Insulator-like behavior coexisting with metallic electronic structure in strained FeSe thin films grown by molecular beam epitaxy

This paper reports that ∼10-nm-thick iron selenide (FeSe) thin films exhibit insulator-like behavior in terms of the temperature dependence of their electrical resistivity even though bulk FeSe has a metallic electronic structure that has been confirmed by photoemission spectroscopy and first-principles calculations. This apparent contradiction is explained by potential barriers formed in the conduction band. Very thin FeSe epitaxial films with various atomic composition ratios ([Fe]/[Se]) were fabricated by molecular beam epitaxy and classified into two groups with respect to lattice strain and electrical properties. Lattice parameter $a$ increased and lattice parameter $c$ decreased with increasing [Fe]/[Se] up to 1.1 and then $a$ leveled off and $c$ began to decrease at higher [Fe]/[Se]. Consequently, the FeSe films had the most strained lattice when [Fe]/[Se] was 1.1, but these films had the best quality with respect to crystallinity and surface flatness. All the FeSe films with [Fe]/[Se] of 0.8–1.9 exhibited insulator-like behavior, but the temperature dependences of their electrical resistivities exhibited different activation energies $E_{\mathrm{a}}$ between the Se-rich and Fe-rich regions; i.e., $E_{\mathrm{a}}$ were small (a few meV) up to $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ but jumped up to ∼25 meV at higher [Fe]/[Se]. The film with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ had the smallest $E_{\mathrm{a}}$ of 1.1 meV and exhibited an insulator–superconducting transition at 35 K with zero resistance under gate bias. The large $E_{\mathrm{a}}$ of the Fe-rich films was attributed to the unusual lattice strain with tensile in-plane and relaxed out-of-plane strains. The large $E_{\mathrm{a}}$ of films with [Fe]/[Se] > 1.1 resulted in low mobility with a high potential barrier of ∼50 meV in the conduction band for percolation carrier conduction compared with that of the $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ film (∼17 meV). Therefore, the Fe-rich films exhibited remarkable insulator-like behavior similar to a semiconductor despite their metallic electronic structure. The high potential barrier of Fe-rich films is tentatively attributed to the presence of large amounts of excess Fe, which could plausibly cause a broad superconducting transition without zero resistance under gating.

Figure 1

Overview of FeSe thin films grown by MBE. (a) Relationship between $T_{\mathrm{s}}$ and chemical composition ([Fe]/[Se]) of the fabricated films. Different symbols represent the obtained crystalline phases and orientations. Filled squares denote the epitaxial growth region, open squares the $00l$-oriented FeSe and an unidentified impurity, closed triangles the $00l$-oriented FeSe and impurity Fe, open triangles the $00l$-preferentially oriented FeSe with other orientations and $\mathrm{F}{\mathrm{e}}_7\mathrm{S}{\mathrm{e}}_8$, and closed circles the $00l$-preferentially oriented FeSe with other orientations. (b) Schematics of the strain in FeSe thin films with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ (left) and >1.1 (right) introduced via thin-film growth. The arrows indicate the directions of the introduced strain. $E_{\mathrm{a}}$ is the activation energy obtained from the electronic transport properties for each strained film.

Figure 2

Structure and surface morphology of FeSe films grown at a constant ratio of Fe flux rate to Se flux rate of ∼1:10 and $T_{\mathrm{s}}=350-700{}^{\circ }\mathrm{C}$. (a) Out-of-plane XRD patterns. The asterisks indicate the substrate diffraction peaks, the solid circle at $2\theta =33.5^{\circ }$ an unidentified phase, and “Fe” at $2\theta =44.6^{\circ }$ iron metal. AFM images of films grown at $T_{\mathrm{s}}$ of (b) 700, (c) 530, and (d) 350 °C. Horizontal bars represent height scales. (e) Out-of-plane rocking-curve FWHM for the FeSe 001 diffraction (Δω, red circles) and root-mean-square roughness ($R_{\mathrm{rms}}$, blue squares) of the film surface as a function of $T_{\mathrm{s}}$.

