Calculation of Penetration Depth and $T_c$ in $\kappa $-$($ET$)_2$Cu(NCS)$_2$ under Pressure

TL;DR

This paper models the pressure dependence of the penetration depth and critical temperature in $$-based organic superconductors using an effective dimer Hubbard model, revealing mechanisms behind experimental observations.

Contribution

It provides a theoretical calculation of $T_c$ and $$ under pressure, explaining experimental behaviors with a focus on bandwidth, Fermi surface changes, and vertex corrections.

Findings

$$ behaves differently under low and high pressure.

$T_c$ increases with c-axis pressure up to 1kbar, then decreases.

The behavior is explained by competing effects of Fermi surface proximity and electron correlation suppression.

Abstract

The pressure dependence of the inverse square of the magnetic penetration depth $\lambda ^{- 2}$ in $\kappa$-$($ET$)_2$Cu(NCS)$_2$ was measured by Larkin, et al According to the paper, $\lambda ^{- 2}$ behaves differently under low pressure and under high pressure. Under low pressure, the development of $\lambda ^{- 2}$ just below $T=T_c$ is rapid compared to the case under high pressure. Moreover, $T_c$ in $\kappa$-$($ET$)_2$Cu(NCS)$_2$ increases under c-axis pressure up to 1kbar and decreases under higher pressure, while $T_c$ decreases monotonically under the hydrostatic pressure, or under the uniaxial pressure parallel to other axes. In order to explain these behaviors, we calculate $T_c$ and $\lambda ^{- 2}$ for $\kappa$-$($ET$)_2$Cu(NCS)$_2$ under pressure. In the calculation we mainly use an effective dimer Hubbard model. In conclusion, the behavior of $\lambda ^{- 2}$ results from three effects: the variation of the bandwidth of quasiparticles, the change of the Fermi surfaces, and the effect of vertex correction. This is a different mechanism from that of $\lambda ^{- 2}$ in cuprates which we observe when the doping varies. Moreover, we explain the increase in $T_c$ under the c-axis pressure up to 1kbar and the decrease in $T_c$ over 1kbar from our calculation. With the increase in the c-axis pressure, two competitive effects with respect to $T_c$ appear. One is the approach of the Fermi surface to the antiferromagnetic Brillouin zone boundary, and the other is the suppression of the electron correlation. Under the low c-axis pressure, $T_c$ increases since the former effect is dominant. On the other hand, $T_c$ decreases since the latter effect is dominant under the high c-axis pressure.