论文标题
Moiré材料中的广义Wigner结晶
Generalized Wigner crystallization in moiré materials
论文作者
论文摘要
关于扭曲的过渡金属二分裂基因（TMD）材料的最新实验，$ \ rm WSE_2/WS_2 $，已经观察到Moiré带的分数占用率的绝缘状态。这种状态被认为是广义的wigner晶体（GWC）。在本文中，我们研究了在存在基础（Moiré）晶格的情况下Wigner结晶的问题。基于对系统参数的最佳估计，我们发现各种同型和Heterobilayer TMD是实现GWC的出色候选者。特别是，我们基于$ r_ {s} $的分析表明$ \ rm mose_ {2} $（在同型章中）和$ \ rm mose_2/ wse_2 $或$ \ rm mos_2/ ws_2 $（在HeteroBilayers中）是现实的gccs。我们还确定，由于较大的价值带的有效质量，通常，孔 - 结晶更容易意识到，如实验中所见的电子晶体。为了完整，我们表明，满足Mott Criterion $ n _ {\ rm Mott}^{1/2} a _ {\ ast} = 1 $需要密度近三个数量级，比GWC形成的最大密度大。这表明对于典型的操作密度，HOM或HEM系统远离Mott绝缘状态。这些晶体在Moiré晶格上（与常规的Wigner晶体不同，由于与晶格固定的缝隙产生的间隙，都无法压缩。最后，我们通过将振动模式的分散剂变异归一化来捕获这种多体差距。我们显示了这些低能模式是由WC与Moiré晶格的耦合产生的，可以有效地建模为正弦戈登的波动理论。
Recent experiments on the twisted transition metal dichalcogenide (TMD) material, $\rm WSe_2/WS_2$, have observed insulating states at fractional occupancy of the moiré bands. Such states were conceived as generalized Wigner crystals (GWCs). In this article, we investigate the problem of Wigner crystallization in the presence of an underlying (moiré) lattice. Based on the best estimates of the system parameters, we find a variety of homobilayer and heterobilayer TMDs to be excellent candidates for realizing GWCs. In particular, our analysis based on $r_{s}$ indicates that $\rm MoSe_{2}$ (among the homobilayers) and $\rm MoSe_2/WSe_2$ or $\rm MoS_2/ WS_2$ (among the heterobilayers) are the best candidates for realizing GWCs. We also establish that due to larger effective mass of the valence bands, in general, hole-crystals are easier to realize that electron-crystals as seen experimentally. For completeness, we show that satisfying the Mott criterion $n_{\rm Mott}^{1/2} a_{\ast} = 1$ requires densities nearly three orders of magnitude larger than the maximal density for GWC formation. This indicates that for the typical density of operation, HoM or HeM systems are far from the Mott insulating regime. These crystals realized on a moiré lattice, unlike the conventional Wigner crystals, are incompressible due the gap arising from pinning with the lattice. Finally, we capture this many-body gap by variationally renormalizing the dispersion of the vibration modes. We show these low-energy modes, arising from coupling of the WC with the moiré lattice, can be effectively modeled as a Sine-Gordon theory of fluctuations.
