**4. Results and discussion**

#### **4.1. Magnetotransport measurement**

In our observation and study, we confirm the weak antilocalization (WAL) effect and the origin of this research phenomenon is investigated. If we consider, interaction between time-reversal pair of electronic waves, then there is a constructive interference of this two phase-coherent electronic waves propagating in opposite directions along the same closed path, in the absence of spin-orbit interaction, which gives rise to Weak-Localization (WL) effect. This effect gives results in increase of resistance or decrease of conductance. But the constructive interference is broken as a result of a phase difference between the two electronic waves, when the magnetic field is applied perpendicular to the plane of the system. By increasing the magnetic field, the increase of resistance can gradually be removed and consequently negative magnetoresistivity occurs. It finally gives rise to increase of the resistance or reduction in the conductance around zero magnetic field as the resistance correction influenced by this localization. In the presence of the spin-orbit interaction, there is a significant enhancement in the resistance, which is known as weak antilocalization effect [23, 24]. As far as the quality of the grown thin film is concerned, it has significant impact on the studies of transport properties of charge carriers and the weak antilocalization (WAL) behavior is an evaluation and indication for such improvement in the quality of the thin film, which manifests both the Dirac nature of the surface states in the bulk of Topological Insulators [8, 25] and strong spin-orbit interaction. If we Compare the 2D electron system, the 2D surface state of the three-dimensional topological insulator is different [26] as an odd number of Dirac points are considered to be encircled by Fermi arc [27, 28]. If we evaluate the topological insulator, its surface remains metallic and cannot be localized by disorder [29]. By Hikami et al. [30], the surface state of the topological insulator is well described. The **Figure 3a** shows the results of the magnetotransport measurement for the temperature ranges from T = 4 to 100 K and fields up to 9 T. The pronounced effect of WAL cusps are marked at low temperature between 4 and 10 K and in the low field regions as shown in the **Figure 3a**. Also we observe the enhancement of peak and the dip structure behaviors in the magnetoresistance, which is quite remarkable with decreasing temperatures. We have defined the normalized magnetoresistance (MR) as a function of magnetic field as MR = [[R (B) − R (0)]/R (0)] × 100%., where R (B) and R (0) are the resistances at field B and at zero field, respectively. The WAL cusps disappear, as the temperature is increased from 10 K onwards. We observe the WAL characteristic behaviors in the temperature ranges from 4 to 10 K as shown in the **Figure 3a**, and disappearance of WAL cusp from 10 K onwards. The MR curves seems to be quadratic like B dependence at low fields between 2 and 6 T and at higher fields from 6 T onwards, the MR follows linear like behavior and does not saturate. The quadratic growth here can be well explained and analyzed by semi-classical model, where the magnetic field drifts the conduction electrons and these conduction electrons are deflected by the Lorentz force. At T = 4 K, the thickness dependent WAL behavior is shown in the **Figure 3b** showing the WAL cusps for 10, 20, 50 nm thickness film, where as there is no observable WAL effect in ultra-thin films like 4 and 2 nm and the magnetoresistance (MR) curve attains to be flat w.r.t. magnetic field (B). The Fermi level is not in the gap but crosses the Surface State, as the film is thinned enough. Hence, the observed drastic suppression of the surface transport is likely due to an enhanced scattering of the carriers. The phase breaking length (Lϕ), which is of temperature dependence is extracted from the Hikami-Larkin-Nagaoka (HLN) model fit [30] for 10 nm thickness film is shown in the **Figure 3c**, which reveals the relatively large phase coherent length of 155.8 nm at 4 K, by fitting to the HLN model. The **Figure 3d** shows the Conductance change with respect to low magnetic field region with the HLN model fit for 10 nm thickness film.

surfaces with large area terraces. In **Figure 2b**, the dashed line drawn, reveals 10 nm thickness film and **Figure 2c** illustrates 10 nm thin film, by the formation of 4–5 stacked layer comprising of domains of triangular terraces. This suggests a favorable growth dynamics accounting

Te3

thin film.

absence of spirals on the terraces together with the shape of the terrace. The XRD experiments were further conducted to investigate the crystalline quality and orientations. With

In our observation and study, we confirm the weak antilocalization (WAL) effect and the origin of this research phenomenon is investigated. If we consider, interaction between time-reversal pair of electronic waves, then there is a constructive interference of this two phase-coherent

thin film. The result of the Angle Resolved Photo Emission Spectroscopy (ARPES),

O3

substrate, **Figure 2d** displays (003) family diffraction peak

substrate with the

for the high crystalline quality of Topological Insulator thin film on Al<sup>2</sup>

O3

implying strong surface states is shown in **Figure 2a**.

