Disorder-driven localization and electron interactions in ${\mathrm{Bi}}_x\mathrm{TeI}$ thin films

Strong disorder has a crucial effect on the electronic structure in quantum materials by increasing localization, interactions, and modifying the density of states. ${\mathrm{Bi}}_x\mathrm{TeI}$ films grown at room temperature and $230\mathrm{K}$ exhibit dramatic magnetotransport effects due to disorder, localization, and electron correlation effects, including a metal-insulator transition at a composition that depends on growth temperature. The increased disorder caused by growth at 230 K causes the conductivity to decrease by several orders of magnitude for several compositions of ${\mathrm{Bi}}_x\mathrm{TeI}$. The transition from metal to insulator with decreasing composition $x$ is accompanied by a decrease in the dephasing length, which leads to the disappearance of the weak-antilocalization effect. Electron-electron interactions cause low temperature conductivity corrections on the metallic side and Efros-Shklovskii variable range hopping on the insulating side, effects which are absent in single crystalline ${\mathrm{Bi}}_x\mathrm{TeI}$. The observation of a tunable metal-insulator transition and the associated strong localization and quantum effects in ${\mathrm{Bi}}_x\mathrm{TeI}$ shows the possibility of tuning spin transport in quantum materials via disorder.

Figure 1

Structural disorder in ${\mathrm{Bi}}_x\mathrm{TeI}$ thin films. (a) HRTEM images ${\mathrm{Bi}}_x\mathrm{TeI}$ for varying composition and growth temperature. Cold grown ($230\mathrm{K}$, LT) films are amorphous for low $x$, then nucleate crystallites with larger sizes as Bi concentration is increased. RT-BiTeI is amorphous with a few nanocrystals embedded in the matrix. RT growths $x=2-3$ are nanocrystalline, showing crystallites larger in size compared to $x=1$. The volume fraction of nanocrystals is greater for $x=3$. Example nanocrystallites indicated by arrows. Inset of (a): Diffraction patterns for ${\mathrm{Bi}}_x\mathrm{TeI}$ for varying composition and growth temperature. LT-BiTeI is amorphous. $\mathrm{LT}\text{−}{\mathrm{Bi}}_2\mathrm{TeI}$ and $\mathrm{LT}\text{−}{\mathrm{Bi}}_3\mathrm{TeI}$ contain nanocrystallites in an amorphous matrix, with increasing nanocrystalline volume fraction for increasing $x$, evidenced also by the transition of broad to sharp rings with increasing $x$. RT-BiTeI has broad rings from small nanocrystals and the amorphous matrix, then, as Bi concentration is increased, there is an increase in the intensity of the rings. (b) Variance in the diffracted intensity as a function of scattering vector $k$ for RT and LT BiTeI, ${\mathrm{Bi}}_2\mathrm{TeI}$ showing large differences in the relative peak heights at different scattering vectors $k$. The film grown at higher $T$ has more MRO and less disorder, evidenced by the large second peak in the variance.

Figure 2

Metal-insulator transition in ${\mathrm{Bi}}_x\mathrm{TeI}$ for $x=1-3$. (a) Conductivity $\sigma$ vs temperature for ${\mathrm{Bi}}_x\mathrm{TeI}$ films grown at room temperature (RT) and (b) with substrates cooled down to $\approx$ $230\mathrm{K}$ (LT). (c)–(e) Left: RT; right: 230 K (or LT). (c) Fits to the conductivity based on the presence of interactions, $\sigma \left(T\right)={\sigma }_0+a{T}^{1/2}$, where ${\sigma }_0=\sigma (T=0\mathrm{K})$ and the $T^{1/2}$ term is due to Coulomb interactions which produce a precursor Coulomb gap in the density of states in a disordered system. (d) ${\sigma }_0$ vanishes as a power law for the metal-insulator transition approached from the metallic side for both RT and LT films. The critical Bi composition $x$ for RT grown is $x_c=1.35\pm 0.19$ and for LT films grown at $230\mathrm{K}$ is $x_c=2.38\pm 0.43$. This significant difference in $x_c$ displays how the increased disorder in films grown at reduced temperature affects the electronic properties of the material, significantly increasing the localization of carriers. (e) VRH fits $\propto e^{-{(T_0/T)}^{\nu }}$ to ${\mathrm{Bi}}_x\mathrm{TeI}$ films that show insulating behavior. The fit range is indicated by the black bars. The hopping regime is well described with $\nu =1/2$, indicating Coulomb interactions have to be taken into consideration and are of a relevant strength compared to the hopping energy.

Figure 3

Magnetotransport in RT ${\mathrm{Bi}}_x\mathrm{TeI}$ thin films. (a) Normalized resistance of RT-BiTeI as a function of temperature and field. The film is highly resistive in the hopping regime and shows a positive MR that decreases with increasing measurement temperature. The low-temperature data is fit well by the wave-function shrinkage model. (b) Magnetoconductance of $\mathrm{RT}\text{−}{\mathrm{Bi}}_2\mathrm{TeI}$, again negative and decreasing in magnitude with increasing measurement temperature but two orders of magnitude larger than in $x=1$. Fits shown are 3D weak antilocalization. (c) Magnetoconductance of $\mathrm{RT}\text{−}{\mathrm{Bi}}_3\mathrm{TeI}$ with 3D weak antilocalization fits. The sharp dip in the MC with field for $2\mathrm{K}$ data is from the WAL effect. (d) Dephasing length versus temperature for $\mathrm{RT}\text{−}{\mathrm{Bi}}_2\mathrm{TeI}$ and $\mathrm{RT}\text{−}{\mathrm{Bi}}_2\mathrm{TeI}$. The $\mathrm{RT}\text{−}{\mathrm{Bi}}_2\mathrm{TeI}$ data is fit best as $l_{\varphi }$ proportional to $T^{-0.47\pm 0.12}$, indicating dephasing due to electron interactions. For $\mathrm{RT}\text{−}{\mathrm{Bi}}_3\mathrm{TeI}$, the data is fit best as $l_{\varphi }$ proportional to $T^{-1.49\pm 0.16}$, indicating dephasing due to electron-phonon interactions. (e) Hall resistance for $\mathrm{RT}\text{−}{\mathrm{Bi}}_2\mathrm{TeI}$. $R_{xy}$ is nonlinear and the Hall coefficient is negative. Below $5\mathrm{K}$ the Hall coefficient is a factor of 2 smaller than above $5\mathrm{K}$. (f) Hall resistance for RT-Bi3TeI. $R_{xy}$ is linear, electronlike, and temperature independent.

Figure 4

Electron interactions in RT ${\mathrm{Bi}}_x\mathrm{TeI}$ thin films. (a) ${\sigma }_{xx}$ vs $T$ for different applied fields in RT ${\mathrm{Bi}}_2\mathrm{TeI}$ films. The low-temperature conductivity decreases with increasing applied field as quantum interference is destroyed and the dip below $5\mathrm{K}$ scales as $\sqrt{T}$, indicating electron interactions dominate below 5 K, and do not change with magnetic field. Blue line is zero-field data which decreases with decreasing temperature, an indication that WAL is not relevant. The purple dashed line shows the low-temperature conductivity modifications from electron interactions. (b) ${\sigma }_{xx}$ vs $T$ for different applied fields in RT ${\mathrm{Bi}}_3\mathrm{TeI}$ films. Blue line is zero-field data, which increases with decreasing temp (below 2 K) due to WAL. Applying a magnetic field eliminates WAL, such that the conductivity decreases with decreasing temperature at all temperatures in fields; the application of a field destroys this effect and the the conductivity decreases for all temperatures.