**5.1. The epitaxial growths of bismuth chalcogenide thin films**

Topological insulator (TI), a new class of quantum matter, possesses insulating in bulk and robust gapless topological surface states (TSSs) in which the spin of the electron is locked perpendicular to its momentum by strong spin-orbit interaction [6, 50, 51]. TIs have been identified as promising materials for exploiting exciting physics and developing potential applications in optoelectronics, spintronics, and quantum computations [50–54]. Dirac fermions in TIs have also been studied by angle-resolved photoemission spectroscopy [55–57] or scanning tunneling microscopy [58, 59]. In magnetotransport studies, TSS can be studied by weak antilocalization (WAL) [4, 9, 60, 61] and Shubnikov-de Haas oscillations [3, 62].

Topological insulator bismuth chalcogenide thin films have been grown epitaxially on various substrates using PLD. Onose et al. reported the epitaxial growth of Bi2Se3 thin films on InP (1 1 1) substrates (the lattice mismatch of 0.2%) [7]. A designed Se-rich target with an atomic ratio of Bi:Se = 2:8 was used to compensate for the issue of high doping carriers and to avoid unwanted Se-deficient phases. The pulsed laser power and repetition were 140 mJ and 10–20 Hz, respectively. The Bi2Se3 films obtained a small full-width at half-maximum (FWHM) for the XRD rocking curve of (0 0 0 6) peak. The surfaces of the films are composed of triangular pyramids with step-and-terrace structures, reflecting the hexagonal symmetry of Bi2Se3. The epitaxial relationship is Bi2Se3 (0 0 1) || InP (1 1 1) and Bi2Se3 [1 1 2 0] InP [0 0 1]. Le et al. reported the epitaxial growth of Bi2Se3 films on SrTiO3 (STO) (1 1 1) substrates using PLD at *T*<sup>S</sup> of 300 and 350°C [63]. The PLD conditions were the pulse fluence of 3.7 J/cm2 , helium pressure of 40 Pa (300 mTorr), and repetition rate of 2 Hz. The laser source was KrF excimer laser (*λ* = 248 nm, duration 20 ns). By comparing the Bi2Se3 {0 1 5} and STO {2 0 0} diffraction peaks, the epitaxial relationship between the film and substrate was determined to be Bi2Se3 (0 0 1) || STO (1 1 1) and Bi2Se3 [1 1 0] || STO [1− 1 0] [63].

**Figure 10** presents the PLD epitaxial growths of Bi2Te3, Bi2Se3, and Bi3Se2Te thin films on largemisfit substrates [9, 53, 64]. The PLD conditions for growing Bi2Te3 films on STO (1 0 0) were as follows: substrate temperature of 300°C; helium ambient pressure of 40 Pa; repetition rate of 2 Hz; pulsed fluence of approximately 3.4 J/cm2 . As shown in **Figure 10a**, a *φ*-scan was conducted on the (0 1 5) plane of a 200-nm-thick Bi2Te3 film and the (1 1 1) plane of an STO (1 0 0) substrate in skew symmetric geometry by tilting the samples. The in-plane orientation of a hexagonal *h*-Bi2Te3/STO (1 0 0) film displayed a 12-fold symmetry instead of the expected six-

In contrast, the 200-nm-thick Bi3Se2Te films with *D* of 16.1–25.1 nm grown at a larger *P*He range of 2.0 × 10−5 to 6.5 × 10−1 Torr exhibited the nanomechanical followed Hall-Petch relationship [44, 49]. The hardness and Young's modulus of the Bi3Se2Te thin films monotonically increased with increasing *P*He because of a corresponding decrease in grain sizes (**Figure 9a**–**c**). **Figure 9d** shows that hardness (*H*) increased linearly with *D−1/2* (where *D* is the grain size of the Bi3Se2Te films in the nanoscale regime) which is the typical Hall-Petch relationship [44, 49]. This is because the multiplication and mobility of dislocations are hindered by reducing the grain size [44]. It is reasonable for the observed phenomenon when the present grain sizes ranged between 25.1 and 16.1 nm which is larger than the typical critical *Dc* of 10 nm [44, 49]. It is demonstrated that the hardness and Young's modulus of the Bi2Te3 and Bi3Se2Te thin films can be enhanced by proper selection of the ambient pres-

