Electronic nematic susceptibility of iron-based superconductors

We review our recent experimental results on the electronic nematic phase in electron- and hole-doped BaFe$_2$As$_2$ and FeSe. The nematic susceptibility is extracted from shear-modulus data (obtained using a three-point-bending method in a capacitance dilatometer) using Landau theory and is compared to the nematic susceptibility obtained from elastoresistivity and Raman data. FeSe is particularly interesting in this context, because of a large nematic, i.e., a structurally distorted but paramagnetic, region in its phase diagram. Scaling of the nematic susceptibility with the spin lattice relaxation rate from NMR, as predicted by the spin-nematic theory, is found in both electron- and hole-doped BaFe$_2$As$_2$, but not in FeSe. The intricate relationship of the nematic susceptibility to spin and orbital degrees of freedom is discussed.Comment: Invited review article for a special issue on Fe-based superconductors in Comptes Rendus Physiqu

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, $T_\mathrm{c}$, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.Comment: Topical Review submitted to Journal of Physics: Condensed Matte

Competing Phases in Iron-Based Superconductors Studied by High-Resolution Thermal-Expansion and Shear-Modulus Measurements

Die thermodynamischen Phasen von eisenbasierten Supraleitern, hauptsächlich von K-substituiertem BaFe2As2 und von FeSe, wurden mittels hochaufgelöster Messungen der thermischen Ausdehnung und des elastischen Schermoduls untersucht. Für Letzteres wurde eine neue Messmethode entwickelt. Insbesondere wird der Zusammenhang von Magnetismus und strukturellem Phasenübergang betrachtet

Shape- and orientation-dependence of surface barriers in single crystalline d-wave Bi_2Sr_2CaCu_2O_8+delta

7 pages, submitted to Phys. Rev. BMagneto-optical imaging and Hall-probe array magnetometry are used to measure the field of first flux entry, H_p, into the same Bi_2Sr_2CaCu_2O_8+delta single crystal cut to different crystal thickness-to-width ratios (d/w), and for two angles alpha between the edges and the principal in-plane crystalline (a,b) axes. At all temperatures, the variation with aspect ratio of H_p is qualitatively well described by calculations for the so-called geometric barrier [E.H. Brandt, Phys. Rev. B 60, 11939 (1999)]. However, the magnitude of H_p is strongly enhanced due to the square shape of the crystal. In the intermediate temperature regime (T < ~ 50 K) in which the Bean-Livingston barrier limits vortex entry, there is some evidence for a tiny crystal-orientation dependent enhancement when the sample edges are at an angle of 45° with respect to the crystalline axes, rather than parallel to them

Non-monotonic pressure evolution of the upper critical field in superconducting FeSe

The pressure dependence of the upper critical field, $H_\textrm{c2,c}$, of single crystalline FeSe was studied using measurements of the inter-plane resistivity, $\rho_{\textrm{c}}$ in magnetic fields parallel to tetragonal $c$-axis. $H_\textrm{c2,c}(T)$ curves obtained under hydrostatic pressures up to $1.56$ GPa, the range over which the superconducting transition temperature, $T_\textrm{c}$, of FeSe exhibits a non-monotonic dependence with local maximum at $p_1\approx$ 0.8 GPa and local minimum at $p_2\approx$ 1.2 GPa. The slope of the upper critical field at $T_\textrm{c}$, $\left(\textrm{d}H_\text{c2,c}/\textrm{d}T\right)_{T_\textrm{c}}$, also exhibits a non-monotonic pressure dependence with distinct changes at $p_1$ and $p_2$. For $p<p_1$ the slope can be described within multi-band orbital model. For both $p_1p_2$ the slope is in good quantitative agreement with a single band, orbital Helfand-Werthamer theory with Fermi velocities determined from Shubnikov-de Haas measurements. This finding indicates that Fermi surface changes are responsible for the local minimum of $T_\textrm{c}(p)$ at $p_2\approx$ 1.2 GPa.Comment: 5 pages, 4 figure

Dome of magnetic order inside the nematic phase of sulfur-substituted FeSe under pressure

The pressure dependence of the structural, magnetic and superconducting transitions and of the superconducting upper critical field were studied in sulfur-substituted Fe(Se$_{1-x}$S$_{x}$). Resistance measurements were performed on single crystals with three substitution levels ($x$=0.043, 0.096, 0.12) under hydrostatic pressures up to 1.8 GPa and in magnetic fields up to 9 T, and compared to data on pure FeSe. Our results illustrate the effects of chemical and physical pressure on Fe(Se$_{1-x}$S$_{x}$). On increasing sulfur content, magnetic order in the low-pressure range is strongly suppressed to a small dome-like region in the phase diagrams. However, $T_s$ is much less suppressed by sulfur substitution and $T_c$ of Fe(Se$_{1-x}$S$_{x}$) exhibits similar non-monotonic pressure dependence with a local maximum and a local minimum present in the low pressure range for all $x$. The local maximum in $T_c$ coincides with the emergence of the magnetic order above $T_c$. At this pressure the slope of the upper critical field decreases abruptly. The minimum of $T_c$ correlates with a broad maximum of the upper critical field slope normalized by $T_c$