Current-current Fermi-liquid corrections to the superconducting fluctuations on conductivity and diamagnetism

We analyze the behavior of the superconducting-fluctuations contribution to diamagnetism and conductivity in a model system having current-current interactions. We show that in proximity to a Mott-insulating phase, one recovers an overall suppression of the fluctuating contribution to the conductivity with respect to diamagnetism, in close analogy with recent experiments on the underdoped phase of cuprate superconductors.

Figure 1

Fermionic bubbles: (a) is the $\Pi \left(q\right)$ bubble associated with the ${\Delta }^2$ term, while (b) is the fermionic bubble relative both to $\mathbf{A}{\Delta }^2$ and ${\phi }^s{\Delta }^2$ terms. The solid lines are the Green's functions $\mathcal{G}$ containing the full quasiparticle dispersion $\xi$. The dashed lines are the pairing field $\Delta$. The wavy line represents either the electromagnetic potential $\mathbf{A}$ or the current field ${\mathit{\phi }}^s$, both associated with the quasiparticle current $\mathbf{J}\propto \partial {\xi }^0$.

Figure 2

AL contribution of the SCF to the current-current correlation function. The dashed lines represent the SCF propagator, while the red dots reduce to the constant $c$ in the ordinary case, Eq. (27), and to the momentum and frequency-dependent vertex $c\left(q\right)$ in the presence of current-current interactions, see Eq. (32).