In-depth analysis of anisotropic magnetoconductance in Bi₂Se₃ thin films with electron–electron interaction corrections

Abstract

A combination of out-of-plane (OOP) and in-plane (IP) magnetoconductance (MC) study in topological insulators (TI) is often used as an experimental technique to probe weak anti-localization (WAL) response of the topological surface states (TSSs). However, in addition to the above WAL response, weak localization (WL) contribution from conducting bulk states are also known to coexist and contribute to the overall MC; a study that has so far received limited attention. In this article, we accurately extract the above WL contribution by systematically analyzing the temperature and magnetic field dependency of conductivity in Bi 2 Se 3 films. For accurate analysis, we quantify the contribution of electron-electron interactions to the measured MC which is often ignored in the WAL studies. Moreover, we show that the WAL effect arising from the TSSs with finite penetration depth, for OOP and IP magnetic field can together explain the anisotropic magnetoconductance (AMC) and, thus, the investigated AMC study can serve as a useful technique to probe the parameters like phase coherence length and penetration depth that characterise the TSSs in 3D TIs. We also demonstrate that increase in bulk-disorder, achieved by growing the films on amorphous SiO 2 substrate rather than on crystalline Al 2 O 3 (0001), can lead to stronger decoupling between the top and bottom surface states of the film.

Electron–phonon coupling in copper intercalated Bi$$_{2}$$Se$$_{3}$$

“…1 . Fitting of the results was based on a modified Hikami–Larkin–Nagaoka approach 25 – 27 . Besides the quantum corrections, we employed both linear ( ) and quadratic ( ) magnetoresistance components.…”

“…The magnetoconductivity for Bi Se can be written in the form 26 , 27 , 31 : where denotes the strength and nature of quantum corrections and defines a characteristic field related to dephasing length . The term where the first term denotes the classical, mobility- -dependent magnetoresistance ( ), while the latter terms are the quantum corrections specified using characteristics fields given by spin-orbit scattering length and the mean free path , respectively.…”

Electron-phonon coupling in copper intercalated Bi$_{2}$Se$_{3}$

“…1. Fitting of the results was based on a modified Hikami-Larkin-Nagaoka approach [23][24][25]. Besides the quantum corrections, we employed both linear (∝ B) and quadratic (∝ B 2 ) magnetoresistance components.…”

“…The magnetoconductivity ∆σ = σ (B, T ) − σ (T ) for Bi 2 Se 3 can be written in the form [24,25,29]:…”

“…In general, the parameter α is a measure of the relative strengths of the spin-orbit interaction, inter-valley scattering, magnetic scattering, and dephasing, as discussed in Ref. 30 for topological insulators, and their value may vary between −1 • • • + 1 (or even down to -2 [25]). Using weak localization α = 1, our fit displayed in Fig.…”