BCS-like critical fluctuations with limited overlap of Cooper pairs in FeSe

In conventional superconductors, very narrow superconducting-fluctuation regions are observed above $T_c$, because strong overlap of Cooper pairs occurs in a coherence volume $4\pi {\xi }^3/3$ with $\xi$ being the coherence length. In the bulk form of iron-chalcogenide superconductor FeSe, it is argued that the system may be located in the crossover region from Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BEC), where strong superconducting fluctuations are expected. In this respect, we carried out magnetization, specific heat, and Nernst effect measurements on FeSe single crystals in order to investigate the superconducting fluctuation effect near $T_c$. The temperature range of diamagnetization induced by superconducting fluctuations seems very narrow above $T_c$. The temperature-dependent magnetization curves measured at different magnetic fields do not cross at a single point. This is in sharp contrast to the situation in many cuprate superconductors, where such a crossing point has been taken as a clear signature of strong critical fluctuations. The magnetization data can be scaled according to the Ginzburg-Landau fluctuation theory for a quasi-two-dimensional system. However the scaling result cannot be described by the theoretical function of the fluctuation theory due to the limited fluctuation regions. The specific heat jump near $T_c$ is rather sharp without the trace of strong superconducting fluctuations. This is also supported by the Nernst effect measurements which indicate a very narrow region for vortex motion above $T_c$. Associated with a very small value of Ginzburg number and further analyses, we conclude that the superconducting fluctuations are vanishingly weak above $T_c$ in this material. Our results are strongly against the picture of significant phase fluctuations in FeSe single crystals, although the system has a very limited overlap of Cooper pairs in the coherence volume. This dichotomy provides new insights into the superconducting mechanism when the system is with a dilute superfluid density.

Figure 1

(a) Temperature dependence of resistivity at zero magnetic field. The inset shows the temperature dependence of magnetization measured in ZFC and FC modes at 20 Oe. (b) Temperature dependent resistivity measured at magnetic fields of 0, 8, 12, and 16 T. (c) Temperature dependence of excess conductivity at 0 T calculated by the data in (b).

Figure 2

(a) Temperature dependence of mass magnetization measured at different fields. The open and solid symbols are the data measured with ZFC and FC modes, respectively. The black solid lines are the fitting curves by using Curie-Weiss law. (b) The enlarged view of the magnetization data at 7 T and the definitions of characteristic temperatures at characteristic magnetic fields. (c) The ${\mu }_{0}H-T$ vortex phase diagram of FeSe from the magnetization measurements. The solid squares represent the experimental data of ${\mu }_0{H}_{c2}\left(T\right)$. The solid blue line is a linear fit to the upper critical field ${\mu }_0{H}_{c2}\left(T\right)$ near $T_c$.

Figure 3

(a) Temperature dependence of diamagnetic magnetization $M_{\mathrm{dia}}$ at different fields obtained by subtracting the fitted background by Eq. (1) from the experimental data. (b) Scaling curves from (a) by using the Ginzburg-Landau fluctuation theory for a quasi-2D system. The solid line is the expected scaling function of the quasi-2D scaling theory.

Figure 4

(a) Temperature-dependent specific heat measured at 0 T. The red solid line is the normal state fitting curve. The inset shows the enlarged view of the specific heat jump near $T_c$, and $\mathrm{\Delta }C/T_c$ is estimated by entropy conservation near $T_c$. (b) Temperature dependence of superconducting electronic specific heat. The transition temperature $T_c^{SH}$ from specific heat jump estimated by entropy conservation as show in (b) or the inset in (a) is about 8 K. The blue line represents the fitting curve using the BCS formula. The inset shows the angle-dependent gap functions used in the fitting.

Figure 5

(a) Field-dependent Nernst signal $S_{xy}$ at different temperatures above 7 K. (b) Field dependence of Nernst transverse voltage $V_{xy}$ at different temperatures with tiny exchange helium gas to lower down the base temperature of the sample.

Figure 6

Temperature dependence of the Nernst coefficient at different fields. The filled symbols represent the data obtained by the field-dependent Nernst signal. The open triangles are Nernst coefficients measured at 4 T and different temperatures. Nernst voltage values measured with some exchange helium gas are shown as open circles with the arbitrary unit, i.e., the $V_{xy}$ values are multiplied by a necessary factor to make the data have a smooth connection to the Nernst signal $S_{xy}$ measured at the same field and temperature. The inset shows the enlarged view of the Nernst coefficient at low temperatures and 8 T.