Electron-electron interactions and weak antilocalization in few-layer $\mathrm{Zr}{\mathrm{Te}}_5$ devices

Much effort has been devoted to the electronic properties of relatively thick $\mathrm{Zr}{\mathrm{Te}}_5$ crystals, focusing on their three-dimensional topological effects. Thin $\mathrm{Zr}{\mathrm{Te}}_5$ crystals, on the other hand, were much less explored experimentally. Here we present detailed magnetotransport studies of few-layer $\mathrm{Zr}{\mathrm{Te}}_5$ devices, in which electron-electron interactions and weak antilocalization are observed. The coexistence of the two effects manifests itself in corroborating evidence presented in the temperature and magnetic field dependence of the resistance. Notably, the temperature-dependent phase coherence length extracted from weak antilocalization agrees with strong electron-electron scattering in the sample. Meanwhile, universal conductance fluctuations have temperature and gate voltage dependence that is similar to that of the phase coherence length. Last, all the transport properties in thin $\mathrm{Zr}{\mathrm{Te}}_5$ crystals show strong two-dimensional characteristics. Our results provide insight into the highly intricate properties of topological material $\mathrm{Zr}{\mathrm{Te}}_5$.

Figure 1

(a) Temperature dependent resistance of $\mathrm{Zr}{\mathrm{Te}}_5$ device 1. The upturn of the resistance at low temperature is marked by a small red box and is converted to conductance as shown in (b). The optical micrograph of the device is shown in the lower inset and the AFM section height data is shown in the upper inset. The scale bar in the lower inset is 5 um, and the white dashed line marks the position where the AFM section height data is acquired. (b) The conductance of device 1 as a function of temperature in semilog scale. The red line is the linear fit to Eq. (1). (c) Scattering rate $1/\tau$ as a function of $T^2$. The red line is a linear fit to the data at the temperature range of 50–260 K. The inset depicts the carrier density (left axis, black dots) and mobility (right axis, red dots) at different temperatures. (d) Longitudinal (left axis, red curve) and Hall (right axis, black curve) resistance at $T=2\mathrm{K}$ under perpendicular magnetic field.

Figure 2

Weak antilocalization data of $\mathrm{Zr}{\mathrm{Te}}_5$ device 1. (a) Magnetoconductance $\delta \sigma$ at small magnetic field in the unit of $e^2/h$ at temperatures between 2 and 30 K. Solid lines are fits to the experimental data using Eq. (2). (b) The extracted phase coherence length from the fitting of (a). Inset: the fitting parameter ${\alpha }_2$ at different temperatures. (c) Magnetoconductance versus perpendicular component of the magnetic field with the sample titled at different angles at 2 K. θ is the angle between the direction of the total magnetic field and the perpendicular axis of the sample plane. (d) The angular dependence of Hall coefficient $R_{\mathrm{H}}$ and fit to $cos\theta$. The angle is shifted by $7^{\circ }$ for simplicity.

Figure 3

Gate dependence of WAL in $\mathrm{Zr}{\mathrm{Te}}_5$ device 2-1. (a) Representative traces of magnetoconductance with different back gate voltages at 2 K. Solid lines are fits to the experimental data using Eq. (2). (b) The extracted phase coherence length at various back gate voltages. Inset: gate dependence of resistance at $B=0, T=2\mathrm{K}$.

Figure 4

Universal conductance fluctuations in thin $\mathrm{Zr}{\mathrm{Te}}_5$. (a) Magnetoconductance fluctuation $\delta G$ in $\mathrm{Zr}{\mathrm{Te}}_5$ device 2-2 (after subtracting a smooth background, in units of $e^2/h$) versus magnetic field at different temperatures. Curves are shifted for clarity. (b) Root mean square of the magnetoconductance fluctuation in (a) as a function of temperature (left axis, black open squares); phase coherence length extracted from WAL of the same device (right axis, red solid squares). (c) Magnetoconductance fluctuation $\delta G$ at different back gate voltages at $T=2\mathrm{K}$ in device 2-1. (d) Gate dependence of rms($G$) from (c). (e) Magnetoconductance fluctuations at tilted magnetic field. Marked circles are several representative peaks or valleys of fluctuation. (f) The magnetic field corresponding to circles in (e) and their fits to $1/cos\theta$ (solid lines). All the curves in (f) are shifted by $3^{\circ }$ for simplicity.