70 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

**5. Topological insulator bismuth chalcogenide thin films and their novel**

Topological insulator (TI), a new class of quantum matter, possesses insulating in bulk and robust gapless topological surface states (TSSs) in which the spin of the electron is locked perpendicular to its momentum by strong spin-orbit interaction [6, 50, 51]. TIs have been identified as promising materials for exploiting exciting physics and developing potential applications in optoelectronics, spintronics, and quantum computations [50–54]. Dirac fermions in TIs have also been studied by angle-resolved photoemission spectroscopy [55–57] or scanning tunneling microscopy [58, 59]. In magnetotransport studies, TSS can be studied by weak antilocalization (WAL) [4, 9, 60, 61] and Shubnikov-de Haas oscillations [3,

Topological insulator bismuth chalcogenide thin films have been grown epitaxially on various substrates using PLD. Onose et al. reported the epitaxial growth of Bi2Se3 thin films on InP (1 1 1) substrates (the lattice mismatch of 0.2%) [7]. A designed Se-rich target with an atomic ratio of Bi:Se = 2:8 was used to compensate for the issue of high doping carriers and to avoid unwanted Se-deficient phases. The pulsed laser power and repetition were 140 mJ and 10–20 Hz, respectively. The Bi2Se3 films obtained a small full-width at half-maximum (FWHM) for the XRD rocking curve of (0 0 0 6) peak. The surfaces of the films are composed of triangular pyramids with step-and-terrace structures, reflecting the hexagonal symmetry of Bi2Se3. The epitaxial relationship is Bi2Se3 (0 0 1) || InP (1 1 1) and Bi2Se3 [1 1 2 0] InP [0 0 1]. Le et al. reported the epitaxial growth of Bi2Se3 films on SrTiO3 (STO) (1 1 1) substrates using PLD at *T*<sup>S</sup> of 300 and 350°C [63]. The PLD conditions were the pulse

laser source was KrF excimer laser (*λ* = 248 nm, duration 20 ns). By comparing the Bi2Se3 {0 1 5} and STO {2 0 0} diffraction peaks, the epitaxial relationship between the film and sub-

strate was determined to be Bi2Se3 (0 0 1) || STO (1 1 1) and Bi2Se3 [1 1 0] || STO [1

, helium pressure of 40 Pa (300 mTorr), and repetition rate of 2 Hz. The

<sup>−</sup> 1 0] [63].

**5.1. The epitaxial growths of bismuth chalcogenide thin films**

sure in PLD growths.

**properties**

62].

fluence of 3.7 J/cm2

**Figure 10.** Bi2Te3 films grown on SrTiO3 (1 0 0) substrates [53]: (a) XRD *φ*-scan patterns of the 200-nm-thick Bi2Te3 (0 1 5) plane and the SrTiO3 (1 1 1) plane; (b) schematics of the in-plane arrangement of *h*-Bi2Te3 / SrTiO3 (1 0 0). Bi2Se3 films grown on *c*-plane sapphire substrates [64]; (c) in-plane *φ*-scan 011 5 planes of the film and 011 2 planes of the substrate; (d) the schematic depicting twin/domain growth: in one case, the basal plane of Bi2Se3 is aligned with that of Al2O3, and in the other, there is a rotation of 60°/180°. Bi3Se2Te films grown on *c*-plane sapphire substrates [9]; (e) *φ*-scan patterns of hexagonal *h*-Bi3Se2Te thin films grown on Al2O3 (0 0 0 1) substrates; and (f) schematics of the inplane arrangement of hexagonal *h*-Bi3Se2Te/*h*-Al2O3 (0 0 0 1).

