Ingredients for the electronic nematic phase in FeSe revealed by its anisotropic optical response

Nematicity is a hallmark in iron-based superconductors and was originally invoked in order to account for the anisotropy in the dc transport properties of the 122-materials Ba(Fe1-xCox)2As2 below the structural tetragonal-to-orthorhombic phase transition. Scenarios for the origin of the anisotropic physical properties, arising from nematicity, primarily range between visions based on the imbalance of the Fermi surface parameters (like effective mass and carrier concentration, incorporated in the plasma frequency) or of the charge carrier scattering rate. The optical response is a suitable tool in this respect, since it gives access to both quantities. Here, we provide data of a thorough optical investigation of FeSe, consisting in the measurement of the optical reflectivity over a broad spectral range and as a function of temperature (T) for samples experiencing a tunable degree of detwinning. We extract the optical conductivity from the far-infrared up to the ultraviolet, thus expanding our initial study mainly limited to the anisotropic electronic excitations. The low energy scales addressed here allow determining the Drude parameters of the transport properties.

Enlarged view: Fig. 2.22
Fig. 2.22: Experimental setup as well as T and p dependence of the optical anisotropy: The upper-left panel schematically shows a sample inside the mechanical device and emphasizes the orientation of its a- and b-axis with respect to the direction of the applied stress p. Polarized light parallel to the orthorhombic (elongated) a- and (short) b-axis (in our experimental set-up Pol 90 and Pol 0, respectively) illuminates the sample. (a) Representative data of the optical reflectivity (R(ω)) of FeSe at 10 K for p = 1.2 bar (i.e., at saturation) after a ZPC experiment; it emphasizes the previously discussed optical anisotropy at mid-infrared frequencies. The inset shows Ra(ω) and Rb(ω) from the far-infrared up to the ultraviolet range with a logarithmic frequency scale. (b) Real part σ1(ω) of the optical conductivity and its blow up pertinent to the far-infrared range (inset) at 10 K forp = 1.2 bar. (c)-(e) T dependence of the dichroism defined as Δσ1(ω) = σ1(ω) - σ1(ω) at 0, 1.2 and released 0 bar after the p-loop experiment. The thick horizontal dashed line marks Ts. The thin vertical dotted lines in panels (a) and (d) mark the frequencies 1000 and 3000 cm-1. (f)-(i) Δσ1(ω) at selected T below and above Ts within each p-loop experiment. The thin horizontal dashed line marks p = 1.2 bar (i.e., at saturation). A first-neighbor interpolation procedure is used in order to generate the color maps. Released p is denoted by '(r)'.

Representative R(ω) data of FeSe in the far- (FIR) and mid-infrared (MIR) spectral range (i.e., for ω < 7000 cm-1) are shown in the main panel of Fig. 2.22(a) at 10 K and with a pressure applied by the spring bellows of pbellows = 1.2 bar, which correspond to the situation for a fully detwinned specimen. The anisotropy of R(ω) between the two polarization directions is clearly visible in the raw data and occurs at FIR-MIR frequencies, within an energy interval of about 0.5 eV, which is fairly consistent with the extent from the Fermi level of the correlated (squeezed) 3d iron bands. The optical anisotropy of R(ω) at FIR-MIR frequencies is also reflected in the excitation spectrum, represented by σ1(ω), as shown at saturation in Fig. 2.22(b). Here, we highlight the T evolution of the so-called dichroism Δσ1(ω) = σ1a(ω) – σ1b(ω) at three selected p of 0, 1.2 and released 0 bar after the p-loop experiment within the ZPC protocol (Fig. 2.22(c)-(e)). The optical anisotropy sets in at Ts and is particularly well identified by the change of sign of Δσ1(ω) around 1000, 3000 and 5000 cm-1 at saturation. Figures 2.22(f)-(i) show Δσ1(ω) at selected T within each p-loop experiments, which emphasise the evolution of the optical anisotropy at T < Ts upon sweeping p. We can recognise the hysteretic behavior of the optical anisotropy, since its saturation value tends to persist at low temperatures, while it vanishes for TTs, upon releasing p (see also Fig. 2.22(d)-(e)).

Enlarged view: Fig. 2.23
Fig. 2.23: T dependence of the Drude parameters and dc transport properties for fully detwinned samples and of the nematic order parameter as evinced from optics: (a)-(c) T dependence of the anisotropic scattering rates (ΓN,Ba,b) for the narrow (N) and broad (B) Drude term as well as of the total Drude spectral weight SWDa,b (see text), at p = 1.2 bar along both orthorhombic a- and b-axis. The measured, average dc resistivity between the two axes is shown as comparison. Panel (c) also reproduces the average dc resistivity (ρavDrude), calculated within the Drude model from the fit parameters, as alternative reliability check of our analysis. All quantities are normalized by their respective values at 100 K. (d) T dependence of ΔRratiosat(ω) = (Ra(ω)/Rb(ω)) - 1 at 1000 and 3000 cm-1 (thin vertical dotted lines in Fig. 2.22(a) and (d)) in FeSe at 1.2 bar (i.e., at saturation (sat)). ΔRratiosat is normalized by its value at To = 5 K. ΔRratiosat is compared to the T dependence of the mean-field (MF) order parameter. The thick vertical dashed line in all panels marks Ts.

In order to elaborate on possible ingredients for nematicity in FeSe, we first present the results of our analysis from a different perspective in Fig. 2.23, where the T dependence of the anisotropic Drude parameters at saturation is compared to the average dc resistivity. We emphasise again the anisotropy in all Drude quantities, which is mostly evident around 60-70 K, consistent with the anisotropy of the transport dc properties for the strained sample. The comparison reveals that, at variance with early conclusions drawn from our optical results in 122 materials, the Drude weight has a less strong impact on the T dependence of the dc resistivity (Fig. 2.23(c)) than the scattering rates for both narrow and broad Drude terms. In particular, the scattering rates closely follow the dc resistivity as a function of T (Fig. 2.23(a) and (b)). Such a dominant role of our phenomenological Drude scattering rates convincingly supports previous conjectures that inelastic scattering of electrons (e.g., off magnetic fluctuations) would mainly affect the dc transport properties.

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