Edge states and integer quantum Hall effect in topological insulator thin films

Zhang, Song-Bo; Lu, Hai‐Zhou; Shen, Shun-Qing

doi:10.1038/srep13277

Cited by 51 publications

(30 citation statements)

References 55 publications

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“…This treatment is capable of giving the quantization in graphene [61], which is massless in 2D. Because of the relation with the Chern number [2], the quantum Hall effect can be theoretically studied in the absence of disorder, as those in topological insulators [62][63][64][65]. To verify the numerical result in Fig.…”

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confidence: 89%

3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals

et al. 2017

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The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d-2)-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1/B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd_{3}As_{2}, or Na_{3}Bi. This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.

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confidence: 89%

3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals

et al. 2017

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“…A straightforward calculation of these two contributions yields C 0 = −τ /2 + 2τ = 3τ /2. While in graphene this half-integer Chern number is compensated by spin and valley degeneracies, in strong TIs, where the surface encloses an odd number of Kramers degenerate Dirac points, a half-integer Chern number results for example when exposing the material to a static magnetic field [9,51,[54][55][56][57].…”

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confidence: 99%

Floquet interface states in illuminated three-dimensional topological insulators

et al. 2015

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Recent experiments showed that the surface of a three-dimensional topological insulator develops gaps in the Floquet-Bloch band spectrum when illuminated with a circularly polarized laser. These Floquet-Bloch bands are characterized by nontrivial Chern numbers which only depend on the helicity of the polarization of the radiation field. Here we propose a setup consisting of a pair of counterrotating lasers, and show that one-dimensional chiral states emerge at the interface between the two lasers. These interface states turn out to be spin polarized and may trigger interesting applications in the field of optoelectronics and spintronics.Introduction. Amid the excitement sparked by graphene [1,2] and its record properties [3], the discovery of topological insulators (TIs) [4,5] developed with surprising speed. Indeed, TIs were predicted two years earlier in graphene [6], but the necessary spin-orbit interactions were too weak for this to be observed and a different playground was needed to realize them [7]. Most TIs are three-dimensional (3D) materials as are usual solids, but with a special property: They have a bulk band gap while keeping states that propagate with unprecedented robustness at the periphery of the sample [8,9]. These peculiar states hold great promise for quantum computation [10] but at the same time open up a major challenge: Controlling them is particularly demanding for 3D TIs.Encompassing the rapid progress in graphene photonics [11] and optoelectronics [12,13], theoretical studies predicted the formation of laser-induced band gaps [14] in graphene when properly tuning the laser polarization, frequency, and intensity [15][16][17][18]. More recently, these gaps were unveiled at the surface of a TI through angle-resolved photoemission spectroscopy (ARPES) [19]. This triggered great expectations for achieving laser-assisted control not only in the form of an on-off switch for the available states, but also because theoretically nontrivial topological states [14,20,21] can be induced on a diversity of materials [22][23][24][25][26], and also in cold matter physics [27,28]. Exciting questions arise about the nature of these novel states [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], the possibilities for manipulating them [31], the associated topological invariants [32-36], their statistical properties [37-40], and their twoterminal [41,42] and multiterminal (Hall) responses [43,44]. Still, an experimental realization of the Floquet chiral edge states is missing. Most studies considered two-dimensional (2D) systems, except for Refs. [45,46], where the target was a 3D semiconductor.Here, we show that, besides opening a band gap as in Ref. [19], illuminating a 3D TI with a suitable set of lasers can confine the surface states into one-dimensional states which also bear a topological origin. The proposed setup is represented in Fig. 1: two lasers with opposite circular polarization incident perpendicularly to a face of a 3D TI. This can be devised through, e.g., a single laser beam...

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“…These models predict a variety of intriguing phenomena at surfaces, interfaces, and thin films of TIs [20][21][22][23]. A fundamental issue here is the topological phase transition between an ordinary 2D insulator and a quantum spin Hall insulator (QSHI).…”

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Relativistick·pHamiltonians for centrosymmetric topological insulators fromab initiowave functions

Nechaev

Krasovskii

2016

Phys. Rev. B

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We present a method to microscopically derive a small-size k·p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three-and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3, Bi2Te3, and Sb2Te3. It turns out that the effective continuous k·p models with open boundary conditions often incorrectly predict the topological character of thin films.PACS numbers: 71.18.+y, 71.70.Ej, Electronic structure of topological insulators (TIs) has been in focus of theoretical research regarding linear response, transport properties, Hall conductance, and motion of Dirac fermions in external fields [1,2]. These problems call for a physically justified model Hamiltonian of small dimension. As in semiconductors, it is thought sufficient that the model accurately reproduces the TI band structure near the inverted band gap [3]. The desired Hamiltonian is derived either from the theory of invariants [4] or within the k·p perturbation theory using the symmetry properties of the basis states [5].In Ref.[3], along with the pioneering prediction of the topological nature of Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 , a 4-band Hamiltonian was first constructed from the theory of invariants, which is presently widely used to analyze the properties of bulk TIs as well as their surfaces and thin films [6][7][8][9][10][11][12][13][14]. The Hamiltonian parameters in Ref. [3] were obtained by fitting ab initio band dispersion curves. Later, an attempt was made [15] to recover the Hamiltonian of Ref.[3] by a k·p perturbation theory with symmetry arguments and to derive its parameters from the ab initio wave functions of the bulk crystals. Furthermore, in Ref. To analyze how the properties of thin films are inherited from the bulk TI features, effective continuous models have been developed: they are based on the substitution k z → −i∂ z (originally introduced for slowly varying perturbations [16]) in the Hamiltonian of Ref.[3] and on the imposition of the open boundary conditions [15,[17][18][19]. These models predict a variety of intriguing phenomena at surfaces, interfaces, and thin films of TIs [20][21][22][23]. A fundamental issue here is the topological phase transition between an ordinary 2D insulator and a quantum spin Hall insulator (QSHI). Apart from the theoretical prediction, the model parameters are fitted to the measured band dispersion to deduce the topological phase from the experiment [24,25]. By analyzing the signs and relative values of the parameters of the empirically obtained effective model a judgement is made on whether the edge states would exist in a given TI film, the logic being similar to that of Ref. [26]: The valence band should have a positive and conduction band a negative effective mass.In order to avoid any ambiguity in deriving the model Hamiltonian and to treat 3D and 2D s...

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Edge states and integer quantum Hall effect in topological insulator thin films

Cited by 51 publications

References 55 publications

3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals

3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals

Floquet interface states in illuminated three-dimensional topological insulators

Relativistick·pHamiltonians for centrosymmetric topological insulators fromab initiowave functions

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