1109.2307 (Qijin Chen)
Qijin Chen
BCS--Bose-Einstein condensation (BEC) crossover is effected by increasing
pairing strength between fermions from weak to strong in the particle-particle
channel. Here we study the effect of the particle-hole channel on the zero $T$
gap $\Delta(0)$, superfluid transition temperature $T_{\text{c}}$ and the
pseudogap at $T_{\text{c}}$, as well as the mean-field ratio
$2\Delta(0)/T_{\text{c}}^{\text{MF}}$, from BCS through BEC regimes, in the
framework of a pairing fluctuation theory which includes self-consistently the
contributions of finite-momentum pairs. These pairs necessarily lead to a
pseudogap in single particle excitation spectrum above and below
$T_{\text{c}}$. We sum over the infinite particle-hole ladder diagrams so that
the particle-particle and particle-hole $T$-matrices are entangled with each
other. We find that the particle-hole susceptibility has a complex dynamical
structure, with strong momentum and frequency dependencies, and is sensitive to
temperature, gap size and interaction strength. We conclude that neglecting the
self-energy feedback causes a serious over-estimate of the particle-hole
susceptibility. In the BCS limit, the particle-hole channel effect may be
approximated by the same reduction in the overall pairing strength so that the
ratio $2\Delta(0)/T_{\text{c}}$ is unaffected, in agreement with Gor'kov
\textit{et al.} to the leading order. However, the effect becomes more complex
and pronounced in the crossover regime, where the particle-hole susceptibility
is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the
BEC regime, the particle-hole channel contributions drop to zero. We propose
that precision measurements of the magnetic field for Feshbach resonance at low
temperatures as a function of density can be used to quantify the particle-hole
susceptibility and test different theories.
View original:
http://arxiv.org/abs/1109.2307
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