Evidence of lattice deformation induced metal-insulator transition in ${\mathrm{Ti}}_2{\mathrm{O}}_3$

We synthesized ${\mathrm{Ti}}_2{\mathrm{O}}_3$ epitaxial films with continuously varying ratios of the c-axis to a-axis lattice constants ($c/a$ ratios) on 4H-SiC (0001) substrates and investigated their structural and electronic properties. ${\mathrm{Ti}}_2{\mathrm{O}}_3$ films with a wide range of $c/a$ ratios were fabricated in a controllable fashion by changing the growth temperature. As the $c/a$ ratio at room temperature increased, the metal-insulator transition (MIT) temperature systematically decreased and eventually the MIT disappeared. Detailed analyses revealed that the MIT occurred at a critical $c/a$ ratio of 2.68. The critical $c/a$ ratio for the occurrence of the MIT was also reproduced by density functional theory calculations. These results provide evidence for the origin of the MIT in ${\mathrm{Ti}}_2{\mathrm{O}}_3$. The MIT is not a Mott transition induced by temperature, but a gradual semimetal-to-semiconductor transition induced by lattice deformation.

Figure 1

Reciprocal space maps around 4H-SiC 10–19 reciprocal points for ${\mathrm{Ti}}_2{\mathrm{O}}_3$ films grown at (a) $1050{}^{\circ }\mathrm{C}$, (b) $1000{}^{\circ }\mathrm{C}$, (c) $800{}^{\circ }\mathrm{C}$, (d) $750{}^{\circ }\mathrm{C}$, (e) $700{}^{\circ }\mathrm{C}$, (f) $650{}^{\circ }\mathrm{C}$, (g) $600{}^{\circ }\mathrm{C}$, and (h) $500{}^{\circ }\mathrm{C}$. ${\mathrm{Ti}}_2{\mathrm{O}}_3$ 11–212 reciprocal points are indicated by the red markers.

Figure 2

(a) $a$ axis and $c$ axis lattice constants and (b) $c/a$ ratios at RT ($c_{\mathrm{RT}}/a_{\mathrm{RT}}$) of the ${\mathrm{Ti}}_2{\mathrm{O}}_3$ films prepared at growth temperatures ($T_{\mathrm{g}}$) of $500–1050{}^{\circ }\mathrm{C}$. Solid lines indicate the values for bulk ${\mathrm{Ti}}_2{\mathrm{O}}_3$ [5, 6]. The dashed lines are guides to the eye.

Figure 3

Temperature dependence of resistivity ($\rho –T$ curve) for the ${\mathrm{Ti}}_2{\mathrm{O}}_3$ films grown at temperatures of $500–1050{}^{\circ }\mathrm{C}$. The $\rho –T$ curve for bulk ${\mathrm{Ti}}_2{\mathrm{O}}_3$ is also shown as a reference [4]. Filled and open triangles indicate $T_{\mathrm{MIT}}$ and $T_{\mathrm{MC}}$ that were determined from the first derivative of the $\rho –T$ curves, respectively. (See Fig. S5 in the the Supplemental Material [23]).

Figure 4

(a) Plots of $T_{\mathrm{MIT}}$ and $T_{\mathrm{MC}}$ as a function of $c_{\mathrm{RT}}/a_{\mathrm{RT}}$. The dashed lines are guides for the eye. (b) Plots of $T_{\mathrm{MIT}}$ and $T_{\mathrm{MC}}$ as a function of the $c/a$ ratios that were calibrated by the temperature-induced lattice deformation. (See Fig. S6 in the the Supplemental Material [23]). Dotted diagonal lines indicate the coordinate for the same $c/a$ ratio. Red open squares indicate the data of the ${\mathrm{Ti}}_2{\mathrm{O}}_3$ film grown on $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ (0001) substrates ($c_{\mathrm{RT}}/a_{\mathrm{RT}}=2.696$ and $T_{\mathrm{MIT}}=206\mathrm{K}$) [14]. Blue open circles indicate $T_{\mathrm{MC}}$ of the films in which the MIT is absent.

Figure 5

(a) Energy gap at the Fermi level ($E_{\mathrm{F}}$) as a function of the $c/a$ ratios. The energy gap was obtained from DFT calculations with $U=2.2\mathrm{eV}$ [11, 14, 15]. The inset shows schematic band diagrams of insulating and metallic ${\mathrm{Ti}}_2{\mathrm{O}}_3$ near $E_{\mathrm{F}}$. Calculated densities of states near $E_{\mathrm{F}}$ with $c/a$ ratios of (b) 2.66 and (c) 2.70. Insets of (b) and (c) show the corresponding magnifications near $E_{\mathrm{F}}$.