Weak localization effects as evidence for bulk quantization in Bi2Se3thin films

Abstract

Strong spin-orbit coupling in topological insulators results in the ubiquitously observed weak antilocalization feature in their magnetoresistance. Here we present magnetoresistance measurements in ultra thin films of the topological insulator Bi2Se3, and show that in the 2D quantum limit, in which the topological insulator bulk becomes quantized, an additional negative magnetoresistance feature appears. Detailed analysis associates this feature with weak localization of the quantized bulk channels, providing thus evidence for this quantization. Examination of the dephasing fields at different temperatures indicates different scattering mechanism in the bulk vs the surface states.A three-dimensions (3D) topological insulator (TI) is fully gapped in the bulk, but exhibits an odd number of surface 2D massless cones of helical Dirac fermions, which are protected by time reversal symmetry (TRS) and thus cannot be destroyed by any non-magnetic impurities [1,2]. The Dirac fermions are helical in the sense that the electron spin points perpendicularly to the momentum, forming a lefthanded helical texture in momentum space. This strong coupling of spin and momentum leads to a range of new phenomena, especially when the TI is brought in contact with either a superconductor or an insulating ferromagnet, giving rise to possible observations of Majorana fermions [3,4], the topological magneto-electric effect [5], and quantum anomalous Hall effect [6].An important consequence of spin-momentum locking is the full suppression of backscattering resulting in a relative π Berry phase acquired by electrons executing time-reversed paths. As a consequence, at low temperatures, when the dephasing length (ℓ φ ) of the surface state electrons is long, this results in destructive interference, which give rise to positive quantum corrections ∆σ > 0, to the Drude conductivity. The result of these quantum corrections to the conductivity are called weak antilocalization (WAL) effects, and are expected to occur in general when spin-orbit (SO) interaction is strong [7][8][9]. When weak magnetic field H H φ ≡ Φ 0 /(8πℓ 2 φ ) (Φ 0 = hc/e is a flux quantum) is applied, these interference effects are reduced giving rise to positive magnetoresistance (MR) which is therefore a hallmark of WAL.While an ideal TI is a true bulk insulator, this property has proven to be very difficult to achieve. Interstitials, vacancies, and antisite doping, are only a few of the common issues that give rise to a substantial bulk carrier density causing the chemical potential to be pinned at the bulk conduction band. Focusing on the Bi 2 Se n Te 3−n system (where n=0,1,2 and 3), partial mitigation of the problem is commonly achieved by compensation (e.g. doping Bi 2 Se 3 with Sb) [10,11], or by controlling the Fermi energy via a gate bias [12][13][14]. However, unless the Fermi energy is tuned to be much below the bottom of the bulk conduction band, transport in such TI systems has been shown to be a complicated combination of surface and bulk states, which in principl...

Observation of quantum oscillations in FIB fabricated nanowires of topological insulator (Bi2Se3)

“…Also, previous theory suggests that diffusive paths add random phases to electron wave which make the conductance oscillations sample specific. AB dephasing length , the length over which electron phase is maintained before getting disturbed due to inelastic interactions [32], was shown proportional to with a gap in surface states [35]. In Ar + ion implementation study it was observed that the implementation of Ar + ions increases the disorder by increasing defect states in TI band structure.…”

Conductivity corrections for topological insulators with spin-orbit impurities: Hikami-Larkin-Nagaoka formula revisited

“…Surprisingly this problem has received virtually no attention [12] and so far the Dirac nature of the states, that manifest itself in the angular dependence of the Green functions, has not been taken into account in studies of spin-orbit impurities [7]. The problem is even more complicated in a transverse magnetic field.The formula commonly used to fit the magnetoconductance experiments on 3DTIs [13][14][15][16][17][18][19][20] was derived by Hikami, Larkin and Nagaoka (HLN) [21]. The HLN formula, however, lacks important features relevant to 3DTIs: it is derived for quasi-2DEGs with a parabolic electron dispersion (impurities are treated as threedimensional objects), so it accounts neither for the Dirac nature of the surface states nor for their strictly twodimensional character.…”

Top gating of epitaxial (Bi1−xSbx)2Te3 topological insulator thin films

“…The WAL in TIs has been intensively studied both theoretically 32,33 and experimentally 16,17,21,22,[34][35][36] . The peculiar magnetic-field dependence of the electrical conductivity σ associated with WAL is described by the simplified Hikami-Larkin-Nagaoka (HLN) formula…”