**Figure 2.** Characterization evidences of topological insulator Bi<sup>2</sup>

the diffraction peak from Al<sup>2</sup>

56 Heterojunctions and Nanostructures

**4. Results and discussion**

**4.1. Magnetotransport measurement**

from Bi<sup>2</sup>

Te3

found in silver rich or silver deficient chalcogenides [35] by the application of hydrostatic pressure. Hence, the gap less linear energy spectrum, which is suggested by this, such as the surface states of topological insulators is required for the observation of Linear MR in high fields. As there exists a bulk band gap for the bulk state, in this analysis, the possible bulk contribution in the quantum LMR is excluded. To the previous literature on topologi-

the **Figure 4**, in our study we report ≅ 3.2% MR value for temperatures ranging from 2 to 20 K. This characteristic feature of Linear MR (LMR), which has been found to be proportional to the magnetic field (B), is suitable for application in high magnetic field sensors.

For observing the temperature dependent resistance, we did the electrical measurements in our study. The longitudinal resistance (R) at zero magnetic field as a function of temperature is shown in the **Figure 5**. From the figure it is evident that, there is a decrease in the resistance in the temperature range from 300 to 240 K. The reason, we can consider with the bulk band

on SiC (0001) by MBE [36], where there is a progressive and systematic increase in the bulk band gap with reducing film thickness, it implies the quantum confinement of the film along the growth direction perpendicular to the substrate. As in our case, the grown film is thin enough, so the result is quite practical and evident at higher temperatures. The longitudinal resistance decreases as the temperature decreases from 240 to 4 K, resembling the metallic like behavior as observed in most of the topological Insulators [37]. Such trend of decrease with temperatures can be analyzed and explained by power law increase of mobility with temperatures and alleviated phonon scattering. The resistance attains to be constant value

**4.3. Temperature-dependent electrical resistance measurement**

thin film hall bar device at high fields.

gap. With the recent report on the ARPES measurements analysis of Bi<sup>2</sup>

nano-sheets [17], our results in linear MR are quite similar. As shown in

Observation of the Weak Antilocalization and Linear Magnetoresistance in Topological…

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59

Se3

thin film grown

cal insulator B<sup>2</sup>

**Figure 4.** LMR of Bi<sup>2</sup>

Te3

Te3

**Figure 3.** Results of Bi<sup>2</sup> Te3 thin films hall bar device with respect to magnetotransport.

#### **4.2. Linear magnetoresistance (LMR)**

We have observed linear magnetoresistance (LMR) behavior as shown in the **Figure 4** in our magnetotransport measurement study and it is found that the observed behavior is found to be seen in higher fields in the ranges from 6 to 9 T. In this linear region, there is a little variation in the slope of *d*MR/*dB* with respect to temperatures. We have observed these linear and non-saturating magnetoresistance features in the temperature ranges from 2 to 20 K. Previous literatures show the same trends and results where the high field LMR was found in single crystal of YPdBi Heusler topological insulator [31] and in Bi<sup>2</sup> Se3 nanoribbons [15]. The topological surface states are manifested by these results. The Linear MR at strong magnetic field is expected to occur in the quantum limit in the linear energy spectrum, in which all the electrons populated into single Landau level as per the theory, proposed by Abrikosov [32, 33]. This is governed and satisfied by the inequality relation (*h/2π*) *× Wc* > *Ef* , where (*h/2π*) *× Wc* is the cyclotron energy and *Ef* is the Fermi energy. So the weak temperature dependence is predicted by quantum LMR theory. However, recent literature shows that linear magnetoresistance (LMR) appears to occur in smaller magnetic field, where several Landau levels are populated by electrons [34]. There are some other research literatures, where it is analyzed that LMR at the high field as a consequence of closing of band gap under certain pressure. This profound alteration of band structure is Observation of the Weak Antilocalization and Linear Magnetoresistance in Topological… http://dx.doi.org/10.5772/intechopen.76900 59

