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Condensed Matter and Materials
Since its foundation in the late fifties, the theory of Fermi liquids has come a long way exploring the limits of its own applicability. Nowadays, the quest for departures from the conventional Fermi liquid behavior is considered one of the central topics in modern condensed matter physics.
The general consensus is that the Fermi liquid can be more readily destroyed in low dimensions and/or in the vicinity of critical points where the fluctuations of an incipient order parameter become important. In one spatial dimension, the Fermi liquid theory utterly fails even for a seemingly innocuous arbitrary weak short-range repulsion between the electrons. The corresponding non-Fermi-liquid (NFL) metallic state is characterized by algebraically decaying correlations and is referred to as the Luttinger liquid that can be thought of as a marginal deformation of the Fermi liquid.
It is generally believed that in higher dimensions a NFL behavior can result from sufficiently long-range and/or retarded ("singular") interactions which either give rise to predominantly small-angle ("forward") scattering or connect nearly parallel ("nested") parts of the Fermi surface or van Hove points. However, the necessary criteria remain unknown, which leaves enough room for the possibility that a NFL regime may occur even as a result of non-singular (e.g. screened), yet strong enough, interactions.
The suspected examples of this behavior include such physically important systems as layered high T_c cuprates, heavy fermion materials, graphene sheets, and low-density two-dimensional electron gas.
Although variety of distinct NFL features manifested by these systems is well-documented, their theoretical interpretation is often hindered by the lack of an appropriate formal description that would be as insightful and powerful as the Fermi-liquid theory when applied to the simple metals (Na, K,..).
The problem becomes especially complex in the presence of disorder or randomness where a simultaneous account of both, inelastic (electron-electron) and elastic (impurity), scattering processes, as well as interference between the two, becomes crucially important.
The goal of one of our ongoing projects is to develop new and advance the existing theoretical and computational tools for analyzing the behavior of electrons governed by the singular interactions, also in the presence of quenched disorder.
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