Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-11-30
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
4+ pages, 3 figures
Scientific paper
We study the properties of 2D insulators and 3D metals which possess both $n$-fold rotational symmetry and broken time-reversal symmetry. For 2D insulators, we show how to determine the Chern number up to a multiple of $n$ by evaluating the eigenvalues of the rotational operator at high symmetry points within the Brillouin zone. For 3D metals these eigenvalues also determine the existence, number and type of the gapless band crossings. We apply this theory to show that $[001]$-axis ferromagnetic HgCr$_2$Se$_4$ in 3D possesses both a $C_4$ symmetry-protected quadratic (in certain directions) band crossing (dubbed double-Weyl) as well as a mirror-symmetry protected nodal line separating regions of different electrical polarization which give rise to a multiferroic behavior. If the direction of the ferromagnetism is shifted away from the [001]- to the [111]-axis, a combined $C_6$ and mirror symmetry reveals a difference of two in the Chern number of different crystalographic planes, giving rise again to a topological metal. The possible quadratic-crossing is, however, not protected by any symmetry, and small spin-orbit coupling terms break it into four linear Weyl fermions.
Bernevig Andrei B.
Dai Xian-Xin
Fang Chen
Gilbert Matthew J.
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