Figure 3

Quality of FeSe thin films with different chemical compositions ($\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=0.7-1.9$) grown at the optimum $T_{\mathrm{s}}$ of 500 °C. (a) Out-of-plane XRD patterns of the films with different [Fe]/[Se]. The black vertical bars and asterisks denote FeSe $00l$ diffractions and STO (001) substrate peaks, respectively. “Fe” indicates the 110 diffraction peak ($2\theta =44.6^{\circ }$) of impurity Fe, which segregates at $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]\ge 1.3$. RHEED patterns of FeSe films with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=\left(\mathrm{b}\right)1.3$ and (c) 1.0. The red vertical arrows in (c) are unidentified diffractions. (d) Rocking-curve FWHMs along the out-of-plane (Δω, red circles) and in-plane (Δϕ, blue squares) directions taken from the FeSe 001 and 200 diffractions, respectively. (e)–(i) AFM images of FeSe films with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=0.7-1.9$ (indicated in each AFM image). An AFM image of FeSe with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ was reported in Ref. [21]. Horizontal bars represent height scales. (j) Surface roughness ($R_{\mathrm{rms}}$) estimated from (e)–(i) as a function of [Fe]/[Se].

Figure 4

Relationship between the lattice strain and chemical composition of FeSe films grown at the optimum $T_{\mathrm{s}}$ of 500 °C with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=0.7-1.9$. (a) $a$-axis (open red circles) and $c$-axis (open blue squares) lattice parameters. The red closed circles and blue closed squares denote the $a$-axis ($a_{\mathrm{bulk}}$) and $c$-axis ($c_{\mathrm{bulk}}$) lattice parameters of bulk FeSe [30, 31, 33]. (b) Introduced strain for the $a$ axis (red circles) and $c$ axis (blue squares) calculated by $\mathrm{\Delta }a=\left(a_{\mathrm{film}}-a_{\mathrm{bulk}}\right)/a_{\mathrm{bulk}}$ and $\mathrm{\Delta }c=\left(c_{\mathrm{film}}-c_{\mathrm{bulk}}\right)/c_{\mathrm{bulk}}$ ($a_{\mathrm{bulk}}=3.7735$ and $c_{\mathrm{bulk}}=5.5238\AA$ at $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.0$ [30]). (c) Lattice strain along the out-of-plane direction ($\mathrm{\Delta }c$) vs that along the in-plane direction ($\mathrm{\Delta }a$). The values in the figure indicate the [Fe]/[Se] values.

Figure 5

Electronic transport properties of FeSe films with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=0.8-1.9$ grown at the optimum $T_{\mathrm{s}}$ of 500 °C. (a) Temperature (T) dependence of resistivity (ρ). (b) Enlarged $\rho -T$ curves inside the dashed square in (a). (c) Arrhenius plots of electrical conductivity (σ) against $T^{-1}$. (d),(e) Lnσ vs $T^{-1/4}$ plots for the films with [Fe]/[Se] of (d) 0.8–1.1 and (e) 1.3 and 1.9. The straight lines in (c) and (d) are the results of the linear least-squares fitting. (f) Activation energy ($E_{\mathrm{a}}$, circles) estimated from the straight lines in (c) and hopping parameter of the variable-range hopping model ($T_0$, squares) estimated from (d) and (e) as a function of [Fe]/[Se].

Figure 6

Fermi surface of the FeSe film grown at the optimum $T_{\mathrm{s}}$ of 500 °C with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ directly observed by ARPES at ∼10 K. The horizontal bar indicates photoelectron intensity. ARPES responses around the (a) Γ and (b) M points. White dashed lines in (a) and (b) represent the Fermi level calibrated using Au as a reference. Second-derivative spectra with respect to energy, where (c) and (d) correspond to (a) and (b), respectively. Black dashed curves in (c) and (d) are a visual guide to help trace the dispersions.

Figure 7

Results of Hall-effect measurements for FeSe films grown at the optimum $T_{\mathrm{s}}$ of 500 °C with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ and 1.9. (a),(b) Transverse resistivity (${\rho }_{xy}$) as a function of external magnetic field (H) at (a) $T=120-300\mathrm{K}$ for the film with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ and (b) $T=170-300\mathrm{K}$ for the film with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.9$. (c) Dependence of the Hall coefficient ($R_{\mathrm{H}}$) of the films with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ and 1.9 on T estimated from (a) and (b), respectively. For the film with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.9$, the $R_{\mathrm{H}}$ values are magnified by one-hundred times. (d) Dependence of the mobilities (μ) on T estimated from the results in (c) and ρ in Fig. 5. Red circles and blue squares in (c) and (d) correspond to the films with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ and 1.9, respectively. Red and blue solid curves in (d) denote quadratic-polynomial fitting results for the films with $\left[\mathrm{Fe}\right]/\left[\mathrm{Se}\right]=1.1$ and 1.9.