Abstract
1. Introduction
Topological insulators (TIs) are a class of materials with special topological features in energy bands. Due to the topological surface states protected by time reversal symmetry (TRS)[
Compared with transition elements, rare earth (RE) elements could be optional dopant candidates for the following reasons. On one hand, they usually possess larger local magnetic moments than transition elements, which implies the possibility of larger interactions between local magnetic moments from 4f electrons with topological states, and might result in reducing the dopant concentration to achieve the desired strength of magnetic interactions. On the other hand, the trivalent state of RE ions can substitute the trivalent Bi/Sb ions in TIs without changing the charge carrier density[
In this work, we reported the electronic transport properties of Ce-doped Bi2Te3 thin films grown on Al2O3(0001) substrate by molecular beam epitaxy (MBE) with various Ce concentrations. X-ray diffraction (XRD) revealed that Ce atoms substituted the Bi sites, resulting in the chemical formula of (CexBi1–x)2Te3. Electronic transport measurements demonstrated Kondo effect and Fermi liquid behavior of (CexBi1–x)2Te3 at low temperature. Weak anti-localization (WAL) effect that is closely related to the topological properties of TIs is experimentally investigated by magnetic transport measurements and theoretically studied by using the Hikami–Larkin–Nagaoka (HLN) model[
2. Experimental methods
Pristine and Ce-doped Bi2Te3 thin films were grown on an Al2O3(0001) substrate by MBE, following the well-established three temperature methods[
3. Results and discussions
Fig. 1(a) shows the crystal structure of Bi2Te3. Bi2Te3 has a layered hexagonal structure. The smallest repeating unit consists of five atomic layers with a stacking sequence of -Te(1)-Bi-Te(2)-Bi-Te(1)-, which is called a quintuple layer (QL). The interaction between neighboring QLs is the relatively weak van der Waals interaction. The thickness of all the samples was kept at 100 QLs, i.e., about 100 nm. Fig. 1(b) shows the XRD results of the (CexBi1–x)2Te3 samples, where only the (00L) peaks of Bi2Te3 are present in the spectra. The absence of other diffraction peaks in the XRD suggests that the sample surface is well oriented in the direction parallel to the (0001) plane of Bi2Te3. The lattice parameters c perpendicular to the sample surface for all the samples were calculated. All the c values disperse within 3.045 ± 0.007 nm for all the samples, where 3.045 nm corresponds to the lattice parameter of the pristine Bi2Te3 thin film. This means that the differences of c between the Ce-doped and pristine Bi2Te3 thin films are less than ~ 0.2 %, indicating that Ce has substituted Bi during the growth, which is consistent with the substitutional doping scenario with the RE3+ ion iso-electronically substituting for Bi3+[
Figure 1.(Color online) (a) Schematic crystal structure of Bi2Te3. (b) XRD patterns of (Ce
Transport measurements were performed above 3.4 K (the onset superconducting transition temperature of indium, which was used as electrode contacts) to eliminate the influence of the superconducting effects from indium. The curves of the longitudinal resistivity versus temperature (
Figure 2.(Color online) (a) Resistivity of (Ce
where
As shown in Table 1, as the dopant concentration increases, the Fermi liquid behavior and the Kondo effect compete with each other, indicated by the gradual decrease of A and increase of B. In general, the low temperature transport behavior of (CexBi1–x)2Te3 films is mainly determined by the Kondo effect of Ce and the Fermi liquid behavior of electrons. The more the dopant, the stronger the Kondo effect and the weaker the Fermi liquid behavior.
Figs. 2(c) and 2(d) show the evolution of normalized magnetoresistance (MR) with Ce concentration x and temperature for x = 0.04, respectively, with MR being defined as:
where R(B) is the resistance measured under magnetic field B, R(0) is the resistance measured under zero field. Similar to the previous report[
The effect of WAL in MR can be described by the HLN model[
Figure 3.(Color online) (a) Magnetoconductance of samples with different dopant concentrations under different perpendicular magnetic field at 4 K (solid lines – fits to Eq. (3)). (b) Magnetoconductance of (Ce0.04Bi0.96)2Te3 under different perpendicular magnetic field at different temperatures (solid lines – fits to Eq. (3)). (c) The change of fitting parameters
where
where
where T is the temperature and the factor m is related to the type of dominant mechanism of WAL. It is reported that for two-dimensional e–e scattering, the power law dependence should be
4. Conclusions
(CexBi1–x)2Te3 (x = 0, 0.01, 0.02, 0.03, 0.04, 0.05) monocrystalline films with a thickness of 100 nm were successfully grown on sapphire substrates by MBE, and the electrical transport properties have been investigated. The resistivity shows metallic behavior at T > 25 K and semiconductor behavior when between 5–25 K. This resistivity behavior at low temperature is mainly due to the Kondo effect of Ce and the Fermi liquid behavior of electrons, which are confirmed by Kondo theory fitting. The contribution of Kondo effect increases with increasing Ce concentration, while the contribution of Fermi liquid decreases. Besides, WAL effect was also observed from the magnetoresistance and magnetoconductance. From the fitting of the HLN model, we confirm that the WAL effect is mainly dominated by the two-dimensional Nyquist e-e interaction. The phase coherence length and the number of conducting channels extracted from HLN fitting decrease as the concentration increases, which indicates a higher concentration of dopant may further suppress or even damage the topological properties of the TI. This indicates that there is a strong competition between the topological surface states and the magnetic order introduced by dopant Ce. Through doping Ce, this work successfully introduces RE elements into topological materials and preliminary investigates its influence on the transportation properties. It may lay the foundation for further research on the influences of RE elements on topological materials, which may open the door to the study of exotic physical properties, such as QAHE of TIs at elevated temperatures.
Acknowledgements
This work was supported by the Key Research and Development Program of China (No. 2017YFA0303104), the SPC-Lab Research Fund (No. WDZC201901) and the National Science Foundation of China (No. U1630248).
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