单层石墨烯中ν=-1量子霍尔态的斯格明子激发
Skyrmion Excitations in the $ν=-1$ Quantum Hall state in Monolayer Graphene
浏览论文内容
中文总结 AI 辅助
该研究针对单层石墨烯ν=-1量子霍尔态，结合有效场论与哈特利-福克近似构建变分框架，确定13种斯格明子相，为多分量量子霍尔铁磁体的斯格明子研究提供系统方法。
中文摘要 AI 辅助
我们研究了单层石墨烯中填充因子ν=-1下，SU(4)量子霍尔铁磁基态之上的斯格明子激发态。短程各向异性相互作用、塞曼耦合及子晶格对称破缺势之间的竞争，产生了四种不同的自旋-谷有序基态相。结合有效场论与哈特利-福克近似，我们构建了一个变分框架，该框架平等纳入长程库仑相互作用与对称破缺项。通过变分最小化确定了最优斯格明子结构，包括其空间径向分布和内部SU(4)旋量结构。我们建立了斯格明子激发的相图，识别出不同外场条件下的13种不同斯格明子相，并确定了它们的自旋-谷结构、能量及特征尺寸。针对不同径向近似的结果鲁棒性，证明了我们变分方法的可靠性。本工作为研究多分量量子霍尔铁磁体中的斯格明子激发提供了系统框架，且可自然扩展至更一般的SU(4)量子霍尔系统。
英文摘要
We investigate the skyrmion excited states atop the $SU(4)$ quantum Hall ferromagnetic ground state at filling factor $ν=-1$ in monolayer graphene. The competition among short-range anisotropic interactions, the Zeeman coupling, and sublattice symmetry-breaking potential gives rise to four distinct spin-valley-ordered ground-state phases. Combining effective field theory with the Hartree--Fock approximation, we develop a variational framework that incorporates both the long-range Coulomb interaction and the symmetry-breaking terms on an equal footing. Variational minimization determines the optimal skyrmion texture, including both its spatial radial profile and internal $SU(4)$ spinor structure. We establish the phase diagram of skyrmion excitations, identify thirteen distinct skyrmion phases under different external-field conditions, and determine their spin-valley textures, energies, and characteristic sizes. The robustness of the results against different radial ansätze demonstrates the reliability of our variational approach. Our work provides a systematic framework for studying skyrmion excitations in multicomponent quantum Hall ferromagnets and can be naturally extended to more general $SU(4)$ quantum Hall systems.
