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22 August 2019
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Potential-energy (BCS) to kinetic-energy (BEC)-driven pairing in the attractive Hubbard model
B. Kyung ; A. Georges ; A. -M. S. Tremblay ;
Rating Members: 3.91/5 (1 reader)
Date 26 Aug 2005
Subject Strongly Correlated Electrons; Superconductivity | cond-mat.str-el cond-mat.supr-con
AbstractThe BCS-BEC crossover within the two-dimensional attractive Hubbard model is studied by using the Cellular Dynamical Mean-Field Theory both in the normal and superconducting ground states. Short-range spatial correlations incorporated in this theory remove the normal-state quasiparticle peak and the first-order transition found in the Dynamical Mean-Field Theory, rendering the normal state crossover smooth. For $U$ smaller than the bandwidth, pairing is driven by the potential energy, while in the opposite case it is driven by the kinetic energy, resembling a recent optical conductivity experiment in cuprates. Phase coherence leads to the appearance of a collective Bogoliubov mode in the density-density correlation function and to the sharpening of the spectral function.
Source arXiv, cond-mat/0508645
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1 message found in this forum:
Subject: A recent progress in the understanding of the BCS-BEC crossover
Author: Riesling
Date: 05 April 2006 at 19:44 GMT.
Message: The authors report on the application of the cellular DMFT (DMFT) method to the attractive Hubbard model (AHM) to gain new insights into the smooth crossover between BCS superconductivity and Bose-Einstein condensation (BEC). CDMFT is an improvement of DMFT that should suppress the effect of infinite dimensions on which DMFT is based.

There has been recently an application of DMFT to the BCS-BEC crossover problem which yielded some surprizes (Capone, Keller). The most interesting point (see below why) is a possible first-order phase transition at T=0 in the normal (metastable) state between a Fermi liquid (weak coupling, UUc). This transition is expected to also affect the finite temperature properties of the model, especially above Tc. Now if we recall that the AHM is one of the simplest model that is able to describe the problematic pseudogap phase of the high Tc superconductore above Tc, then we easily realize that a better understanding of the normal phase of the AHM may also be relevant in this context.

The main result of the paper is that the first-order phase transition obtained with DMFT does not survive in finite dimensions (here D=2). It is replaced by a smooth transition showing however all the expected spectral properties: a pseudogap for small U and a large gap for large Us. I regret that the authors do not discuss more deeply the origins of these properties. Indeed, their study essentially reveals the how the stong coupling gap (~ U for large U) becomes a pseudogap in the weak coupling and eventually vanishes in the limit U->0, yielding the metal phase. It is however well-known that, at least in D=2, an additional effect affects the spectral properties: the enhanced superconducting fluctuations. The interplay between these two factors contributes to the difficulties in understanding the high-Tc. Adding the effect of fluctuations to CDMFT may certainly open new perspectives.

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