Topological States in Ferromagnetic CdO/EuO Superlattices and Quantum Wells

Haijun Zhang, Jing Wang, Gang Xu, Yong Xu, and Shou-Cheng Zhang

Phys. Rev. Lett. 112, 096804 – Published 6 March 2014

Abstract

Based on ab initio calculations, we demonstrate that the ferromagnetic CdO/EuO superlattice is a simple Weyl semimetal with two linear Weyl nodes in the Brillouin zone, and the corresponding CdO/EuO quantum well realizes the stichometric quantum anomalous Hall state without random magnetic doping. In addition, a simple effective model is presented to describe the basic mechanism of spin polarized band inversion in this system.

Received 1 August 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.096804

Authors & Affiliations

Haijun Zhang, Jing Wang, Gang Xu, Yong Xu, and Shou-Cheng Zhang

Department of Physics, McCullough Building, Stanford University, Stanford, California 94305-4045, USA

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Vol. 112, Iss. 9 — 7 March 2014

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Images

Figure 1
(a) The rocksalt crystal structure of CdO and EuO with a $F m \bar{3} m$ space group (No. 225). (b) The Brillouin zone (BZ) for the rocksalt structure. The time-reversal invariant momentum points are marked, for example, $Γ (0, 0, 0)$ , $X (π, π, 0)$ , and $L (π, 0, 0)$ . (c) The schematic of the $(CdO)_{n} (EuO)_{m}$ superlattice. (d) The BZ of the $(CdO)_{n} (EuO)_{m}$ superlattice. (e) The schematic of the $(CdO)_{n} (EuO)_{m}$ quantum Well.
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Figure 2
(a) Band structure of the $(CdO)_{2} (EuO)_{2}$ superlattice with and without SOC. The green (red) dashed lines denote the up-spin (down-spin) bands. The black solid lines represent the SOC bands. There is a band inversion with the SOC bands. The bands around Fermi level at $Γ$ are zoomed in on in the inset. (b) The Weyl nodes with the spin texture at (0, 0, $k_{c}$ ). (c) The schematic of density of states (DOS) without SOC. The right (left) part is the up-spin (down-spin) DOS. (d) Evolution of the band sequence at $Γ$ starting from the atomic levels. Four stages (I—IV) represent turning on the chemical bonding (I), the exchange field (II), the crystal field (III), and the SOC effect, in sequence. The red dashed is the Fermi level.
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Figure 3
(a)–(c) The fat band of the $(CdO)_{2} (EuO)_{2}$ superlattice for the $Γ$ , (0, 0, $k_{c}$ ) and (0, 0, $k_{z}$ ) planes. The black circles mean Cd’s $s$ -orbital projection. A band inversion can be observed at $Γ$ in (a). A Weyl node is located at (0, 0, $k_{c}$ ) (b). (0, 0, $k_{z}$ ) is one point between (0, 0, $k_{c}$ ) and $Z (0, 0, π)$ . (d)–(e) The in-plane spin texture of two Weyl nodes at (0, 0, $\pm k_{c}$ ). The left figure of (d) and (e) is for the upper Weyl cone, and the right one of (d) and (e) is for lower Weyl cone. The flow direction is exactly opposite for these two Weyls nodes.
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Figure 4
(a) Band structure of the $(CdO)_{4} (EuO)_{3}$ quantum Well. The black circles mean Cd’s $s$ -orbital projection. The two conduction bands $| s^{+} ↑ ↓ ⟩$ both cross the valence band $| f_{-}^{-} ↑ ⟩$ . The red region presents a half-metal range with a single Fermi surface. (b) The band structure of the $(CdO)_{4} (EuO)_{3}$ quantum Well with the enlarged in-plane lattice constant by 1%. A full band gap is opened with a band inversion between the $| s^{+} ↑ ⟩$ and $| f_{-}^{-} ↑ ⟩$ bands, which presents a QAH phase. The band structure is zoomed in on in the inset. (c) Band structure of the $(CdO)_{4} (EuO)_{3}$ quantum Well with the enlarged in-plane lattice constant by 2%. No band inversion happens between the bands $| s^{+} ↑ ↓ ⟩$ and $| f_{-}^{-} ↑ ⟩$ , which presents a trivial insulator phase. (d) The schematic of these three different phases in (a)–(c).
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