fold symmetry of the (0 1 5) plane in Bi2Te3. **Figure 10b** shows a schematic drawing of the inplane atomic arrangement between an *h*-Bi2Te3 film and an STO (1 0 0) substrate. Since the principal crystallographic orientations of *h*-Bi2Te3 films grown on STO (1 0 0) substrates can be aligned along either the STO [1 0 0] or STO [0 1 0] directions, the in-plane arrangements result in an observed 12-fold symmetry. The angle differences between STO [0 1 0] and the two orientations of *h*-Bi2Te3 [1 1 0] were 30° and 0°, respectively, as shown in **Figure 10b**. In other words, the in-plane relationships were Bi2Te3 [1 1 0] || STO [0 1 0] and Bi2Te3 [1 0 0] || STO [1 0 0]. Lee et al. reported epitaxial growth via domain matching epitaxy of Bi2Se3 thin films on Al2O3 (0 0 0 1) substrates with over 13% lattice misfit and a critical thickness of less than one monolayer [64]. A relatively low repetition rate of 0.2 Hz and low *T*S of 250°C are key parameters of the PLD growth to achieving high-quality Bi2Se3 epitaxial films. **Figure 10c** shows *φ*scan XRD results performed on 011 5 planes of the film and 011 2 planes of the substrate. Clearly, the presence of six peaks corresponding to the Bi2Se3 011 5 planes confirmed the epitaxy. A schematic depicting twin/domain growth and direction in the study is illustrated in **Figure 10d** [64]. In one case, the Bi2Se3 basal plane is aligned with that of Al2O3, and in the other, there is a rotation of 60°/180°. The epitaxial relationships are written as (0 0 0 1) Bi2Se3 || (0 0 0 1) Al2O3 (out-of-plane) and [2 1 1 0] Bi2Se3 || [2 1 1 0] Al2O3 or [2 1 1 0] Bi2Se3 || [1 1 2 0] Al2O3 (in-plane). **Figure 10e** shows the typical *φ*-scan patterns of hexagonal *h*-Bi3Se2Te/*h*-Al2O3 (0 0 0 1) [9]. With the skew symmetric geometry, the *φ*-scan measurements were performed on the (1 1 6) plane of Al2O3 substrates and the (1 1 12) plane of Bi3Se2Te films. As shown in **Figure 10e**, the in-plane orientations of both Al2O3 (1 1 6) and Bi3Se2Te (1 1 12) exhibited six-fold symmetries with a 30° difference. **Figure 10f** illustrates the in-plane atomic arrangement between *h*-Bi3Se2Te and *h*-Al2O3 (0 0 0 1). The epitaxial relationship between the films and substrates is (0 0 0 1) Bi3Se2Te || (0 0 0 1) Al2O3 and [1 1 0] Bi3Se2Te || [2 1 0] Al2O3 [9]. This in-plane orientation was established to obtain the optimal lattice matching.

### **5.2. Magnetotransport properties of bismuth chalcogenide thin films**

The weak antilocalization (WAL) which is a negative quantum correction to classical MR caused by the wave nature of electrons is used as a signature of TSS. In TIs, WAL is induced by both the helicity of the surface state and the spin-orbit coupling of bulk [4, 61, 65, 66]. In a low *B* field, the 2D WAL MR of a system with strong spin-orbit interaction can be described using the Hikami-Larkin-Nagaoka model [65], which is [4, 60, 61]

$$\frac{\Delta R\_{\rm w}(B)}{\left[R\_{\rm w}(0)\right]^2} = -\alpha \frac{e^2}{2\pi^2 \hbar} \left[\Psi\left(\frac{1}{2} + \frac{B\_{\phi}}{B}\right) - \ln\left(\frac{B\_{\phi}}{B}\right)\right] \tag{8}$$

where W is the sheet resistance, W <sup>=</sup> W() − W(0), () is the digamma function, = ℏ/(4 2) is a magnetic field varying with the coherence length , *α* is a parameter and reflects the number of conduction channels. In a 3D TI, *α* = −1/2 for a single coherent transport channel in the 2D surface states, and *α* = −1 for two independent coherent transport channels with similar *Lφ* in the 2D surface states [60, 65].

