SU(4) spin waves in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mo>±</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> quantum Hall ferromagnet in graphene

Abstract

The lowest energy excitations of a quantum Hall ferromagnet are generalized SU(4) spin waves that can be real spin, valley pseudospin waves, or mixed spin-valley waves (see image). In this paper, the dispersion relations of these different SU(4) spin-wave types are investigated based on the phase diagram of the quantum Hall ferromagnet at filling factor $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}1$. In three of the four phases, there can be one or more linearly dispersing modes at low energy, due to a remaining symmetry in the residual anisotropies.

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