Observation of the universal magnetoelectric effect in a 3D topological insulator

Dziom, V.; Shuvaev, A.; Pimenov, A.; Астахов, Г. В.; Ames, Christopher P.; Bendias, Kalle; Böttcher, J.; Tkachov, G.; Hankiewicz, Ewelina M.; Brüne, C.; Buhmann, H.; Molenkamp, Laurens W.

doi:10.1038/ncomms15197

Cited by 176 publications

(131 citation statements)

References 41 publications

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“…On the surface of a topological insulator there are special states which allow the surface metallic conduction. The electrodynamic properties of the topological insulators closely follow the behavior predicted for the so-called axions [9], including, for example, magneto-electric effect which has been observed in 3D topological insulators [10]. The discovery of topological insulators [11][12][13] has rekindled interest in existence of nontrivial topological phases in optical systems.…”

Section: Introductionmentioning

confidence: 88%

“…The modified constitutive relations (5) and (6) are responsible for observation of magnetoelectric effect in HgT e in 3D TI [10]. To model a periodic photonic crystal, we assume that the above-introduced parameters ǫ (dielectric constant), µ (magnetic constant) and θ (topological number or axion coupling) are periodic with a spacial period equal to d = a + b, that is: Fig.1 illustrates the proposed periodic photonic crystal based on topological insulators with a succession of repeating layers with different values of ǫ, µ, and θ.…”

Section: The Modelmentioning

confidence: 99%

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Gap-dependent mass of a photon in a photonic topological insulator

2017

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By using an analogy with axionic like systems, we study light propagation in periodic photonic topological insulator (PTI). The main result of this paper is an explicit expression for the PTI band structure. More specifically, it was found that for nonzero values of the topological phase difference γ = θ 2 − θ 1 a finite gap δ ∝ γ 2 opens in the spectrum which is equivalent to appearance of nonzero effective photon mass m * (δ) ∝ √ δ δ+2 .c Phone: +55 83 3216 7534

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Section: Introductionmentioning

confidence: 88%

Section: The Modelmentioning

confidence: 99%

Gap-dependent mass of a photon in a photonic topological insulator

2017

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“…Such predictions have been recently confirmed experimentally in graphene [9], where the Faraday angle is additionally doubled as two Dirac cones exist in the Brillouin zone. Very recently [27][28][29], several groups announced the observation of the quantized Faraday and Kerr rotation from the surface states of various topological insulators. In our previous work [29] the universal Faraday rotation has been observed on surface states in three-dimensional topological insulator, realised in thick strained HgTe film.…”

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confidence: 99%

Universal Faraday Rotation in HgTe Wells with Critical Thickness

et al. 2016

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The universal value of Faraday rotation angle close to the fine structure constant (α ≈ 1/137) is experimentally observed in thin HgTe quantum wells with thickness on the border between trivial insulating and the topologically non-trivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the hole-like carriers extracted from the analysis of the transmission data shows theoretically predicted universal value of σxy = e 2 /h consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electron-like part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model. PACS numbers:The strong spin-orbit coupling and an inverted band structure in mercury telluride makes this material to a nearly universal tool to probe novel physical effects with the film thickness being a tuning parameter [1,2]. If the thickness of HgTe wells is below critical, d < d c ≈ 6.3 nm, the sequence of the conduction and valence bands is conventional and a trivial insulating state is realized. For thicker films and in the bulk mercury telluride the inversion of valence and conduction bands leads to topologically non-trivial surface states [3,4]. This state is characterised by the locking of the electron spin and the electron momentum and they are topologically protected against non-magnetic impurity scattering.If the thickness of HgTe well is equal to critical, the gap between valence and conduction bands disappears and a two-dimensional (2D) electron gas is formed with Dirac cone dispersion [1,2]. Close to the center of the Dirac cone the electron spin is not a good quantum number, but has to be replaced by pseudo-spin or helicity [3,5]. Due to the particle-hole symmetry of these states, the quantum Hall effect becomes shifted by a half-integer and takes the form σ xy = γ(n+1/2)e 2 /h. In well-investigated case of graphene [6,7] the states are fourfold degenerate, i.e. γ = 4, as two Dirac cones are present in the Brillouin zone which are both doubly spin-degenerate.Magneto-optics in the terahertz range has been proven to be an effective tool to investigate two-dimensional conducting states in several quantum systems, like graphene [8-10], Bi 2 Se 3 [11][12][13][14], and HgTe [15][16][17][18][19][20][21][22]. Magneto-optical spectroscopy has the advantages of being contact-free and of directly accessing the effective mass m c via the cyclotron resonance Ω c = eB/m c . Here B is the external magnetic field.In the dynamical regime the unusual character of the quantum Hall effect in systems with Dirac cones can be shown [23][24][25][26] to lead to a universal values of the Faraday and Kerr rotation with θ F = α ∼ 1/137 and θ K = π/2, respectively. Such predictions have been recently confirmed experimentally in graphene [9], where the Faraday angle is additio...