fold symmetry of the (0 1 5) plane in Bi2Te3. **Figure 10b** shows a schematic drawing of the inplane atomic arrangement between an *h*-Bi2Te3 film and an STO (1 0 0) substrate. Since the principal crystallographic orientations of *h*-Bi2Te3 films grown on STO (1 0 0) substrates can be aligned along either the STO [1 0 0] or STO [0 1 0] directions, the in-plane arrangements result in an observed 12-fold symmetry. The angle differences between STO [0 1 0] and the two orientations of *h*-Bi2Te3 [1 1 0] were 30° and 0°, respectively, as shown in **Figure 10b**. In other words, the in-plane relationships were Bi2Te3 [1 1 0] || STO [0 1 0] and Bi2Te3 [1 0 0] || STO [1 0 0]. Lee et al. reported epitaxial growth via domain matching epitaxy of Bi2Se3 thin films on Al2O3 (0 0 0 1) substrates with over 13% lattice misfit and a critical thickness of less than one monolayer [64]. A relatively low repetition rate of 0.2 Hz and low *T*S of 250°C are key parameters of the PLD growth to achieving high-quality Bi2Se3 epitaxial films. **Figure 10c** shows *φ*scan XRD results performed on 011 5 planes of the film and 011 2 planes of the substrate. Clearly, the presence of six peaks corresponding to the Bi2Se3 011 5 planes confirmed the epitaxy. A schematic depicting twin/domain growth and direction in the study is illustrated in **Figure 10d** [64]. In one case, the Bi2Se3 basal plane is aligned with that of Al2O3, and in the other, there is a rotation of 60°/180°. The epitaxial relationships are written as (0 0 0 1) Bi2Se3 || (0 0 0 1) Al2O3 (out-of-plane) and [2 1 1 0] Bi2Se3 || [2 1 1 0] Al2O3 or [2 1 1 0] Bi2Se3 || [1 1 2 0] Al2O3 (in-plane). **Figure 10e** shows the typical *φ*-scan patterns of hexagonal *h*-Bi3Se2Te/*h*-Al2O3 (0 0 0 1) [9]. With the skew symmetric geometry, the *φ*-scan measurements were performed on the (1 1 6) plane of Al2O3 substrates and the (1 1 12) plane of Bi3Se2Te films. As shown in **Figure 10e**, the in-plane orientations of both Al2O3 (1 1 6) and Bi3Se2Te (1 1 12) exhibited six-fold symmetries with a 30° difference. **Figure 10f** illustrates the in-plane atomic arrangement between *h*-Bi3Se2Te and *h*-Al2O3 (0 0 0 1). The epitaxial relationship between the films and substrates is (0 0 0 1) Bi3Se2Te || (0 0 0 1) Al2O3 and [1 1 0] Bi3Se2Te || [2 1 0] Al2O3 [9]. This in-plane orientation was established to obtain the optimal lattice

72 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

**5.2. Magnetotransport properties of bismuth chalcogenide thin films**

using the Hikami-Larkin-Nagaoka model [65], which is [4, 60, 61]

2 2

a

[ (0)] 2 2

W

W

2

p

( ) <sup>1</sup> ln

*RB e B B R B B*

The weak antilocalization (WAL) which is a negative quantum correction to classical MR caused by the wave nature of electrons is used as a signature of TSS. In TIs, WAL is induced by both the helicity of the surface state and the spin-orbit coupling of bulk [4, 61, 65, 66]. In a low *B* field, the 2D WAL MR of a system with strong spin-orbit interaction can be described

where W is the sheet resistance, W <sup>=</sup> W() − W(0), () is the digamma function,

reflects the number of conduction channels. In a 3D TI, *α* = −1/2 for a single coherent transport

f

2) is a magnetic field varying with the coherence length , *α* is a parameter and

 f

<sup>D</sup> é ù æ ö æö =- Y + - ê ú ç ÷ ç÷ <sup>h</sup> ë û è ø èø (8)

matching.

= ℏ/(4

The typical magnetoresistance (MR) results of some bismuth chalcogenides (i.e., Bi2Te3, Bi2Se3, and Bi3Se2Te) thin films grown by PLD are presented in **Figure 11** [9, 64, 67]. The Bi2Te3, Bi2Se3,

**Figure 11.** Magnetoresistance (MR) results of the Bi2Te3, Bi2Se3, and Bi3Se2Te thin films grown by PLD [9, 64, 67]. (a and e) The MR (*B* = ±1 T) of a 27-nm-thick Bi2Te3 and a 200-nm-thick Bi3Se2Te films grown on Al2O3 (0 0 0 1) substrates. (b and f) Variation in the extracted electron dephasing length *Lφ* and parameter −*α* of the films as a function of temperatures. (c and d) MR of the epitaxial Bi2Se3 films grown on Al2O3 (0 0 0 1) substrates at *T*S = 250°C as a function of temperatures [64]. The solid green lines in (a) and (e) in low *B* are the theoretical predictions of 2D weak antilocalization (WAL) using Eq. (8).

