Intrinsic large gap quantum anomalous Hall insulators in $\mathrm{La}X(X=\mathrm{Br},\mathrm{Cl},\mathrm{I})$

Intrinsic large gap quantum anomalous Hall insulators in $La X (X = Br, Cl, I)$

Kapildeb Dolui, Sujay Ray, and Tanmoy Das

Phys. Rev. B 92, 205133 – Published 30 November 2015

Abstract

We report a theoretical prediction of a new class of bulk and intrinsic quantum anomalous Hall (QAH) insulators $La X$ $(X$ =Br, Cl, and I) via relativistic first-principles calculations. We find that these systems are innate long-ranged ferromagnets which, with the help of intrinsic spin-orbit coupling, become QAH insulators. A low-energy multiband tight-binding model is developed to understand the origin of the QAH effect. Finally, integer Chern number is obtained via Berry phase computation for each two-dimensional plane. These materials have the added benefit of a sizable band gap of as large as $\sim 25$ meV, with the flexibility of enhancing it to above 75 meV via strain engineering. The synthesis of $La X$ materials will provide the impurity-free single crystals and thin-film QAH insulators for versatile experiments and functionalities.

Received 4 March 2015
Revised 8 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.205133

Authors & Affiliations

Kapildeb Dolui, Sujay Ray, and Tanmoy Das

Department of Physics, Indian Institute of Science, Bangalore 560012, India

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Vol. 92, Iss. 20 — 15 November 2015

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Figure 1
(a) Crystal structure of LaBr, with two inequivalent La atoms forming a bilayer, defined by a hexagonal layer with a triangle layer on its top or bottom plane, respectively. (b) Top view of two bilayers. The middle bilayer in (a) is same as other bilayers, but shifted in the $a − b$ plane. (c) Primitive rhombohedral unit cell of LaBr. (d) Brillouin zone with space group of $R \bar{3} m$ .
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Figure 2
(a) Band structure of LaBr in the FM state without SOC. The horizontal dashed line gives the Fermi level. Blue and green colors indicate $d_{z^{2}}$ and $d_{x^{2} - y^{2}}$ orbitals weight of the La atoms, while the black color is the weight of the other orbitals. Open and filled symbols represent spin-up and spin-down states, respectively. (b) Low-energy view of the same band structure, but with SOC and plotted only along representative directions where the band gap opens across the Fermi level. The overall band structure at other directions and higher energy is similar to that of (a). Black solid lines are the guide to the eyes, where symbols are the calculated points.
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Figure 3
(a) Tight-binding band structure (red lines), overlayed on top of the DFT band structure (black lines) of LaBr with FM order and SOC. (b) Computed Berry curvature along the same high-symmetry directions as in (a), exhibiting spikes at the momenta where SOC gaps the FM Weyl points.
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Figure 4
Edge states (red lines) along representative high-symmetry directions where SOC opens a gap in Fig. 2.
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Figure 5
Strain engineering and band-gap tuning. (a) Insulating band structure of LaBr in the FM + SOC state with only 0.24% uniaxial strain. (b) Strain-induced band-gap evolution for all three QAH systems.
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Figure 6
Band progression of $La X$ materials. (a–d) The upper panel schematically illustrates the band structure around the band crossings between two different orbitals near the Fermi level for four different cases. (a) Band structure in the absence of FM order and SOC. (c) Same as (a) but with SOC. This particular example is representative of the $La X$ materials where SOC splitting can be anisotropic across the band crossing points. (c) Bands with FM order and without SOC. (c) Once SOC is included, an insulating gap forms between different orbitals and spins. (e–h) DFT band structure for the four cases discussed in the upper panels in the same order. Various insets highlight the low-energy regions where SOC induces a band gap.
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Physical Review B

covering condensed matter and materials physics

Intrinsic large gap quantum anomalous Hall insulators in $La X (X = Br, Cl, I)$

Kapildeb Dolui, Sujay Ray, and Tanmoy Das

Phys. Rev. B 92, 205133 – Published 30 November 2015

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Physical Review B

covering condensed matter and materials physics

Intrinsic large gap quantum anomalous Hall insulators in LaX(X=Br,Cl,I)

Kapildeb Dolui, Sujay Ray, and Tanmoy Das

Phys. Rev. B 92, 205133 – Published 30 November 2015

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Intrinsic large gap quantum anomalous Hall insulators in $La X (X = Br, Cl, I)$