Physical review. B, Condensed matter

Eikonal approximation in the theory of two-dimensional fermions with long-range current-current interactions

Dmitri V. Khveshchenko, Philip C. E. Stamp

Published Feb 15, 1994• 40 citations

Abstract

We study the behavior of response functions of two-dimensional (2D) fermions interacting via a long-range transverse gauge field in the eikonal approximation. We observe that an exponentially vanishing wave-function renormalization prevents divergences in the density-density correlation function and the pairing susceptibility. The wave-function renormalization also shows up in a suppression of the dHvA effect. Elaborating on an observation recently made by Ioffe, Lidsky, and Altschuler, we also infer an effective bosonic description which makes it possible to reproduce our eikonal results in terms of free 2D bosons.

DOI: 10.1103/physrevb.49.5227

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Low-energy properties of two-dimensional fermions with long-range current-current interactions

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Physical review. B, Condensed matter

Eikonal approximation in the theory of two-dimensional fermions with long-range current-current interactions

Dmitri V. Khveshchenko, Philip C. E. Stamp

Published Feb 15, 1994• 40 citations

Publisher

Abstract

DOI: 10.1103/physrevb.49.5227

Related papers

Low-energy properties of two-dimensional fermions with long-range current-current interactions

Dmitri V. Khveshchenko, Philip C. E. Stamp

Physical Review LettersSep 27, 199380 citations

Low-energy properties of two-dimensional fermions with long-range current-current interactions

Philip C. E. Stamp, Dmitri V. Khveshchenko

We calculate the one-particle Green function of 2D fermions interacting via a long-range transverse gauge field. Its asymptotic low-energy behavior is found within the eikonal expansion which consistently sums the infrared divergent terms given by "maximally crossed diagrams." Instead of power law corrections to Fermi liquid theory we observe a much stronger singularity which implies a more radical breakdown of Fermi liquid theory than the usual orthogonality catastrophe.

May 5, 20230 citations

Spectral and dynamic properties of a 2D Luttinger liquid with current-current interactions

J. W. Rasul, Yujoung Bai

We calculate the Green function, particle-hole susceptibility and Cooper pair susceptibility of a 2D Luttinger liquid that results from an electron gas with long-range current-current interactions. The Haldane bosonization scheme allows this model to be written in terms of boson operators, from which the required fermion operators are constructed. We find weakly decaying power law tails in the spectral function and a Kohn anomaly in the 2k F particle-hole susceptibility, but no divergence in the Cooper amplitude.We calculate the Green function, particle-hole susceptibility and Cooper pair susceptibility of a 2D Luttinger liquid that results from an electron gas with long-range current-current interactions. The Haldane bosonization scheme allows this model to be written in terms of boson operators, from which the required fermion operators are constructed. We find weakly decaying power law tails in the spectral function and a Kohn anomaly in the 2k F particle-hole susceptibility, but no divergence in the Cooper amplitude.

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Matthew S. Foster, Andreas W. W. Ludwig

We study the effects of generic short-ranged interactions on a system of two-dimensional (2D) Dirac fermions subject to a special kind of static disorder, often referred to as ``chiral.'' The noninteracting system is a member of the disorder class $BD\mathrm{I}$ [M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as a low-energy description of a time-reversal invariant tight-binding model of spinless fermions on a honeycomb lattice, subject to random hopping, and possessing particle-hole symmetry. It is known that, in the absence of interactions, this disordered system is special in that it does not localize in 2D, but possesses extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states. In the context of the hopping model, the short-range interactions that we consider are particle-hole symmetric density-density interactions. Using a perturbative one-loop renormalization group analysis, we show that the same mechanism responsible for the divergence of the density of states in the noninteracting system leads to an instability, in which the interactions are driven strongly relevant by the disorder. This result should be contrasted with the limit of clean Dirac fermions in 2D, which is stable against the inclusion of weak short-ranged interactions. Our work suggests a mechanism wherein a clean system, initially insensitive to interaction effects, can be made unstable to interactions upon the inclusion of weak static disorder. We dub this mechanism a ``disorder-driven Mott transition.'' Our result for 2D fermions also contrasts sharply with known results in one dimension, where a similar delocalized phase has been shown to be robust against the inclusion of weak interaction effects.We study the effects of generic short-ranged interactions on a system of two-dimensional (2D) Dirac fermions subject to a special kind of static disorder, often referred to as ``chiral.'' The noninteracting system is a member of the disorder class $BD\mathrm{I}$ [M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as a low-energy description of a time-reversal invariant tight-binding model of spinless fermions on a honeycomb lattice, subject to random hopping, and possessing particle-hole symmetry. It is known that, in the absence of interactions, this disordered system is special in that it does not localize in 2D, but possesses extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states. In the context of the hopping model, the short-range interactions that we consider are particle-hole symmetric density-density interactions. Using a perturbative one-loop renormalization group analysis, we show that the same mechanism responsible for the divergence of the density of states in the noninteracting system leads to an instability, in which the interactions are driven strongly relevant by the disorder. This result should be contrasted with the limit of clean Dirac fermions in 2D, which is stable against the inclusion of weak short-ranged interactions. Our work suggests a mechanism wherein a clean system, initially insensitive to interaction effects, can be made unstable to interactions upon the inclusion of weak static disorder. We dub this mechanism a ``disorder-driven Mott transition.'' Our result for 2D fermions also contrasts sharply with known results in one dimension, where a similar delocalized phase has been shown to be robust against the inclusion of weak interaction effects.

arXiv:cond-mat/0510830Physical Review BApr 7, 200630 citations

{\mathit{k}}_{\mathit{F}}

, in addition to the Kohn anomaly we find other nonanalytic behavior. In the appendies we present a numerical calculation of the spectral function for a Fermi liquid with Landau parameter

{\mathit{f}}_{0}

\ensuremath{\ne}0. We also show how Kohn's theorem is satisfied within the bosonization framework.

BD\mathrm{I}

[M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as a low-energy description of a time-reversal invariant tight-binding model of spinless fermions on a honeycomb lattice, subject to random hopping, and possessing particle-hole symmetry. It is known that, in the absence of interactions, this disordered system is special in that it does not localize in 2D, but possesses extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states. In the context of the hopping model, the short-range interactions that we consider are particle-hole symmetric density-density interactions. Using a perturbative one-loop renormalization group analysis, we show that the same mechanism responsible for the divergence of the density of states in the noninteracting system leads to an instability, in which the interactions are driven strongly relevant by the disorder. This result should be contrasted with the limit of clean Dirac fermions in 2D, which is stable against the inclusion of weak short-ranged interactions. Our work suggests a mechanism wherein a clean system, initially insensitive to interaction effects, can be made unstable to interactions upon the inclusion of weak static disorder. We dub this mechanism a ``disorder-driven Mott transition.'' Our result for 2D fermions also contrasts sharply with known results in one dimension, where a similar delocalized phase has been shown to be robust against the inclusion of weak interaction effects.