and Bi3Se2Te thin films were grown on Al2O3 (0 0 0 1) substrates using PLD at *T*<sup>S</sup> of 225, 250, and 250°C, respectively [9, 64, 67]. The WAL effect which presents as a sharp increase in resistance when *B* increases in the low magnetic field *B* regime is clearly observed on the films. **Figure 11a**, **b**, **e** and **f** show MR curves at several temperatures (*T*) and the extracted *α*(*T*) and () values using Eq. (8) for the 27-QL (~27 nm)-thick Bi2Te3 and 200-nm-thick Bi3Se2Te thin films [9, 67]. At 2 K, *Lφ* are 158.1 and 195.2 nm, and *Lφ* decreases monotonically with increasing *T*, obeying the power laws, as *Lφ* ~ *T*−0.50 and *Lφ* ~ *T*−0.79 for the Bi2Te3 and Bi3Se2Te films, respectively (**Figure 11b** and **f**). Theoretically, the result of *Lφ* ~ *T*−0.50 observed in the 27-QL-thick Bi2Te3 thin film indicates the predominant electron-electron scattering in 2D weakly disordered systems. The *Lφ* ~ *T*−0.79 is closed to the *Lφ ~ T*−0.75 for 3D systems, if e-e scattering is the dominant dephasing source [9]. The electron screening effect in 3D system is more effective than that in 2D systems. However, the e-e scattering is strongly weakened with high carrier densities (*n* = 1020 cm−3 for the Bi3Se2Te films [9]). In 3D disordered conductors (namely, in the bulk state), dephasing by electron-phonon (e-ph) scattering would be significant and dominant. The e-ph scattering also causes a faster decay rate on *Lφ*, that is, *Lφ ~ T*−1.0 [68]. Additionally, the combination of 2D e-e scattering in the TSS thin layer and e-ph scattering in the bulk would further result in the *Lφ* ~ *T*−0.79. Consequently, e-ph scattering could be the force of channel separation as temperatures increase. It is worthy of mentioning that the MR result is a signature (not conclusive evidence) for the presence of TSS on Bi3Se2Te films. Further theoretical calculations and experiments are needed for reaching a final conclusion.

**Figure 11b** and **f** also present the –*α*(*T*) results of the Bi2Te3 and Bi3Se2Te films. The –*α* values of the Bi2Te3 film increase with increasing *T* from 0.43 at 2 K to 0.45 at 10 K, indicating the existence of a single coherent transport channel (i.e., likely a single surface state) [61]. Meanwhile, the –*α* values of the 200-nm-thick Bi3Se2Te film increase with increasing *T* from 0.5 at 2 K to 0.85 at 10 K and to 0.71 at 15 K, suggesting increased channel separation with *T* [69]. In WAL, the independent phase-coherent channels occur when the carriers in one channel lose phase coherence before being scattered into the other channel.

In **Figure 11c**, the MR (*B*,*T*) of a 50-nm-thick Bi2Se3 film was measured with *B* perpendicular to the film plane and ranging from −9 T to +9 T. At low *B* and T, the distinctive dips of WAL are clearly observed. The WAL effect results from strong spin-orbit coupling, showing the absence of backscattering giving rise to the destructive interference between the two time reversal symmetry loops when there is no magnetic field [64]. Resistance increases sharply with increasing *B* because the quantum interference is destroyed and backscattering increases (**Figure 11c**). **Figure 11d** is the enlarged MR at low *B* (–2 T to +2 T), and it reveals the existence of WAL as a function of *T* in a discernible way [64]. WAL gradually weakens as temperature increases, eventually disappearing entirely at *T* = 48 K; thus, the dependence on *B* is quadraticlike at low field. The MR cusp feature at low *B* is broadened and finally disappears with increasing temperature owing to the decrease in the phase coherence length. In addition to the WAL effect, **Figure 11c** shows a 2D, non-saturating linear MR at high *B*, which usually occurs with several TI materials of Bi2Se3 [70], Bi2Te3 [71], Bi2Te2Se [72], and Bi3Se2Te [9]. Theoretical models propose that the linear MR can appear in the gapless linear-dispersive energy spectrum when only the first landau level is filled [73, 74], or in the presence of both the gapless linear spectrum and Landau level overlaps [75]. Noticeably, the WAL and linear MR simultaneously reflect the 3D contribution of spin-orbit coupling in bulk and the Dirac nature of the 2D surface states. Because the magneto transport is a bulk sensitive measurement, it remains a major challenge to directly probe the topological nature [64].

