One-Dimensional Weak Antilocalization Due to the Berry Phase in HgTe Wires

Mühlbauer, Mathias; Budewitz, Andreas; Büttner, Bastian; Tkachov, G.; Em, Hankiewicz; Brüne, C.; Buhmann, H.; Molenkamp, L. W.

doi:10.1103/physrevlett.112.146803

Cited by 13 publications

(32 citation statements)

References 31 publications

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“…We have renormalized these corrections by δσ 0 = e 2 πh ln τ φ τe , where τ e depends on the model and is a function ofλ. We have set the ratio τ φ τ0 where τ 0 is the value of τ e in the absence of spin-orbit scattering τ 0 =h πρ(EF)γ0 to be equal to 10 in agreement with what is measured experimentally [22][23][24]. We observe that the Dirac fermions remain in the same symmetry class (symplectic, with WAL), whereas the HLN formula shows a crossover from the orthogonal symmetry class (WL) to either no correction for strictly 2DEG, or WAL for quasi-2DEG.…”

mentioning

confidence: 76%

“…For metals, where the ratio τ φ /τ e is very large (of the order of 1000 [27]) this crossover occurs for a value ofλ small enough that a perturbative treatment is possible. However, for the parameters experimentally relevant for 3DTIs, with a smaller ratio τ φ /τ e around 10 [22][23][24], this crossover occurs for values ofλ of the order of the unity, which is beyond the range of validity of the HLN derivation. We have plotted in Fig.…”

Section: Expression For the Cooperon Modes And Their Contribution To Walmentioning

confidence: 98%

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

et al. 2015

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The Hikami-Larkin-Nagaoka (HLN) formula [Prog. Theor. Phys. 63, 707 (1980)] describes the quantum corrections to the magnetoconductivity of a quasi-2D electron gas (quasi-2DEG) with parabolic dispersion. It predicts a crossover from weak localization to antilocalization as a function of the strength of scattering off spin-orbit impurities. Here, we derive the conductivity correction for massless Dirac fermions in 3D topological insulators (3DTIs) in the presence of spin-orbit impurities. We show that this correction is always positive and therefore we predict weak antilocalization for every value of the spin-orbit disorder. Furthermore, the correction to the diffusion constant is surprisingly linear in the strength of the impurity spin-orbit. Our results call for a reinterpretation of experimental fits for the magnetoconductivity of 3D TIs which have so far used the standard HLN formula.PACS numbers: 73.20.Fz, 73.43.Qt, 73.25.+i Introduction. The problem of the diffusion of the surface states of 3DTIs is a complex one due to a variety of competing phenomena. The most striking is the fact that these surface states are described by a Dirac Hamiltonian [1,2], which gives rise to weak antilocalization (WAL) in the presence of scalar disorder [3][4][5]. The WAL correction can be affected by the interaction of the surface states with the residual bulk states [6], the thickness of the film [7], or electron-electron interactions [8,9] changing its sign and turning it into weak localization (WL). At the same time, since 3DTIs have strong spin-orbit coupling, one expects spin-orbit coupled impurities to have a strong effect on transport, different however than in graphene where two valleys are present [10,11]. 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. Fig. 1 is the main result of this paper, and shows the different effects of spin-orbit scatter- * The two first authors contributed equally.† Author to whom correspondence should be addressed : hankiewicz@physik.uni-wuerzburg.de ing for the HLN formula, namely WL to WAL crossover with the strength of spin-orbit impurity scattering, and for Dirac fermions, where WAL appears regardless of the strength of spin-orbit impurities. We only observe a convergence of the two formulas for large values of the strength of the impurity spin-orbit sc...

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mentioning

confidence: 76%

Section: Expression For the Cooperon Modes And Their Contribution To Walmentioning

confidence: 98%

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

et al. 2015

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“…The difference in the magnitude of the effect for normal‐gap and inverted‐gap setups observed in Ref. () can be possibly related to a stronger block mixing in the inverted case (cf. Fig.…”

Section: Summary and Discussionmentioning

confidence: 86%

“…For higher temperatures, when τ φ τ m , these two copies of a unitary-class system (2U) become two copies of the (approximately) symplectic class, with the correction given by Eq. (23).…”

Section: Symmetry Analysis Of the Low-energy Hamiltonianmentioning

confidence: 99%

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Quantum interference in HgTe structures

Gornyi

Kachorovskii

Mirlin

et al. 2014

Physica Status Solidi (b)

