@article { ISI:000510176900007, title = {Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene}, journal = {Phys. Rev. Lett.}, volume = {124}, number = {4}, year = {2020}, month = {JAN 30}, pages = {046403}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We present a microscopic theory for collective excitations of quantum anomalous Hall ferromagnets (QAHF) in twisted bilayer graphene. We calculate the spin magnon and valley magnon spectra by solving Bethe-Salpeter equations and verify the stability of QAHF. We extract the spin stiffness from the gapless spin wave dispersion and estimate the energy cost of a skyrmion-antiskyrmion pair, which is found to be comparable in energy with the Hartree-Fock gap. The valley wave mode is gapped, implying that the valley polarized state is more favorable compared to the valley coherent state. Using a nonlinear sigma model, we estimate the valley ordering temperature, which is considerably reduced from the mean-field transition temperature due to thermal excitations of valley waves.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.124.046403}, author = {Wu, Fengcheng and Das Sarma, Sankar} }