Suppression of nematicity by tensile strain in multilayer ${\mathrm{FeSe}/\mathrm{SrTiO}}_3$ films

The nematicity in multilayer $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$ films has been previously suggested to be enhanced with decreasing film thickness. Motivated by this, there have been many discussions about the competing relation between nematicity and superconductivity. However, the criterion for determining the nematicity strength in FeSe remains highly debated. The understanding of nematicity as well as its relation to superconductivity in FeSe films is therefore still controversial. Here, we fabricate multilayer $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$ films using molecular beam epitaxy and study the nematic properties by combining angle-resolved photoemission spectroscopy, ${}^{77}\mathrm{Se}$ nuclear magnetic resonance, and scanning tunneling microscopy experiments. We unambiguously demonstrate that, near the interface, the nematic order is suppressed by the ${\mathrm{SrTiO}}_3$-induced tensile strain; in the bulk region further away from the interface, the strength of nematicity recovers to the bulk value. Our results not only solve the recent controversy about the nematicity in multilayer FeSe films, but also offer valuable insights into the relationship between nematicity and superconductivity.

Figure 1

[(a),(b)] RHEED images of ${\mathrm{SrTiO}}_3$ substrate and 15-ML film with incident beam along the [110] directions, respectively. The RHEED intensity curve (red dashed curve) is taken along the red solid line. The single set of diffraction peaks reflect the high quality of FeSe film. (c) STM topographic image of 15-ML film ($30\times 30{\mathrm{nm}}^2, V_s=50$ mV, $I=50$ pA). (d) Atomically resolved STM topography of 15-ML film ($10\times 10{\mathrm{nm}}^2, V_s=50$ mV, $I=100$ pA). Blue dashed lines indicate the orientations of Fe vacancies. Inset: Fourier transform (FT) of the defect-free regions in (d).

Figure 2

(a) ${}^{77}\mathrm{Se}$ NMR spectra of 210-ML film and Se-etched ${\mathrm{SrTiO}}_3$ substrate. (b) Multipeak fitting of the green curve in (a) by three Lorentzian peaks (dashed curves) with a linear background (dashed line). Inset: Frequency splitting between $f_1$ and $f_2$ at 40 K as a function of field. Blue triangles represent the values of undoped FeSe crystals, adopted from Refs. [24, 57, 63]. Black triangle indicates the splitting between $f_2$ and $f_3$ of FeSe film at 40 K. The thick line is a guide to the eye. (c) Temperature dependent ${}^{77}\mathrm{Se}$ NMR Knight shift of 210-ML film and ${\mathrm{FeSe}}_{0.95}{\mathrm{S}}_{0.05}$ crystal ($H\parallel$ [100]). Inset: Temperature dependence of Knight shift splittings between $f_1$ and $f_2$ lines in the film and crystal. The translucent blue curve is a guide to the eye.

Figure 3

(a) Intensity plot at $E_F$ [$h\nu =60\mathrm{eV}$, linear horizontal (LH) polarization] of 15-ML film. (b) Intensity plot measured along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction. The intensity is the sum of data acquired with linearly horizontal and vertical polarized photons. [(c),(d)] Intensity plots ($h\nu =37$ eV, LH polarization, $k_z=0$) recorded along the $\mathrm{\Gamma }\text{−}M$ and $\mathrm{\Gamma }\text{−}X$ directions, respectively. (e) MDCs of [(c),(d)] taken at $E_F$. [(f)–(h)] Same as [(c)–(e)] measured in the $k_z=\pi$ plane ($h\nu =23$ eV). (i) Same as (f) of 115-ML film. (j) Curvature intensity plot of (i). Red arrows indicate the splitting of $\alpha$ band. (k) Band structure cartoons of 15- and 115-ML films along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ directions at low temperatures. (l) Schematic low-temperature FS around $\overline{\mathrm{\Gamma }}$ of single-domained FeSe without nematicity (15-ML film). (m) Same as (l) of twinned FeSe with nematicity (115-ML film). Insets of (l) and (m) show the schematic illustrations of 15- and 115-ML films, respectively.