and Bi3Se2Te thin films were grown on Al2O3 (0 0 0 1) substrates using PLD at *T*<sup>S</sup> of 225, 250, and 250°C, respectively [9, 64, 67]. The WAL effect which presents as a sharp increase in resistance when *B* increases in the low magnetic field *B* regime is clearly observed on the films. **Figure 11a**, **b**, **e** and **f** show MR curves at several temperatures (*T*) and the extracted *α*(*T*) and () values using Eq. (8) for the 27-QL (~27 nm)-thick Bi2Te3 and 200-nm-thick Bi3Se2Te thin films [9, 67]. At 2 K, *Lφ* are 158.1 and 195.2 nm, and *Lφ* decreases monotonically with increasing *T*, obeying the power laws, as *Lφ* ~ *T*−0.50 and *Lφ* ~ *T*−0.79 for the Bi2Te3 and Bi3Se2Te films, respectively (**Figure 11b** and **f**). Theoretically, the result of *Lφ* ~ *T*−0.50 observed in the 27-QL-thick Bi2Te3 thin film indicates the predominant electron-electron scattering in 2D weakly disordered systems. The *Lφ* ~ *T*−0.79 is closed to the *Lφ ~ T*−0.75 for 3D systems, if e-e scattering is the dominant dephasing source [9]. The electron screening effect in 3D system is more effective than that in 2D systems. However, the e-e scattering is strongly weakened with high carrier densities (*n* = 1020 cm−3 for the Bi3Se2Te films [9]). In 3D disordered conductors (namely, in the bulk state), dephasing by electron-phonon (e-ph) scattering would be significant and dominant. The e-ph scattering also causes a faster decay rate on *Lφ*, that is, *Lφ ~ T*−1.0 [68]. Additionally, the combination of 2D e-e scattering in the TSS thin layer and e-ph scattering in the bulk would further result in the *Lφ* ~ *T*−0.79. Consequently, e-ph scattering could be the force of channel separation as temperatures increase. It is worthy of mentioning that the MR result is a signature (not conclusive evidence) for the presence of TSS on Bi3Se2Te films. Further theoretical calculations

74 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

**Figure 11b** and **f** also present the –*α*(*T*) results of the Bi2Te3 and Bi3Se2Te films. The –*α* values of the Bi2Te3 film increase with increasing *T* from 0.43 at 2 K to 0.45 at 10 K, indicating the existence of a single coherent transport channel (i.e., likely a single surface state) [61]. Meanwhile, the –*α* values of the 200-nm-thick Bi3Se2Te film increase with increasing *T* from 0.5 at 2 K to 0.85 at 10 K and to 0.71 at 15 K, suggesting increased channel separation with *T* [69]. In WAL, the independent phase-coherent channels occur when the carriers in one channel lose

In **Figure 11c**, the MR (*B*,*T*) of a 50-nm-thick Bi2Se3 film was measured with *B* perpendicular to the film plane and ranging from −9 T to +9 T. At low *B* and T, the distinctive dips of WAL are clearly observed. The WAL effect results from strong spin-orbit coupling, showing the absence of backscattering giving rise to the destructive interference between the two time reversal symmetry loops when there is no magnetic field [64]. Resistance increases sharply with increasing *B* because the quantum interference is destroyed and backscattering increases (**Figure 11c**). **Figure 11d** is the enlarged MR at low *B* (–2 T to +2 T), and it reveals the existence of WAL as a function of *T* in a discernible way [64]. WAL gradually weakens as temperature increases, eventually disappearing entirely at *T* = 48 K; thus, the dependence on *B* is quadraticlike at low field. The MR cusp feature at low *B* is broadened and finally disappears with increasing temperature owing to the decrease in the phase coherence length. In addition to the WAL effect, **Figure 11c** shows a 2D, non-saturating linear MR at high *B*, which usually occurs with several TI materials of Bi2Se3 [70], Bi2Te3 [71], Bi2Te2Se [72], and Bi3Se2Te [9]. Theoretical models propose that the linear MR can appear in the gapless linear-dispersive energy spectrum when only the first landau level is filled [73, 74], or in the presence of both the gapless linear

and experiments are needed for reaching a final conclusion.

phase coherence before being scattered into the other channel.
