Disentangling the magnetoelectric and thermoelectric transport in topological insulator thin films

We report transport studies on ${\left(\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{b}}_x\right)}_2\mathrm{T}{\mathrm{e}}_3$ topological insulator thin films with tunable electronic band structure. We find a doping and temperature regime in which the Hall coefficient is negative indicative of electron-type carriers, whereas the Seebeck coefficient is positive indicative of hole-type carriers. This sign anomaly is due to the distinct transport behaviors of the bulk and surface states: the surface Dirac fermions dominate magnetoelectric transport while the thermoelectric effect is mainly determined by the bulk states. These findings may inspire new ideas for designing topological insulator-based high-efficiency thermoelectric devices.

Figure 1

Schematic diagram for transport measurements and the results of 5 QL $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ and $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ films. (a) Schematic device for the thermoelectric measurements. (b) The sheet resistance $\left(R_{\square }\right)$ of $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ and $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ shows metallic behavior at high $T$ and turns to weakly insulating at low $T$. (c) In $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ and $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ the $S_{xx}$ has a quasilinear $T$ dependence, but with opposite signs. (d) The Hall coefficient of $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ is negative, indicating electronlike charge carriers which contribute negative $S$; whereas in $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ the holelike charge carriers contribute positive $S$. The solid symbols are obtained by fitting the slope of field-dependent Hall traces at fixed temperatures, and the lines are measured by switching the current and voltage contacts at fixed magnetic field when the temperature is slowly swept [31].

Figure 2

The temperature dependence of the sheet resistance for the 5 QL ${\left(\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{b}}_x\right)}_2\mathrm{T}{\mathrm{e}}_3$ films with $0.7\le x\le 0.97$. $R_{\square }$ shows an enhanced insulating tendency when $x$ is close to 0.95.

Figure 3

The Hall effect for the 5 QL ${\left(\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{b}}_x\right)}_2\mathrm{T}{\mathrm{e}}_3$ films with $0.7\le x\le 0.97$. (a) Field dependence of the Hall resistance measured at constant temperatures. (b) The Hall coefficient $R_{\mathrm{H}}$ as a function of continuously increased (red lines) and constant (black squares) temperatures. For each sample the sign of $R_{\mathrm{H}}$ is unchanged with increasing $T$ (negative for $x\le 0.9$ and positive for $x\ge 0.95$).

Figure 4

The Seebeck coefficient for the 5 QL ${\left(\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{b}}_x\right)}_2\mathrm{T}{\mathrm{e}}_3$ films with $0.7\le x\le 0.97$. In samples with $x=0.7\mathrm{and}0.8$, a sign reversal of $S$ from negative to positive is revealed as $T$ rises. As $x$ is further increased from $x=0.9\mathrm{to}0.97$, the sign reversal totally disappears and a maximum positive value is found with $x=0.95$. At high $T$, the sign anomaly between $S$ and $R_{\mathrm{H}}$ is clearly revealed for $0.7\le x\le 0.9$.

Figure 5

The phase diagram of ${\left(\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{b}}_x\right)}_2\mathrm{T}{\mathrm{e}}_3$ films summarizing the $S_{xx}$ as a function of $x$ and $T$. The contours with $S=0$ (maroon dashed line) and $R_{\mathrm{H}}=0$ (blue dash-dotted line) divide this phase diagram into three regions: negative $S_{xx}$ and $R_{\mathrm{H}}$ (region I), positive $S_{xx}$ but negative $R_{\mathrm{H}}$ (region II), and positive $S$ and $R_{\mathrm{H}}$ (region III).

Figure 6

The band structure of 5 QL ${\left(\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{b}}_x\right)}_2\mathrm{T}{\mathrm{e}}_3$ calculated by the density functional theory with $x=0.75$ (a), 0.9 (b), and 1.0 (c). Red dashed lines indicate the position of the Dirac point, and black dashed lines represent the locations of the Γ points. The bulk VBM is selected as the energy reference $(E=0)$.

Figure 7

The calculated distribution of conduction modes $M$($E$) as a function of energy for the 5 QL ${\left(\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{b}}_x\right)}_2\mathrm{T}{\mathrm{e}}_3$ film with $x=0.9$.

Figure 8

The Seebeck coefficient as a function $T$ and $E_{\mathrm{F}}$ calculated based on the band structure in Fig. 6. While $S_{xx}$ is always positive for $E_{\mathrm{F}}\le 0$, $S_{xx}$ changes from negative to positive with increasing $T$ for $E_{\mathrm{F}}>0$.

Figure 9

(a) Schematic drawing shows the coexistence of electron-type surface Dirac fermions and hole-type bulk carriers in a TI thin film. (b) A theoretical phase diagram for TI thin films with $n$-type surface and $p$-type bulk charge carriers. When increasing ${\sigma }_{\mathrm{b}}/{\sigma }_{\mathrm{s}}$ (realized by increasing $T$ and Sb content in experiment), a negative-to-positive sign change happens for both $S$ and $R_{\mathrm{H}}$ but at distinctly different conditions: ${\sigma }_{\mathrm{b}}/{\sigma }_{\mathrm{s}}=\left|S_{\mathrm{s}}/S_{\mathrm{b}}\right|\ll 1$ for $S$ and ${\sigma }_{\mathrm{b}}/{\sigma }_{\mathrm{s}}={\mu }_{\mathrm{s}}/{\mu }_{\mathrm{b}}\gg 1$ for $R_{\mathrm{H}}$. Three different regions (I,II,III) are defined according to the signs of $S$ and $R_{\mathrm{H}}$, the same as in Fig. 5.