Figure 4

(a) EDC curvature intensity plots ($h\nu =23$ eV, LH polarization) taken on 15-ML film along the $Z\text{−}A$ direction at 30 and 150 K. (b) Respective EDCs of raw data ($-0.40<k_{\parallel }<0.40 {\AA }^{-1}$). Diamond markers indicate the $\beta$ bands. (c) Extracted dispersions of $\alpha$ and $\beta$ bands at 30 and 150 K from EDCs and MDCs together. Solid curves are the parabolic fittings, which are also superimposed on (a). (d) Temperature dependent MDCs taken at $-40$ meV. Triangle and diamond markers indicate the $\alpha$ and $\beta$ bands, respectively.

Figure 5

Single FT of the sweep spectra of Se-etched ${\mathrm{SrTiO}}_3$ substrate at 114.06 MHz. These NMR spectra are recorded with the same experimental settings as the FeSe film, except the green line with a repetition time of 800 ms between the scans and the orange line with a lower radio frequency pulse power of 6 dB.

Figure 6

NMR line-shape fitting by Lorentzian [(a)–(c)] and Gaussian [(d)–(f)] peaks with linear backgrounds (BGs) at three studied temperatures.

Figure 7

Temperature dependent ${}^{77}\mathrm{Se}$ NMR Knight shift of the 210-ML FeSe film and an ${\mathrm{FeSe}}_{0.95}{\mathrm{S}}_{0.05}$ crystal ($H\parallel \left[100\right]$), adopted from Fig. 2. The strain effect ($K^{\mathrm{stra}}$, indicated by the green arrow) is determined by the average splitting between $K_3$ and $K_{1,2}^{\mathrm{ave}}$ at 30, 35, and 40 K. Black hollow stars indicate the Knight shifts after including the strain effect in the crystal at $T>T_{\mathrm{nem}}$.

Figure 8

(a) Constant-energy ARPES image around $Z$ ($h\nu =23$ eV, LH polarization, $k_z=\pi$) of another 15-ML FeSe film obtained by integrating the photoemission intensity within $E_F\pm 20$ meV. (b) Same as (a) recorded at $h\nu =23$ eV ($k_z=\pi$) with LV polarization. The red arrows in [(a),(b)] indicate that the analyzer slit is parallel to the [110] direction.

Figure 9

(a) ARPES intensity plot ($h\nu =23$ eV, LH polarization, $k_z=\pi , T=15$ K) of the 115-ML FeSe film recorded along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction. (b) Second derivative intensity plot of (a). Red arrows indicate the splitting of the $\alpha$ band at $Z$. Red solid curves are guides to the eye, determined according to the right branch of the split $\alpha$ band. The green dashed line indicates the energy scale ($\sim 20$ meV) of the band splitting.

Figure 10

(a) EDC curvature intensity plots ($h\nu =23$ eV, LH polarization, $k_z=\pi$) taken on the 15-ML FeSe film along the $Z\text{−}A$ direction at different temperatures. (b) Respective EDC plots of raw data at different temperatures over the momentum range of $-0.40<k_{\parallel }<0.40$ Å${}^{-1}$. The diamond markers indicate the $\beta$ bands around $Z$.

Figure 11

(a) Temperature dependent MDCs of the 115-ML FeSe film taken at $-40$ meV. Triangle and diamond markers indicate the $\alpha$ and $\beta$ bands around $Z$, respectively. Red and purple dashed lines show the peak positions of $\alpha$ and $\beta$ at 30 and 150 K, respectively. (b) Band structure diagrams of the 115-ML FeSe film along the $Z\text{−}A$ direction below and above $T_{\mathrm{nem}}$. The splitting of $\alpha$ band below $T_{\mathrm{nem}}$ is not considered here for better visualization of the band shifts.

Figure 12

Schematic illustration of the 210-ML FeSe film with three regions, whose respective thicknesses are denoted as $\delta , \eta$, and $\kappa$.