Gate-Voltage Control of Chemical Potential and Weak Antilocalization in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

We report that ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films can be epitaxially grown on ${\mathrm{SrTiO}}_3$ substrates, which allow for very large tunablity in carrier density with a back gate. The observed low field magnetoconductivity due to weak antilocalization (WAL) has a very weak gate-voltage dependence unless the electron density is reduced to very low values. Such a transition in WAL is correlated with unusual changes in longitudinal and Hall resistivities. Our results suggest a much suppressed bulk conductivity at large negative gate voltages and a possible role of surface states in the WAL phenomena.

Figure 1

(a) STM image and low energy electron diffraction pattern (inset) of a ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystalline thin film grown on a ${\mathrm{SrTiO}}_3(111)$ substrate; (b) $T$ dependence of ${\rho }_{xx}$ of samples $A$ (lower) and $B$ (upper) at $B=0$; (c) normalized magnetoresistance of samples $A$ (lower) and $B$ (upper); (d) relative changes in carrier density with respect to $V_G=0$ extracted from Hall measurements (circles) and charging effects (squares).

Figure 2

Plotted as a function of $\Delta n_s$ are (a) ${\rho }_{xx}^0$ (hexagons) and its derivative (diamonds); (b) $n_s^{\mathrm{\text{Hall}}}$ (pentagons) and its derivative (triangles). The negative gate voltages are partitioned into three zones (I, II, III) according to the degree of carrier depletion. (c) Calculated band diagrams based on a simple model described in the text.

Figure 3

Magnetoconductivity, defined as $\Delta \sigma (B)={\sigma }_{xx}(B)-{\sigma }_{xx}{|}_{B=0}$ of (a) sample $A$; (b) sample $B$ at $V_G=0$, 60, and 150 V; (c) sample $B$ at $V_G=-150\mathrm{V}$, $-140$, $-130$, $-120$, $-110$, $-100$, $-80$, and $-60\mathrm{V}$ (from top to bottom). Fitted curves (lines) with Eq. (1) are also shown in (d) $V_G=-150\mathrm{V}$, (e) $-110\mathrm{V}$, and (f) 150 V for sample $B$.

Figure 4

(a) $B_{\varphi }$ (solid squares) and $\alpha$ (open circles), (b) $B_{\varphi }{\sigma }_{xx}^0$, as a function of $\Delta n_s$. Here ${\sigma }_{xx}^0$ is the conductivity at $B=0$. The partition of the negative $V_G$ region is the same as that in Fig. 2. (c) Calculated chemical potential on the top surface with respect to the conduction band minimum (CBM). The Dirac point (DP) is located at $-0.2\mathrm{eV}$.