly correlated one-dimensional metallic systems, modelled by Tomonaga-Luttinger liquids (TLLs). We concentrate on the exact analytic solutions for the cumulant generating function (CGF), which became available recently and apply these methods in order to obtain the FCS of a non-trivial contact between two crossed TLL.
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