Fluctuation-enhanced electron-phonon coupling in FeSe

Abstract

The interactions among lattice, charge, and spin degrees of freedom fundamentally shape material properties. In FeSe, symmetry-breaking perturbations serve as highly sensitive probes of these couplings. Previous work has shown that defects and isoelectronic substitution can substantially alter these interactions, giving rise to additional phonon modes. In this study, uniaxial strain is employed as a tunable symmetry-breaking control parameter to probe the intrinsic lattice response in the absence of disorder. The temperature evolution of phonon excitations was examined with fine temperature resolution in the vicinity of the nemato-structural transition temperature $T_s$, under strain applied along the $\langle 110 \rangle$ and $\langle 100 \rangle$ crystallographic directions. A subtle asymmetry of the $A_{1g}^{ph}$ mode appears in the unstrained crystal within a narrow temperature window around $T_s$, originating from the emergence of an additional mode in the fully symmetric channel. With applied strain, this feature becomes more distinctly resolved. The anomaly is attributed to modifications of the coupling between lattice and electronic degrees of freedom driven by the ordering fluctuations right above the nematic transition. These fluctuations enhance susceptibility for phonon-electron-phonon coupling in the vicinity of the X and R points of the Brillouin zone and promote two-phonon scattering close to the $A_{1g}^{ph}$ mode. The presence of this two-phonon scattering depends on both the strength and the direction of the applied strain, indicating a high sensitivity of FeSe to local symmetry breaking.

Figures (4)

• Figure 1: (a) and (b) Diagram showing the applied strain direction with respect to the 1-Fe unit cell. Fixed and movable sample plate integrated to piezo-electric device are labeled as FP and MP, respectively. (c) Schematic representation of the FeSe 2-Fe Brillouin zone and Fermi surface in tetragonal and (d) nematic phase $\left( \text{Adapted from Ref.~}Rhodes2022FeSe \right)$. (e) Crystal structure of FeSe in the $ab$ plane ($b=a$). The solid line represents the 2-Fe crystallographic unit cell determining the symmetry of the lattice vibrations. The dashed line represents the 1-Fe unit cell with axes $a'$ and $b'$ relevant for electronic and spin excitations. (f) Selection rules for four main linear polarization configurations. The light polarizations $x$ and $y$ are aligned with the crystallographic axes ($a,a$). The Raman-active A1gph and B1gph phonons are projected in parallel $x'x'$ and perpendicular $x'y'$ scattering configurations, respectively. Electronic and spin excitations are preferably described in the 1-Fe cell, where B1g and B2g are swapped with respect to the $xy$ system (symmetries in brackets). These symmetries are used for the application of strain (blue and orange, respectively).
• Figure 2: Top panel: Illustrations at left (right) schematically depict distortion of 1-Fe unit cell and sample orientation under corresponding strain $\varepsilon_{B1g}$$(\varepsilon_{B2g})$, while the middle one represents atomic displacement of (acoustic) vibration at the X-point of the Brillouin zone (2-Fe crystallographic unit cell). Spectra panels: Strain-dependent Raman spectra in $x'x'$ scattering geometry at temperatures indicated, in the spectral range where the A1gph phonon is expected. Note that the $xy$ system of the polarizations is always aligned parallel to $ab$. Arrows in the legend indicate change in temperature and in strain configuration, i.e. $\varepsilon^{\mathrm{high}}_{B1g}$, and $\varepsilon^{\mathrm{low}}_{B1g}$ denote spectra obtained under uniaxial tensile strain applied along $a'$-axis, while $\varepsilon^{\mathrm{high}}_{B2g}$ and $\varepsilon^{\mathrm{low}}_{B2g}$ correspond to spectra obtained under tensile strain along the diagonal of 1-Fe unit cell. $\varepsilon_{\mathrm{zero}}$ labels the spectra recorded in the absence of applied strain. The blue-shaded area marks the symmetry-allowed A1gph mode, and the green-shaded area highlights an additional feature emerging near $T_\mathrm{s}$, labeled A1g'.
• Figure 3: Strain-dependent B1gph Raman spectra at temperatures as indicated. At 269 K strain has only very little effect. Upon approaching the transition at $T_\mathrm{s}$, B1g strain leads to a blue shift (blue) of the phonon, while B2g strain causes a red shift (orange) with respect to the unstrained case (green).
• Figure 4: Temperature dependence of the A1gph and A1g' mode energies (left panel) and Lorentzian linewidths (right panel) for different strain configurations. From top to bottom, panels show the phonon energy and linewidth evolution for (a,f) $\varepsilon_{B1g}^{\mathrm{high}}$, (b,g) $\varepsilon_{B1g}^{\mathrm{low}}$, (c,h) $\varepsilon_{\mathrm{zero}}$, (d,i) $\varepsilon_{B2g}^{\mathrm{low}}$, and (e,j) $\varepsilon_{B2g}^{\mathrm{high}}$. The black (a-e) dashed and (f-i) solid lines represent the temperature dependencies of the phonon energies [according to Eq. (\ref{['eq:energy']})] and linewidths [according to Eq. (\ref{['eq:linewidth']})], respectively.