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“…Such half-integer quantum Hall effect on TI surface can lead to a variety of exotic phenomena such as the quantum anomalous Hall (QAH) effect [3,[8][9][10][11][12][13][14][15], the quantized magneto-optical effect [3,16,17], the topological magnetoelectric (TME) effect [3][4][5][6]18], and the image magnetic monopole [19]. The QAH and quantized magneto-optical effects have been experimentally demonstrated in pure or magnetic TI films [10][11][12][13][20][21][22]. The TME effect refers to the quantized response of electric 3 polarization to applied magnetic fields and vice versa.…”

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confidence: 99%

Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures

et al. 2018

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Three-dimensional (3D) topological insulators (TIs) are unusual quantum materials that host conducting helical Dirac states on their surfaces, which are protected by time reversal symmetry (TRS), but are electrically insulating in the bulk [1,2]. TI is distinct from a trivial insulator by its unique electromagnetic response, described by the so-called  term shown below in addition to the ordinary Maxwell terms [3][4][5][6]. Here E and B are the conventional electric and magnetic fields inside an insulator, e is electron charge, and θ is the dimensionless pseudo-scalar parameter describing the insulator. For a trivial insulator, θ=0, while for a TI, θ=. When TRS is preserved, θ is either 0 or , reflecting its topological nature. This  term is related to the axion electrodynamics in particle physics [7]. Since the EB  term can be rewritten as a total derivative, its effect manifests on the surface states. A half-integer quantum Hall effect on the TI surface occurs once the surface Dirac Fermions acquire a mass, i.e. the surface state is gapped by magnetism. Such half-integer quantum Hall effect on TI surface can lead to a variety of exotic phenomena such as the quantum anomalous Hall (QAH) effect [3,[8][9][10][11][12][13][14][15], the quantized magneto-optical effect [3,16,17], the topological magnetoelectric (TME) effect [3][4][5][6]18], and the image magnetic monopole [19]. The QAH and quantized magneto-optical effects have been experimentally demonstrated in pure or magnetic TI films [10][11][12][13][20][21][22]. The TME effect refers to the quantized response of electric 3 polarization to applied magnetic fields and vice versa. The realization of the TME effect requires the following three conditions: (i) the TI film should be in the 3D regime; (ii) all the surfaces are gapped with the chemical potential lying within the gaps; (iii) the interior of the TI maintains TRS or inversion symmetry to maintain  in the bulk. A material system allowing for the realization of TME effect is known as an axion insulator [3][4][5].Recently, two papers reported the possible realization of the axion insulator. (Figs. 3k and 3m). We note that the zero  yx plateau is absent in either uniformly doped or the Cr modulation doped QAH samples [23,26,31,32]. The 3-5-3 SH2 was magnetically trained first by an upward sweep up to  0 H=1.5T before being swept downward. When  0 H=-0.01T, the MFM contrast is uniform (red), indicating that both top V-and bottom Cr-doped TI layers have upward magnetization (Fig. 3c). At  0 H=-0.05T, some reversed magnetic domains (green regions in Fig. 3d) appear, presumably in the 'softer' Cr-doped TI layer. As  0 H is swept further, the green regions expand and fill up the whole scan area at  0 H=-0.09T, indicating the uniform antiparallel magnetization alignment over the entire 3-5-3 SH2. When  0 H is further swept toward H c1 , new reversed magnetic domains (blue regions in Fig. 3g) nucleate at different locations, presumably in the 'harder' V-doped TI layer. Downward parallel magnetiza...

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Observation of the universal magnetoelectric effect in a 3D topological insulator

Cited by 176 publications

References 41 publications

Gap-dependent mass of a photon in a photonic topological insulator

Gap-dependent mass of a photon in a photonic topological insulator

Universal Faraday Rotation in HgTe Wells with Critical Thickness

Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures

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