Dynamic nonlinear σ‐model of electron localization

Horbach, M. L.; Schön, Gerd

doi:10.1002/andp.19935050106

Cited by 33 publications

(44 citation statements)

References 24 publications

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“…Collecting the terms in the action bilinear in φ → and → K and making use of the relation (4.19) we get an effective action for the electromagnetic field propagation in the disordered metal [22]: 26) where V has the meaning of a dynamically screened Coulomb interaction in the RPA approximation, 27) where P 0 (q, ω) is the bare density-density correlator. The matrix V (q, ω) has the structure of a bosonic propagator in the Keldysh space [22]:…”

Section: Electromagnetic Field Fluctuationsmentioning

confidence: 99%

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Keldysh action for disordered superconductors

2000

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Keldysh representation of the functional integral for the interacting electron system with disorder is used to derive microscopically an effective action for dirty superconductors. In the most general case this action is a functional of the 8×8 matrix Q(t, t ′ ) which depends on two time variables, and on the fluctuating order parameter field and electric potential. We show that this approach reproduces, without the use of the replica trick, the well-known result for the Coulomb-induced renormalization of the electron-electron coupling constant in the Cooper channel. Turning to the new results, we calculate the effects of the Coulomb interaction upon: i) the subgap Andreev conductance between superconductor and 2D dirty normal metal, and ii) the Josephson proximity coupling between superconductive islands via such a metal. These quantities are shown to be strongly suppressed by the Coulomb interaction at sufficiently low temperatures due to both zero-bias anomaly in the density of states and disorder-enhanced repulsion in the Cooper channel.

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Section: Electromagnetic Field Fluctuationsmentioning

confidence: 99%

“…A similar approach was also recently developed in [23], where Finkelstein's renormalization group equations for dirty metals were rederived for the case of short-range electron-electron interaction. For the earlier approaches to develop functional integral methods in the Keldysh representation see [24][25][26][27].…”

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confidence: 99%

Keldysh action for disordered superconductors

2000

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“…8 and later used in Ref. 9 for derivation of a σ-model for non-interacting systems. More recently, σ-models based on the Keldysh formalism and the fermionic representation of Ref.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetry for disordered systems with interaction

Schwiete¹,

Efetov²

2005

Phys. Rev. B

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Considering disordered electron systems we suggest a scheme that allows us to include an electronelectron interaction into a supermatrix σ-model. The method is based on replacing the initial model of interacting electrons by a fully supersymmetric model. Although this replacement is not exact, it is a good approximation for a weak short range interaction and arbitrary disorder. The replacement makes the averaging over disorder and further manipulations straightforward and we come to a supermatrix σ-model containing an interaction term. The structure of the model is rather similar to the replica one, although the interaction term has a different form. We study the model making perturbation theory and renormalization group calculations. We check the renormalizability of the model in the first loop approximation and in the first order in the interaction. In this limit we reproduce the renormalization group equations known from earlier works. We hope that the new supermatrix σ-model may become a new tool for nonperturbative calculations for disordered systems with interaction.

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“…We use the Schwinger-Keldysh method 37 to normalize this path integral to unity in order to perform the disorder average; in this method, we exploit the fact that the normalization factor 1/Z T can be written simply as an anti-timeordered (T -ordered) path integral ZT for the same theory. This construction works regardless of whether the model includes interparticle interactions or not.…”

Section: B Adding Interactionsmentioning

confidence: 99%

“…(8), and in the paragraph following that equation. We use the Schwinger-Keldysh method 37 to perform the ensemble average over realizations of the disorder. We then employ a one-loop renormalization group treatment to investigate the stability of the disordered, critically delocalized phase to interaction effects.…”

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confidence: 99%

Interaction effects on two-dimensional fermions with random hopping

Foster

Ludwig

2006

Phys. Rev. B

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We study the effects of generic short-ranged interactions on a system of 2D Dirac fermions subject to a special kind of static disorder, often referred to as "chiral." The non-interacting system is a member of the disorder class BDI [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 non-interacting 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 novel 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 1D, where a similar delocalized phase has been shown to be robust against the inclusion of weak interaction effects.

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Dynamic nonlinear σ‐model of electron localization

Cited by 33 publications

References 24 publications

Keldysh action for disordered superconductors

Keldysh action for disordered superconductors

Supersymmetry for disordered systems with interaction

Interaction effects on two-dimensional fermions with random hopping

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