Peng Teng, Tong Zhou, Yonghuan Wang, Ke Zhao, Xiegang Zhu,†, and Xinchun Lai

1Southwest Jiaotong University, School of Physical Science and Technology, Chengdu 610031, China

2Science and Technology on Surface Physics and Chemistry Laboratory, Jiangyou 621908, China

3Institute of Materials, China Academy of Engineering Physics, Mianyang 621700, China

4Beijing Institute for Advanced Study, National University of Defense Technology, Beijing 100020, China

Abstract: Introducing magnetism into topological insulators (TIs) can tune the topological surface states and produce exotic physical effects. Rare earth elements are considered as important dopant candidates, due to their large magnetic moments from heavily shielded 4f electrons. As the first element with just one 4f electron, cerium (Ce) offers an ideal platform for exploring the doping effect of f-electron in TIs. Here in this work, we have grown cerium-doped topological insulator Bi2Te3 thin films on an Al2O3(0001) substrate by molecular beam epitaxy (MBE). Electronic transport measurements revealed the Kondo effect,weak anti-localization (WAL) effect and suppression of surface conducting channels by Ce doping. Our research shows the fundamental doping effects of Ce in Bi2Te3 thin films, and demonstrates that such a system could be a good platform for further research.

Key words: topological insulators; molecular beam epitaxy; Kondo effect; weak anti-localization effect

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)[1−3], three-dimensional topological insulators (3D-TIs),such as Bi2Se3[1,4], Bi2Te3[5]and Sb2Te3[6]have attracted great attention in the past few decades. TRS can be broken by introducing magnetism, which could unlock many exotic physical phenomena, such as quantum anomalous Hall effect(QAHE)[7], topological magnetoelectric effect[8]and mirror magnetic monopole[9],etc. The method of doping magnetic elements was widely adopted to introduce magnetism into TIs.Conventionally, transition elements (such as Mn, Fe, V, Co, Cr,etc.[10-20]) were used as dopants to study the doping effect of d electrons in TIs, among which the discovery of QAHE in Crdoped Cr0.15(Bi0.1Sb0.9)1.85Te3thin films was well noted[10]. It should be stressed that the typical dopant concentration of transition elements was considerably high (from ～ 0.03 to 0.075 at.), which might complicate the structural phases and chemical homogeneity of the pristine topological materials.What is more, extremely low temperature environment,i.e.,in the range of sub-kelvin, was needed for the interplay between magnetism and topological states taking effects.

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[21]. Research on doping TIs with various rare earth elements (such as Ce, Sm, Eu, Gd, etc.[22−26]) have been reported, and strong competition between anti-ferromagnetism and topological states was observed. Among all the RE elements, the isolated Ce atom has only one f electron, and it is ionized into the trivalent state (Ce3+) when diluted doped into other materials. This implies that Ce doped topological insulators might serve as a prototypical platform to study the interactions between f-electron and topological states and explore possible exotic physical phenomena.

In this work, we reported the electronic transport properties of Ce-doped Bi2Te3thin 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)2Te3at 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[27]. Our analysis showed that the surface conducting channels persisted to be two forxin the range from 0 to 0.02, and the conducting ability is suppressed as Ce concentration further increased, indicating the possible competition between magnetic order and topological states.

Fig. 1. (Color online) (a) Schematic crystal structure of Bi2Te3. (b) XRD patterns of (CexBi1-x)2Te3 thin films (x = 0, 0.01, 0.02, 0.03, 0.04, 0.05).

2. Experimental methods

Pristine and Ce-doped Bi2Te3thin films were grown on an Al2O3(0001) substrate by MBE, following the well-established three temperature methods[28]. The base pressure of the MBE chamber was better than 1 × 10-10mbar and rose to less than 5 × 10-10mbar during the growth. Standard Knudsen cells were used to evaporate Ce(3N), Bi(5N) and Te(5N)sources. The flux rates of the sources were calibrated byinsituquartz crystal microbalance (QCM). Ce doping was realized by co-evaporating Ce during the MBE growth of Bi2Te3thin films, and its concentration was carefully tuned by finely adjusting the evaporating temperature of the Ce source.During the growth, Bi and Te sources were kept at 530 and 315 °C, corresponding to flux rate of 0.199 and 0.779 Å/s, respectively. The Ce source was kept at 1280, 1310, 1340, 1360,and 1370 °C, to grow (CexBi1-x)2Te3thin films with various Ce concentration (x= 0, 0.01, 0.02, 0.03, 0.04, 0.05, respectively).ex-situX-ray diffraction (XRD) measurements were performed to characterize the out-of-plane lattice parameters.Transport measurements were performed with the standard four-probe method by a physical property measurement system (Quantum Design PPMS-9). High purity Indium (5N) was used as electrode contacts.

