High-quality FeSe Single Crystal Research Articles

Recent progress on the high-pressure studies of FeSe single crystal

Among the iron-based superconductors, the structurally simplest FeSe and FeSe-derived materials have attracted enormous research interest recently due to its unusual electronic properties and the great tunability of the superconducting transition temperature <italic>T</italic>_c. For the bulk FeSe single crystal, it shows a relatively low <italic>T</italic>_c<x content-type=symbol>»</x>8 K within the unusual nonmagnetic nematic phase below <italic>T</italic>_s<x content-type=symbol>»</x>90 K. It has been reported that the application of high pressure can induce a long-range antiferromagnetic order below <italic>T</italic>_m<x content-type=symbol>»</x>20 K at <italic>P</italic><x content-type=symbol>»</x>1 GPa, and then achieve a high <italic>T</italic>_c<x content-type=symbol>»</x>37 K at <italic>P</italic><x content-type=symbol>»</x>8 GPa. It remains unclear how the high-<italic>T</italic>_c superconductivity is achieved in FeSe under pressure. In this regard, a detailed temperature-pressure phase diagram mapping out the exact relationship between the high-<italic>T</italic>_c superconductivity and the normal-state nematic order and the pressure-induced antiferromagnetic order is indispensable for achieving a better understanding. By taking advantage of the cubic anvil cell apparatus that can maintain an excellent hydrostatic pressure condition up to 15 GPa, we recently undertook a comprehensive high-pressure magnetotransport study on high-quality FeSe single crystals and obtained important results. In this article, we give a brief review on the recent progresses about the high-pressure studies of FeSe. By tracking the characteristic resistivity anomalies at the nematic order, the pressure-induced antiferromagnetic order, and the superconducting transition, we constructed for FeSe a comprehensive temperature-pressure phase diagram, which depicts explicitly the detailed evolution of these competing electronic orders. We observed a dome-shaped antiferromagnetic phase boundary <italic>T</italic>_m(<italic>P</italic>), and revealed the competitive relationship between these electronic orders. The superconducting <italic>T</italic>_c experiences two successive step increases at the critical pressures when the nematic order and the antiferromagnetic order are respectively suppressed, and finally the highest <italic>T</italic>_c^max=38.5 K is realized near <italic>P</italic>_c≈6 GPa when the antiferromagnetic order just collapses. We further measured the Hall effect of FeSe to extract the electronic structure information under high pressure. Our Hall data show that the Fermi surface of FeSe in the normal state undergoes a reconstruction at <italic>P</italic><x content-type=symbol>»</x>2 GPa, when the nematic order is suppressed and the antiferromagnetic order just emerges. The dominant charge carriers for the transport properties in the normal state change from the electron to the hole type. In addition, in the high-<italic>T</italic>_c phase near the optimal<italic> </italic><italic>T</italic>_c^max at <italic>P</italic>_c<x content-type=symbol>»</x>6 GPa, the Hall coefficient experiences a dramatic enhancement and the magnetoresistance exhibits anomalous scaling behaviors, signaling the presence of strongly enhanced inter-band spin fluctuations. These results suggest that the critical antiferromagnetic fluctuations play an important role for achieving the high-<italic>T</italic>_c superconductivity in FeSe. Aided by the first-principles calculations, we further confirmed that both electron-like and hole-like Fermi surfaces are present in FeSe under high pressures, in favor of the Fermi surface nesting scenario as in the FeAs-based high-<italic>T</italic>_c<italic> </italic>superconductors. These above results on FeSe suggest great similarities with other FeAs-based superconductors, and thus constitute an important step toward a unified understanding of iron-based superconductivity.

Two-gap features revealed by specific heat measurements in FeSe

The symmetry of superconducting gap is a key to understand the mechanism of superconductivity. FeSe, which has the simplest structure among iron-based superconductors, is most suitable for the understanding of the superconducting mechanism. Specific heat measurements have been performed on a high-quality FeSe single crystal with Tc ∼ 8.8 K and ΔC/γnTc = 1.62. A sharp jump of specific heat at Tc and the second drop around 1.2 K are observed, suggesting the presence of two superconducting gaps in FeSe. Furthermore, the electronic specific heat under zero field can be well fitted by the two-gap model. Besides, the kink structure observed in the magnetic-field dependence of the electronic specific heat coefficient γ(H) at low temperatures also support the two-gap nature of FeSe.

Structural-transition-induced quasi-two-dimensional Fermi surface in FeSe

We report detailed study of angular-dependent magnetoresistance (AMR) with tilting angel $\theta$ from $c$-axis ranging from 0$^\circ$ to 360$^\circ$ on a high-quality FeSe single crystal. A pronounced AMR with twofold symmetry is observed, which is caused by the quasi two-dimensional (2D) Fermi surface. The pronounced AMR is observed only in the orthorhombic phase, indicating that the quasi-2D Fermi surface is induced by the structural transition. Details about the influence of the multiband effect to the AMR are also discussed. Besides, the angular response of a possible Dirac-cone-like band structure is investigated by analyzing the detailed magnetoresistance at different $\theta$. The obtained characteristic field ($B^*$) can be also roughly scaled in the 2D approximation, which indicates that the Dirac-cone-like state is also 2D in nature.

