Resistor model for the electrical transport in quasi-one-dimensional organic (TMTSF)${}_2$PF${}_6$ superconductors under pressure

We investigate the metallic transport in the organic superconductor (TMTSF)${}_2$PF${}_6$ under pressure within the framework of the spin density wave theory in the proximity of a Peierls quantum critical point (QCP). We use a simple transport model of hot and cold regions around the Fermi surface, driven by the proximity to the QCP in order to provide a template to fit the experimental results. Successful agreement with the data comforts the interpretation of extended criticality around the antiferromagnetic QCP in the normal phase of quasi-one-dimensional organic superconductors.

Figure 1

(a) Brillouin zone with the Fermi surface and the nesting vector $\mathbf{Q}$ connecting two inflection points ${\mathbf{P}}_1$ and ${\mathbf{P}}_3$. Inset shows unit vectors ${\mathbf{e}}_{\parallel }$ and ${\mathbf{e}}_{\perp }$ parallel and perpendicular to the Fermi velocity at ${\mathbf{P}}_3$ that define the coordinates $\mathbf{k}=(k_{\parallel },k_{\perp })$. (b) Polarization bubble for the paramagnon mode. (c) Fermion self-energy. The wavy line represents the effective paramagnon from Eq. (5).

Figure 2

Pressure dependence of the model parameters obtained from the fit: $10B$ (diamonds, in $\mu \Omega \mathrm{cm}/{\mathrm{K}}^2$), $C$ (squares, in $\mu \Omega \mathrm{cm}/{\mathrm{K}}^2$), and $v_h$ (circles) compared to the temperature of the superconducting transition $T_c$ (triangles, in $\mathrm{K}$) from Ref. 4. Inset shows “equivalent circuit” for the dichotomic conductivity model [Eq. (9)].

Figure 3

Pressure-temperature phase diagram of (TMTSF)${}_2$PF${}_6$ displaying the crossover temperatures $T_S$ and $T_0$ from this analysis as well as the long-range-order phases. The lines are guides to the eye. The transition temperatures towards SDW (triangles) and SC (circles) are those from Ref. 4.