Josephson vortex dynamics and Fulde-Ferrell-Larkin-Ovchinnikov superconductivity in the layered organic superconductor ${\beta }^{″}\text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{SF}}_5{\mathrm{CH}}_2{\mathrm{CF}}_2{\mathrm{SO}}_3$

Interlayer resistance is reported in a layered organic superconductor ${\beta }^{″}\text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{SF}}_5{\mathrm{CH}}_2{\mathrm{CF}}_2{\mathrm{SO}}_3$ with $T_{\mathrm{c}}\approx 5$ K. At 0.7 K in parallel magnetic fields, the interlayer resistance has nonzero values in a wide field region from 2 T to the upper critical field $\left(\sim 13\mathrm{T}\right)$, which can be ascribed to the Josephson vortex (JV) dynamics. Significant hysteresis between 2 T and 8 T and a steplike structure between 4 T and 8 T are found, both of which become less evident with increasing temperature. In the second field-derivative curves, successive small dips are observed between 10 T and 12 T, which are ascribed to the commensurability (CM) effect between the JV lattice and the wavelength ${\lambda }_{\mathrm{FFLO}}$ of the order parameter oscillation in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. The CM effect is observed only in nearly parallel fields, showing that the FFLO phase is stabilized only in a limited field angle region. The temperature-field phase diagram and ${\lambda }_{\mathrm{FFLO}}$ values are obtained.

Figure 1

(a) Schematic picture of the crystal structure of ${\beta }^{″}\text{−}{\mathrm{SF}}_5$ salt with the space group $\mathrm{P}\overline{1}$; $a=0.91536\mathrm{nm},b=1.14395\mathrm{nm},c=1.74905\mathrm{nm},\alpha =94.{316}^{\circ },\beta =91.{129}^{\circ },\gamma =102.{764}^{\circ }$ [1]. This salt is composed of BEDT-TTF layers and ${\mathrm{SF}}_5{\mathrm{CH}}_2{\mathrm{CF}}_2{\mathrm{SO}}_3$ layers. The layer spacing $s$ is indicated. (b) Schematic picture of superconducting order parameter $\mathrm{\Delta }\left(r\right)$ and JVs in the FFLO phase. The center-of-mass momentum of the Cooper pair $\mathbf{q}$ gives the wavelength of the order parameter oscillation ${\lambda }_{\mathrm{FFLO}}$. JVs, which are formed in the insulating layers with a lattice constant $l$, can be driven by a perpendicular current $I$.

Figure 2

(a) Interlayer resistance in perpendicular magnetic fields at 1.5 K. Inset: Fourier transform spectrum of the SdH oscillation, and a schematic of the single crystal and the electric contact configuration. (b) Fermi surface calculated by tight-binding approximation (black dots) [1]. For comparison, the 2D Fermi surface determined from AMRO measurements is shown by a red curve [24].

Figure 3

(a) Magnetic field dependence of interlayer resistance and second derivative curve at 0.7 K. The $H_{\mathrm{c}2}$ value was determined by the TE [31] and RF response [17] measurements. (b) Interlayer resistance at various temperatures and (c) second derivative curves of the resistance for the up and down sweeps. $H_{\mathrm{dip}}$ is not evident above 2.1 K. The characteristic fields $H_1\text{−}{H}_3$, and dip fields $H_{\mathrm{dip}}$ are indicated by arrows.

Figure 4

Magnetic phase diagram for $H\parallel$ SC layers. The characteristic fields, $H_1\text{−}{H}_3$ and $H_{\mathrm{dip}}$ are indicated by color symbols. For comparison, $H_{\mathrm{c}2}$ determined by TE and RF, irreversibility field $\left(H_{\mathrm{irr}}\right)$ by torque, and $H_{\mathrm{FFLO}}$ by RF, MCE, and torque measurements are also indicated by black symbols. The SC phase is divided into four regions: (I) $H<H_1$, (II) $H_1<H<H_2$, (III) $H_2<H<H_3$, and (IV) $H_3<H<H_{\mathrm{c}2}$.

Figure 5

Magnetic field dependence of the interlayer resistance at various field angles (a) at 0.7 K and (b) at 1.5 K. Inset in (b): Semilog plot of interlayer resistance as a function of the field angle $\theta$ at 1.5 K for ${\mu }_{0}H=2$ and 4 T.

Figure 6

Second derivative curves $-d^{2}R/d{H}^2$ at various field angles (a) at 0.7 K and (b) at 1.5 K. The curves are shifted for clarity. As the field is tilted from $\theta =0^{\circ }(H\parallel$ SC layers), the dips arising from the CM effect indicated by blue arrows are suppressed and disappear.

Figure 7

Schematic picture of the JV dynamics. The SC phase could be divided into four regions: (I) the JV lattice is strongly pinned, (II) the JV lattice is collectively driven by the current, (III) the JV layers are decoupled and the JV lattice in each layer is driven independently, and (IV) the JV lattice melts.

Figure 8

The estimated wavelength of the FFLO order parameter oscillation, ${\lambda }_{\mathrm{FFLO}}$ at 0.7 K (black circles). The black dashed curve shows a guide to the eye. The calculated JV lattice constant $l$ is shown by red curve. The JV lattice constant $l$ is expected to have discrete values, depending on the boundary condition at the sample edges [33]. For simplicity, the field dependence of $l$ is indicated by a continuous curve. The FFLO phase transition takes place at $\sim 9.5\mathrm{T}\left(H_{\mathrm{FFLO}}\right)$. Above $H_3$, where the JV lattice melts, $l$ is not defined and thus the CM effect is not observed.