墨西哥帽色散中的维格纳晶体形状与空穴自掺杂
Shape of Wigner Crystals and Hole Self-Doping in a Mexican-Hat Dispersion
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中文总结 AI 辅助
该研究针对墨西哥帽色散的环状费米面，通过变分蒙特卡罗计算揭示了维格纳晶体的形状特征，发现其可伴随k=0附近的空穴自掺杂形成，复现了相关实验转变。
中文摘要 AI 辅助
我们研究由墨西哥帽色散εₖ = c₂k² + c₄k⁴的环状费米面产生的强库仑相互作用诱导的维格纳晶体（WCs）。为了最小化维格纳晶体的能量，我们设计了轨道形状，发现低基态能量需要轨道在k=0附近存在电子耗尽。为了捕捉库仑诱导的关联，我们引入了Jastrow因子以及描述电子与掺杂空位关联的因子。通过变分蒙特卡罗计算，我们校准了有效带参数c₂和c₄，以复现实验中随电子密度降低观测到的两个转变：从具有圆盘状费米面的自旋-谷极化费米液体，到具有环状费米面的自旋-谷极化费米液体，最终转变为维格纳晶体。我们发现，即使采用了在k=0附近耗尽电子的优化轨道形状，只要包含电子-空位关联，在维格纳晶体转变附近，k=0附近带有空穴自掺杂的维格纳晶体在能量上仍具有优势，我们还估算了掺杂空穴的色散。
英文摘要
We study Wigner crystals (WCs) induced by a strong Coulomb interaction from the ring-like Fermi surface of a Mexican-hat dispersion $ε_k= c_2k^2+c_4k^4$. We design orbital shape in order to minimize the energy of the WC, and find that a low ground-state energy requires an orbital shape with a depletion of electrons near $k=0$. To capture the Coulomb-induced correlations, we include a Jastrow factor as well as a factor describing the correlation between electrons and doped vacancies. Using variational Monte Carlo calculations, we calibrate the effective band parameters $c_2$ and $c_4$ to reproduce the two transitions observed experimentally as the electron density is lowered: from a spin-valley-polarized Fermi liquid with a disk-like Fermi surface, to one with a ring-like Fermi surface, and finally to a WC. We find that, even with an optimized orbital shape that depletes electrons near $k=0$, a WC with hole self-doping near $k=0$ can still be energetically favorable near the WC transition, provided that the electron-vacancy correlation is included. We also estimate the dispersion of the doped hole.
