Optically tuned dimensionality crossover in photocarrier-doped ${\mathrm{SrTiO}}_3$: Onset of weak localization

We report magnetotransport properties of photogenerated electrons in undoped ${\mathrm{SrTiO}}_3$ single crystals under ultraviolet illumination down to $2\mathrm{K}$. By tuning the light intensity, the steady-state carrier density can be controlled, while tuning the wavelength controls the effective electronic thickness by modulating the optical penetration depth. At short wavelengths, when the sheet conductance is close to the two-dimensional Mott minimum conductivity, we have observed critical behavior characteristic of weak localization. The negative magnetoresistance at low magnetic field is highly anisotropic, indicating quasi-two-dimensional electronic transport. The high mobility of photogenerated electrons in ${\mathrm{SrTiO}}_3$ allows continuous tuning of the effective electronic dimensionality by photoexcitation.

Figure 1

(Color online) Temperature dependence of (a) sheet conductance, (b) sheet carrier density $n_{2\mathrm{D}}$ estimated from the Hall coefficient $R_H$ as $n_{2\mathrm{D}}=1∕R_{H}e$, and (c) Hall mobility for varying light intensity at $370\mathrm{nm}$. The values indicated are relative light intensity $(100\sim 1\mathrm{mW}∕{\mathrm{cm}}^2)$.

Figure 2

(Color online) Absorption coefficient of ${\mathrm{SrTiO}}_3$ as a function of energy of incident light. The low-energy curve is taken from Ref. 20, while the high-energy curve is taken from Ref. 21.

Figure 3

(Color online) Hall mobility as a function of (a) $n_{3\mathrm{D}}$ and (b) $n_{2\mathrm{D}}$ with varying intensity and wavelength of illumination. $n_{2\mathrm{D}}$ is estimated from Hall measurements and the thickness of the conducting layer is approximated by $1∕\alpha$ for $n_{3\mathrm{D}}$. The dashed line in (b) indicates the two-dimensional Mott minimum conductivity $n_{2\mathrm{D}}e\mu =e^2∕h$. (c) Sheet conductance as a function of sheet carrier density near the mobility drop in (b). The measurement temperature for all panels is $2\mathrm{K}$, and the carrier density was controlled by changing the light intensity.

Figure 4

(Color online) Hall mobility as a function of temperature under $330\mathrm{nm}$ illumination for a sample $n_{2\mathrm{D}}\left(2\mathrm{K}\right)=1.0\times {10}^{12}{\mathrm{cm}}^{-2}$ and $\mu \left(2\mathrm{K}\right)=2800{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$. The dashed line is the result of fitting by the equation $\mu \left(T\right)={\mu }_0+A\ln \left(T\right)$, where ${\mu }_0=2600{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and $A=350{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$. The inset shows $n_{2\mathrm{D}}\left(T\right)$ with a constant light intensity.

Figure 5

(Color online) Transverse magnetoresistance under (a) 310, (b) 330, (c) 350, and (d) $370\mathrm{nm}$ illumination with varying light intensity at $2\mathrm{K}$.

Figure 6

(Color online) (a) Schematic diagram of sample geometries with respect to the directions of current and magnetic field. (1) $H\perp I$ and $H\perp$ sample surface; (2) $H\Vert I$ and $H\Vert$ sample surface; and (3) $H\perp I$ and $H\Vert$ sample surface. (b) Magnetoresistance in three geometries under $310\mathrm{nm}$ illumination at $2\mathrm{K}$. $\rho \left(0\right)$ gives the sheet resistance at $H=0$ in units of $\mathrm{k}\mathrm{\Omega }∕◻$. The sample geometries numbered in (a) correspond to the data points numbered in (b).

Figure 7

(Color online) Conductivity correction by magnetic field (a) in geometry 1, (b) in geometry 2, and (c) in geometry 3 as shown in Fig. 6a with varying light intensity. ${\sigma }_0$ gives the sheet conductance at $H=0$.