Synthesis and Study of Magnetic and Magneto-transport properties of some topological Insulators

Spin-orbit induced topological insulator (TI), a new type of materials, which are insulating in bulk but conducting at the surface, has attracted a large interest in the area of condensed matter physics. This is due to the gapless edge or spin resolved surface states (SS), which are topologically protected by time reversal symmetry (TRS). The spins are locked in the perpendicular direction of momentum due to the strong spin-orbit interaction. As a matter of fact, electrical conduction is robust against backscattering at the edge states or on the surfaces in TIs. These special helical spin properties of electrons make TIs interesting and relevant for new physics. Since the locking of spin and orbital states is protected by time reversal symmetry, the delocalized surface states are unaffected from nonmagnetic dopants and defects [1, 2]. Moreover the coupling of the spin and orbital angular momentum of an electron leads to an inversion of the band gap. The possibility of Majorana Fermions, topological superconductivity, novel magnetoelecric quantum states, the absence of backscattering from nonmagnetic impurities, exciton condensation, magnetic monopole, and anomalous quantum Hall effect types of exotic properties in TIs are very promising in the application of spintronic devices and quantum computing [1, 2]. Topological surface states in Bi2Te3 and Bi2Se3 with only one mass less Dirac cone on each surface were studied using Angle-resolved photoemission spectroscopy (ARPES) [1]. Quantum magneto-transport phenomenon such as weak antilocalization, Aharonov-Bohm oscillations and quantum conductance fluctuations are associated with surface states. The time reversal symmetry protection of the Dirac point can be lifted by magnetic dopant, resulting in a band gap due to the separation in the upper and lower branches of the Dirac cone [1]. Both two and three dimensional versions of topological insulators have been theoretically predicted [2] and prepared in laboratories [3, 4]. It has been theoretically predicted that surface state of a topological insulator show a linear energy-momentum relation similar to Dirac fermions. Such type of backscattering free surface with locked spin and momentum may serve as a platform for both fundamental physics and technological applications like spintronics or quantum computing.
An overview of some of the essential properties of these new types of materials as well as related properties of quantum Hall insulators is given. The purpose of this chapter was to give an introduction to some of the most important properties and to provide information on the analogies and differences between the different systems.
Due to the ease in preparation, large observable bulk band gap, Dirac cone on the surfaces, interesting transport and magnetic properties, the materials  Bi2Te3, Sb2Te3 and Bi2Se3 are the most studied 3D topological insulators now a days. Our work is on Bi2Te3 and Sb2Te3 among three materials mentioned above.
Structural, resistivity, magneto-transport and magnetic properties of Bi2CuxTe3-x (x=0, 0.03, 0.06) samples have been investigated. Single crystallinity was further confirmed by Laue pattern. It was also observed that Cu doping tunes the carrier from n to p type which is attributed due to the TeBi and BiTe antisites effects. With Cu doping, resistivity was increasing which may be due to the extra scattering centers produced due to Cu. Subnikov de Hass oscillation has been studied. QAHE has been observed in Hall analysis of the doped samples which was an indication of magnetic ordering in doped samples. Magnetization vs. temperature (MT) and Magnetization vs. field (MH) experiment also confirm the presence of ferromagnetism in Cu doped Bi2Te3 samples. 
Structural, resistivity, thermoelectric power, magneto-transport and magnetic properties of Bi2Cu0.15Te2.85 topological insulators have been investigated. The tuning of charge carriers from n to p type by Cu doping at Te sites of Bi2Te3 is observed both from Hall effect and thermoelectric power measurements. Carrier mobility decreased with the doping of Cu which provides evidence of the movement of Fermi level from bulk conduction band to the bulk valence band. Thermoelectric power was also increasing with doping of Cu. In investigation, we have found room temperature ferromagnetism in x=0.15 sample, additionally, materials with large magnetoresistance (MR) are of great interest from the application point of view as well as for fundamental research. The observed value of MR was as large as 1000% in x=0.15 sample. Presence of QAHE even at 300K was also supporting the presence of ferromagnetism in Cu doped sample. 
Moreover, electrical resistivity, thermoelectric power, magnetotransport and magnetization of Zn doped Bi2Te3 Topological Insulator were studied. Electrical conductivity was enhanced at higher Zn concentration, and the carrier mobility estimated from Hall data reaches a remarkable value of ~7200 cm2 V-1S-1. Large positive magnetoresistance (MR~400%) was observed in high mobility samples. Interestingly, it was found that the coupling between electrical conductivity and Seebeck coefficient was broken for higher Zn doped Bi2Te3 samples which effectively enhances the thermoelectric power factor (from 2.1 mW/K2m for Bi2Te3 to 4.64 mW/K2m for Zn doped Bi2Te3). 
We have also investigated the quantum oscillations both from magneto-transport and magnetic measurements in Cu doped Sb2Te3 sample. Although Shubnikov–de Haas (SdH) oscillations are a powerful means to distinguish between bulk and surface charge carriers via their angle dependence, but their analysis and interpretation remain controversial. On the other hand, the de-Haas van Alphen (dHvA) oscillation study proves a direct way to probe in detail the bulk, full three dimensional Fermi surface, and can also resolve the strength of the many body interactions at the Fermi level. Moreover, for the case of Topological Insulators surface states are not magnetic. Therefore, from the magnetization measurement we mainly observe the bulk property. As a matter of fact, from both the SdH and dHvA oscillations the bulk and surface states in TI can be distinguished without any angle dependent measurements. The magneto-transport and magnetization measurements of Sb1.90Cu0.10Te3 were performed at different temperatures and different fields. Magneto-transport measurement at high field indicated the coexistence of both bulk and surface states whereas magnetization study at high field shows the existence of bulk state.  Lifshitz-Kosevich and first Fourier transform (FFT) analysis supports the signature of bulk and surface states.
Structural and magnetic properties of Co doped Sb2Te3 topological insulators have been investigated. Surface morphology has been studied using scanning electron microscope (SEM) and atomic force microscope (AFM). X-ray photo electron spectroscopy (XPS) study was indicating the mixed states of Co in Co2+ and Co3+. Magnetic study confirmed that the substitution of Co in Sb2Te3 not only tune the materials from diamagnetic to antiferromagnetic (even at room temperature) but also proposed a promising materials for antiferromagnetic TI which may be useful even for room temperature applications.
In next section, conclusions of entire work along with the future prospective of our work have been discussed.

References:
1.	M. Z. Hasan, and C. L. Kane, “Colloquium: topological insulators,” Reviews of Modern Physics, vol. 82, no. 4, pp. 3045, 2010.
2.	B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science, vol. 314, no. 5806, pp. 1757-1761, 2006.
3.	M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, “Quantum spin Hall insulator state in HgTe quantum wells,” Science, vol. 318, no. 5851, pp. 766-770, 2007.
4.	Y. Chen, J. G. Analytis, J.-H. Chu, Z. Liu, S.-K. Mo, X.-L. Qi, H. Zhang, D. Lu, X. Dai, and Z. Fang, “Experimental realization of a three-dimensional topological insulator, Bi2Te3,” science, vol. 325, no. 5937, pp. 178-181, 2009