3. Results and discussions

Fig. 1(a) shows the crystal structure of Bi2Te3. Bi2Te3has 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)2Te3samples, where only the (00L) peaks of Bi2Te3are 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 parameterscperpendicular to the sample surface for all the samples were calculated. All thecvalues disperse within 3.045 ± 0.007 nm for all the samples, where 3.045 nm corresponds to the lattice parameter of the pristine Bi2Te3thin film. This means that the differences ofcbetween the Ce-doped and pristine Bi2Te3thin 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+[21].

Fig. 2. (Color online) (a) Resistivity of (CexBi1-x)2Te3 samples at different temperatures. Curves have been shifted for better visibility. (b) Normalized resistivity of (CexBi1-x)2Te3 at 3.5-25 K. (Solid lines: fits to Eq. (1).) (c) Magnetoresistance of (CexBi1-x)2Te3 at 4 K. (d) Magnetoresistance of(Ce0.04Bi0.96)2Te3 at 4-14 K.

Table 1. Fitting results of the parameters in Eq. (1). All parameters are in corresponding SI units.

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 ofAand increase ofB. In general, the low temperature transport behavior of (CexBi1-x)2Te3films 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 concentrationxand temperature forx= 0.04, respectively, with MR being defined as:

whereR(B) is the resistance measured under magnetic fieldB,R(0) is the resistance measured under zero field. Similar to the previous report[32], all samples have very low MR. WAL is a destructive quantum interference effect caused by two electron scattering trajectories protected by time reversal symmetry, which stems from the π berry phase[33]. Fig. 2(c) shows that the magnetoresistance near zero field increases rapidly with increasing field, and then gradually increases linearly under high field. This trend of magnetoresistance is a distinctive feature of weak anti-localization (WAL)[33], and WAL is gradually suppressed as the dopant concentration increases.It implies the possibilities that the introduced Ce impurity destroys the time reversal invariant symmetry which is crucial to the topological properties of the pristine Bi2Te3thin film.

The effect of WAL in MR can be described by the HLN model[27]. Figs. 3(a) and 3(b) show the magnetic conductance of samples with different concentration. For an ideal TI surface, the change of conductance under fieldBcan be expressed as:

whereG(B) is magnetoconductance,eis the electronic charge,h- is the reduced Planck constant,ψis the digamma function andBφis a characteristic magnetic field expressed as

Fig. 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 lφ and α with different dopant concentration. (d) The change of fitting parameters lφ and α of (Ce0.04Bi0.96)2Te3 and Bi2Te3 at different temperatures (solid line - fit to Eq. (5)).

Table 2. Parameters extracted by fitting magnetoconductance data with Eqs. (3) and (5). lφ is the phase coherence length, α is the coefficient in HLN formula and m is the power factor in Eq. (5).

whereashould be −0.5 for the topological surface states of symplectic universality class, andNis the number of independent conducting channels[27]. The relatively large values ofNandαmay be caused by the thick film's 3D WAL effect and multiple effective surfaces[32]. The fitting results show that the number of conducting channels is about 2 forx= 0, and it still maintains the same state forx= 0.01. However, the surface conducting channels are reduced forx> 0.01. It may indicate that the transportation ability of topological surface states has been suppressed forx> 0.01, which suggests there is a strong competition between magnetic order and the topological surface states forx= 0.01-0.02. The change ofNandαin the doped samples suggested that Ce may have brought certain magnetic order into the TI film, partially suppressing the topological surface states while not creating any additional bulk conducting channel in the body state. The relation betweenlφand temperature can be expressed by a power law[35]:

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 atT> 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 SPCLab Research Fund (No. WDZC201901) and the National Science Foundation of China (No. U1630248).