Band structure reconstruction across nematic order in high quality FeSe single crystal as revealed by optical spectroscopy study

We perform an in-plane optical spectroscopy measurement on high quality FeSe single crystals grown by a vapor transport technique. Below the structural transition at Ts ∽90K, the reflectivity spectrum clearly shows a gradual suppression around 400cm−1 and the conductivity spectrum shows a peak at higher frequency. The energy scale of this gap-like feature is comparable to the width of the band splitting observed by ARPES. The low-frequency conductivity consists of two Drude components and the overall plasma frequency is smaller than that of the FeAs based compounds, suggesting a lower carrier density or stronger correlation effect. The plasma frequency becomes even smaller below Ts which agrees with the very small Fermi energy estimated by other experiments. Similar to iron pnictides, a clear temperature-induced spectral weight transfer is observed for FeSe, being indicative of strong correlation effect.

Critical current density, vortex dynamics, and phase diagram of single-crystal FeSe

We present a comprehensive study of the vortex pinning and dynamics in a high-quality FeSe single crystal, which is free from doping introduced inhomogeneities and charged quasi-particle-scattering because of its innate superconductivity. Critical current density, $J_c$, is found to be almost isotropic, and reaches a value $\sim$ 3 $\times$ 10$^4$ A/cm$^2$ at 2 K (self-field) for both $H$ $\|$ $c$ and $ab$. The normalized magnetic relaxation rate $S$ (= $\mid$dln$M$/dln$t$$\mid$) shows a temperature insensitive plateau behavior in the intermediate temperature range with a relatively high creep rate ($S$ $\sim$ 0.02 under zero field), which is interpreted in the framework of the collective creep theory. A crossover from the elastic to plastic creep is observed, while the fish-tail effect is absent for both $H$ $\|$ $c$ and $ab$. Based on this observation, the origin of the fish-tail effect is also discussed. Combining the results of $J_c$ and $S$, vortex motion in FeSe single crystal is found to be dominated by sparse strong point-like pinning from nm-sized defects or imperfections. The weak collective pinning is also observed and proved in the form of large bundles. Besides, the vortex phase diagram of FeSe is also constructed and discussed.

Study of high-quality superconducting FeSe single crystals: crossover in electronic transport from a metallic to an activated regime above 350 K

We report the growth of high quality FeSe single crystals using chemical vapor transport based on an AlCl3/KCl eutectic and their physical properties were fully characterized by magnetic, transport and specific heat measurements. Their critical superconducting temperature at Tc ∼ 8.7 K (width < 0.7 K) and structural tetragonal–orthorhombic transition at Ts ∼ 85–90 K confirm the values already reported in the literature for similar crystals. In addition, the non-variation of Ts under high magnetic field (up to 14 T) determined by magnetic and specific heat measurements indicates that spin fluctuations are not directly involved in the structural transition. Finally, high temperature electrical resistivity measurements up to 600 K evidence a maximum around 350 K. The origin of this crossover from metallic behavior at low temperature to a semiconducting-like regime at high temperature is discussed and could be associated with a change of carrier density above 350 K. On the other hand, the tentative growth of Te-substituted Fe(Se1−xTex) crystals using the same growth method resulted in crystals with x(Te) < 1% and a slightly lower Tc compared to pure FeSe ones, which may be related to transition metal–chalcogen non-stoichiometry. Finally, Cr doping at the Fe site was also attempted. In contrast to previous reports in the literature, our results suggest that Cr does not substitute for Fe in the FeSe crystal but agglomerates in Cr-rich (Cr,Fe)Se2 inclusions, and Tc of these (Fe1−xCrx)Se crystals is not increased, but slightly decreased in comparison to stoichiometric FeSe crystals.

Temperature dependence of lower critical fieldHc1(T)shows nodeless superconductivity in FeSe

We investigate the temperature dependence of the lower critical field ${H}_{c1}(T)$ of a high-quality FeSe single crystal under static magnetic fields $H$ parallel to the $c$ axis. The temperature dependence of the first vortex penetration field has been experimentally obtained by two independent methods and the corresponding ${H}_{c1}(T)$ was deduced by taking into account demagnetization factors. A pronounced change in the ${H}_{c1}$(T) curvature is observed, which is attributed to anisotopic s-wave or multiband superconductivity. The London penetration depth ${\ensuremath{\lambda}}_{ab}(T)$ calculated from the lower critical field does not follow an exponential behavior at low temperatures, as it would be expected for a fully gapped clean $s$-wave superconductor. Using either a two-band model with $s$-wave-like gaps of magnitudes ${\ensuremath{\Delta}}_{1}=0.41\ifmmode\pm\else\textpm\fi{}0.1$ meV and ${\ensuremath{\Delta}}_{2}=3.33\ifmmode\pm\else\textpm\fi{}0.25$ meV or a single anisotropic $s$-wave order parameter, the temperature dependence of the lower critical field ${H}_{c1}(T)$ can be well described. These observations clearly show that the superconducting energy gap in FeSe is nodeless.

Piezomagnetism of FeSe single crystals

The acoustic-electric transformation in high-quality FeSe single crystals is studied. In zero magnetic field we observe an abnormally strong electromagnetic radiation induced by a transverse elastic wave. Usually a radiation of such intensity and polarization is observed only in metals subjected to a high magnetic field (the radiation is caused by the Hall current). We argue that in FeSe in zero magnetic field it is caused by the piezomagnetic effect which is most probably of dynamical origin. We find that the piezomagnetism survives under the transition from the normal to superconducting state. In the superconducting state the electromagnetic signal decreases with decreasing temperature that is connected with the change in the London penetration depth.