Valley-polarized quantum anomalous Hall insulator in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>u</mml:mi> <mml:mi>B</mml:mi> <mml:msub> <mml:mi>r</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math>

Abstract

Abstract The coexistence of an intrinsic ferrovalley (FV) and nontrivial band topology attracts intensive interest, both for its fundamental physics and for its potential applications, namely a valley-polarized quantum anomalous Hall insulator (VQAHI). Here, based on first-principles calculations by using a generalized gradient approximation plus a U (GGA + U ) approach, the VQAHI induced by electronic correlation or strain can occur in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">R</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> <mml:msub> <mml:mi mathvariant="normal">r</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> . For perpendicular magnetic anisotropy (PMA), the FV to half-valley-metal (HVM) to quantum anomalous Hall (QAH) to HVM to FV transitions can be driven by increasing the electron correlation U . However, there are no special QAH states and valley polarization for in-plane magnetic anisotropy. By calculating the actual magnetic anisotropy energy (MAE), the VQAHI can indeed exist between two HVM states due to PMA, a unit Chern number/a chiral edge state and spontaneous valley polarization. The increasing U can induce VQAHI, which can be explained by a sign-reversible Berry curvature or a band inversion between d xy / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mi>y</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msub> </mml:math> orbitals. Even though the real U falls outside the range, the VQAHI can be achieved by strain. Taking U = 2.25 eV as a concrete case, the monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">R</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> <mml:msub> <mml:mi mathvariant="normal">r</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> can change from a common ferromagentic (FM) semiconductor to VQAHI under about 0.985 compressive strain. It is noted that the edge states of VQAHI are chiral-spin-valley locking, which can achieve complete spin and valley polarizations for low-dissipation electronic devices. Both the energy band gap and the valley splitting of VQAHI in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">R</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> <mml:msub> <mml:mi mathvariant="normal">r</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> are higher than the thermal energy of room temperature (25 meV), which is key for device applications at room temperature . It is found that the electronic correlation or strain have important effects on the Curie temperature of monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">R</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> <mml:msub> <mml:mi mathvariant="normal">r</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> . These results can be readily extended to other monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">X</mml:mi> <mml:mi mathvariant="normal">Y</mml:mi> </mml:mrow> </mml:math> (M = Ru, Os; X/Y = Cl, Br I). Our work emphasizes the importance of electronic correlation and PMA to study FV materials, and provides a pathway to realize VQAHI.

Topics & Concepts