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We study quantum transport in HgTe/HgCdTe quantum wells under the condition that the chemical potential is located outside of the bandgap. We first analyze symmetry properties of the effective Bernevig-Hughes-Zhang Hamiltonian and the relevant symmetry-breaking perturbations. Based on this analysis, we overview possible patterns of symmetry breaking that govern the quantum interference (weak localization or weak antilocalization) correction to the conductivity in two dimensional HgTe/HgCdTe samples. Further, we perform a microscopic calculation of the quantum correction beyond the diffusion approximation. Finally, the interference correction and the low-field magnetoresistance in a quasi-one-dimensional geometry are analyzed.Comment: 15 pages, 6 figures; feature article (topical review) for a special issue "Semiconductor Spintronics" (DFG-SPP 1285) of Physica Status Solidi B: Basic Solid State Physics; partly overviews PRB 86, 125323 (2012) and PRB 90, 085401 (2014) (arXiv:1207.4102 and arXiv:1402.7097, respectively

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Room‐Temperature Quantum Transport Signatures in Graphene/LaAlO₃/SrTiO₃ Heterostructures

et al. 2017

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2Weak localization (WL) and weak antilocalization (WAL) are quantum interference effects [1][2][3][4] resulting from electron phase coherence and spin-orbit interactions in 2-dimensional (2D) electron systems. WL results from constructive interference between pairs of time-reversed closed-loop electron trajectories and provides a positive correction to the Drude resistivity. [2, 4] Spin-orbit coupling (SOC) leads to suppressed backscattering due to destructive interference, leading to WAL and a negative correction to the Drude resistivity.[3]The intrinsic SOC of graphene is weak; [5] however, charge carriers in graphene possess a pseudospin degree of freedom, which arises from the degeneracy introduced by the two inequivalent atomic sites per unit cell in the graphene honeycomb lattice being comprised of A and B sublattices[ Figure 1(a) and (b)]. [6, 7] Recent discovery of unique quantum transport phenomena in graphene, such as unconventional half-integer quantum Hall effect [7, 8] and Klein tunneling [9][10][11] is a direct consequence of non-trivial Berry phase of ! induced by pseudospin rotation. Pseudospin in graphene can be utilized to store and manipulate information, which is analogous to the spin degree of freedom in spintronics. [12][13][14][15][16] Because of pseudospin rotation, each scattering process has a phase difference of ! between two time reversal pair in a closed quantum diffusive path. This results in destructive interference that suppresses backscattering, leading to WAL in graphene, which is analogous to the role of SOC (Figure 1(c) and (d)) in ordinary semiconductors. WAL is theoretically expected in graphene in the absence of inter-valley and chirality breaking scattering. [17] Most studies have not presented clear evidence of WAL via negative magnetoconductance, [18][19][20][21][22] most likely due to presence of point defects in graphene samples that locally break the sublattice degeneracy and smooth out !-phase contribution. Experimental signatures of WAL observed in high-quality epitaxial graphene samples are attributed to suppressed point defects.[23]Interestingly, a WL to WAL transition is achieved in high quality exfoliated samples [24] by decreasing the ratio of the dephasing length to the symmetry-breaking length via decoherence and carrier-density control. 3Preservation of pseudospin quantum interference up to room temperature (RT) is of fundamental importance for a variety of proposed applications, [12-16, 25, 26] but thermal perturbations typically suppress the phase coherence and hinder practical use of the devices. RT operation can be achieved if the high graphene mobility is consistently maintained over a broad temperature range and phonon-scattering contribution is significantly reduced. The mobility of graphene field-effect devices fabricated on SiO 2 /Si substrates is typically reduced at RT due to scattering with surface polar modes. [20,27,28] A significant improvement in quality was achieved by fabricating graphene devices on hexagonal-boron nitride (hBN) ...

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One-Dimensional Weak Antilocalization Due to the Berry Phase in HgTe Wires

Cited by 13 publications

References 31 publications

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

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

Quantum interference in HgTe structures

Room‐Temperature Quantum Transport Signatures in Graphene/LaAlO₃/SrTiO₃ Heterostructures

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One-Dimensional Weak Antilocalization Due to the Berry Phase in HgTe Wires

Cited by 13 publications

References 31 publications

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

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

Quantum interference in HgTe structures

Room‐Temperature Quantum Transport Signatures in Graphene/LaAlO3/SrTiO3 Heterostructures

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Room‐Temperature Quantum Transport Signatures in Graphene/LaAlO₃/SrTiO₃ Heterostructures