Control of band structure of FeSe single crystals via biaxial strain

We performed systematic transport measurements on FeSe single crystals with applying in-plane biaxial strain $\varepsilon$ ranging from $-0.96\%$ to 0.23%. Biaxial strain was introduced by firmly gluing samples to various substrate materials with different thermal expansion. With increasing $\varepsilon$, structural and superconducting transition temperatures monotonically increased and decreased, respectively. We analyzed magnetotransport results using a compensated three-carrier model. The evaluated densities of hole and electron carriers systematically changed with strain. This indicates that we succeeded in controlling the band structure of single-crystalline FeSe.

Figure 1

(a) Temperature dependence of the relative length changes $\mathrm{\Delta }L/L_{300\mathrm{K}}$ of polycarbonate, Stycast 2850FTJ, soda-lime glass, borosilicate glass, and quartz glass. The data for the in-plane length of twinned FeSe are also plotted [15]. (b) Temperature dependence of in-plane strain imposed on FeSe single crystals on the five substrates.

Figure 2

(a) Temperature dependence of resistivity $\rho \left(T\right)$ for the strain-free and strained FeSe. The curves are offset to avoid overlapping. (b) Temperature derivative and (c) second derivative of $\rho \left(T\right)$ in the magnified region around $T_{\mathrm{s}}$. Arrows indicate $T_{\mathrm{s}}$ determined from the peak position of $d^2\rho /d{T}^2$.

Figure 3

Strain dependence of $T_{\mathrm{s}}$ of FeSe. Square symbols represent $T_{\mathrm{s}}$ obtained from the study on thin films [7]. The gray line is a guide to the eye.

Figure 4

Temperature dependence of (a) electrical resistivity normalized at 30 K and (b) Hall coefficient for strain-free and strained FeSe. The displayed $\varepsilon$ corresponds to the value at $T_{\mathrm{c}}$. The arrows indicate the minima of $R_{\mathrm{H}}$ at $T^{*}$.

Figure 5

Strain dependence of $T_{\mathrm{c}}^{\mathrm{zero}}$, $T_{\mathrm{c}}^{\mathrm{onset}}$, and $T^{*}$. Diamond symbols represent $T_{\mathrm{c}}$ obtained from the study on thin films [7]. The gray line is a guide to the eye. Inset shows the strain dependence of $T^{*}/T_{\mathrm{c}}^{\mathrm{onset}}$.

Figure 6

Magnetic-field dependence of (a) Hall resistivity ${\rho }_{xy}$ and (b) magnetoresistance $\mathrm{\Delta }{\rho }_{xx}\left(B\right)/{\rho }_{xx}\left(0\right)$ of FeSe with various degrees of biaxial strain at 30 K. Inset shows the strain dependence of the Hall resistivity and the magnetoresistance at $B=7\mathrm{T}$. A vertical broken line separates distinct strain dependences, which implies the presence of a Lifshitz transition.

Figure 7

Magnetic-field dependence of (a)–(d) Hall resistivity and (e)–(h) magnetoresistance for strain-free and strained FeSe at 30 K. Fitting curves obtained using a compensated three-carrier model are also shown. Strain dependence of (i) carrier densities ($n_{\mathrm{h}}$, $n_{\mathrm{e}1}$, and $n_{\mathrm{e}2}$) and (j) mobilities (${\mu }_{\mathrm{h}}$, ${\mu }_{\mathrm{e}1}$, and ${\mu }_{\mathrm{e}2}$) extracted by the three-carrier fitting.

Figure 8

Histogram of the measured resistivity values for FeSe at 300 K.

Figure 9

Magnetic-field dependence of (a)–(d) Hall resistivity and (e)–(h) magnetoresistance for strain-free and strained FeSe at 30 K. Fitting curves obtained using the compensated two-carrier model are also shown.

Figure 10

Strain dependence of (a) carrier density and (b) mobilities extracted from the magneto-transport data using the two-carrier model. Open triangle symbols represent the fitting result obtained from the thin-film study at 20 K [7]. The gray line is a guide to the eye.

Figure 11

Magnetic-field dependence of (a)–(b) Hall resistivity ${\rho }_{xy}\left(B\right)$ and (c)–(d) magnetoresistance $\mathrm{\Delta }{\rho }_{xx}\left(B\right)/{\rho }_{xx}\left(0\right)$ for strained FeSe with $\varepsilon =0.17\%$ and 0.23% at 30 K. Fitting curves obtained using the compensated three-carrier model are also shown.

Figure 12

Strain dependence of (a) carrier densities ($n_{\mathrm{h}}$, $n_{\mathrm{e}1}$, and $n_{\mathrm{e}2}$) and (b) mobilities (${\mu }_{\mathrm{h}}$, ${\mu }_{\mathrm{e}1}$, and ${\mu }_{\mathrm{e}2}$) extracted by the three-carrier fitting shown in Fig. 11. A vertical broken line indicates the Lifshitz transition.