**Figure 4.** LMR of Bi<sup>2</sup> Te3 thin film hall bar device at high fields.

**4.2. Linear magnetoresistance (LMR)**

Te3

**Figure 3.** Results of Bi<sup>2</sup>

58 Heterojunctions and Nanostructures

> *Ef* , where (*h/2π*) *× Wc*

(*h/2π*) *× Wc*

We have observed linear magnetoresistance (LMR) behavior as shown in the **Figure 4** in our magnetotransport measurement study and it is found that the observed behavior is found to be seen in higher fields in the ranges from 6 to 9 T. In this linear region, there is a little variation in the slope of *d*MR/*dB* with respect to temperatures. We have observed these linear and non-saturating magnetoresistance features in the temperature ranges from 2 to 20 K. Previous literatures show the same trends and results where the high field LMR was found in single crystal of YPdBi Heusler topological insulator [31] and in Bi<sup>2</sup>

thin films hall bar device with respect to magnetotransport.

nanoribbons [15]. The topological surface states are manifested by these results. The Linear MR at strong magnetic field is expected to occur in the quantum limit in the linear energy spectrum, in which all the electrons populated into single Landau level as per the theory, proposed by Abrikosov [32, 33]. This is governed and satisfied by the inequality relation

the weak temperature dependence is predicted by quantum LMR theory. However, recent literature shows that linear magnetoresistance (LMR) appears to occur in smaller magnetic field, where several Landau levels are populated by electrons [34]. There are some other research literatures, where it is analyzed that LMR at the high field as a consequence of closing of band gap under certain pressure. This profound alteration of band structure is

is the cyclotron energy and *Ef*

Se3

is the Fermi energy. So

found in silver rich or silver deficient chalcogenides [35] by the application of hydrostatic pressure. Hence, the gap less linear energy spectrum, which is suggested by this, such as the surface states of topological insulators is required for the observation of Linear MR in high fields. As there exists a bulk band gap for the bulk state, in this analysis, the possible bulk contribution in the quantum LMR is excluded. To the previous literature on topological insulator B<sup>2</sup> Te3 nano-sheets [17], our results in linear MR are quite similar. As shown in the **Figure 4**, in our study we report ≅ 3.2% MR value for temperatures ranging from 2 to 20 K. This characteristic feature of Linear MR (LMR), which has been found to be proportional to the magnetic field (B), is suitable for application in high magnetic field sensors.

#### **4.3. Temperature-dependent electrical resistance measurement**

For observing the temperature dependent resistance, we did the electrical measurements in our study. The longitudinal resistance (R) at zero magnetic field as a function of temperature is shown in the **Figure 5**. From the figure it is evident that, there is a decrease in the resistance in the temperature range from 300 to 240 K. The reason, we can consider with the bulk band gap. With the recent report on the ARPES measurements analysis of Bi<sup>2</sup> Se3 thin film grown on SiC (0001) by MBE [36], where there is a progressive and systematic increase in the bulk band gap with reducing film thickness, it implies the quantum confinement of the film along the growth direction perpendicular to the substrate. As in our case, the grown film is thin enough, so the result is quite practical and evident at higher temperatures. The longitudinal resistance decreases as the temperature decreases from 240 to 4 K, resembling the metallic like behavior as observed in most of the topological Insulators [37]. Such trend of decrease with temperatures can be analyzed and explained by power law increase of mobility with temperatures and alleviated phonon scattering. The resistance attains to be constant value

**Acknowledgements**

are thankfully acknowledged.

**Author details**

Taiwan (ROC)

Rajasthan, India

**References**

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Communications. 2017;**8**:14081

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Sunil Kumar Pradhan<sup>1</sup>

The help and resources received from Department of Engineering and System Science, National Tsing Hua University, Taiwan and Central Electronics Engineering Research Institute, Pilani

Observation of the Weak Antilocalization and Linear Magnetoresistance in Topological…

http://dx.doi.org/10.5772/intechopen.76900

61

1 Department of Engineering and System Science, National Tsing Hua University, Hsinchu,

2 Microwave Tube Division, CSIR-Central Electronics Engineering Research Institute, Pilani,

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\* and Ranjan Barik<sup>2</sup>

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\*Address all correspondence to: sunilpradha@gmail.com

**Figure 5.** Temperature-dependent electrical resistance measurement result of Bi<sup>2</sup> Te3 hall bar device.

in the temperature range between 4 and 2 K. The reason, where the transport is primarily governed by combination of surface states and impurity band conduction is considered to be bulk carrier's freeze out effect. To the previous literature on Bi<sup>2</sup> Se3 grown on Si substrate [38], this temperature dependent result is quite similar. The Current-Voltage curves at different temperature, indicating ohmic contacts over the whole range of temperatures is shown in the insert in the **Figure 5**.
