发表机构
University of Stuttgart（斯图加特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用子晶格极化尖端的量子扭曲显微镜，在二维平带系统中直接探测量子几何张量的动量依赖性和子晶格对称性，为理解相关相提供新途径。
AI 中文摘要
在二维（2D）平带系统中，例如通过堆叠和扭曲范德瓦尔斯材料所工程化的系统，布洛赫态的动量依赖性成为决定相互作用诱导的不同相出现的关键因素。因此，探测这种“量子几何”的方法对于理解这些系统至关重要。然而，在二维中从测量中提取底层量子几何张量的动量依赖性颇具挑战。在此，我们提出使用具有子晶格极化尖端的量子扭曲显微镜（QTM）来填补这一空白。我们展示了如何在扫描的动量路径上探测子晶格泡利矩阵的期望值。这使得能够直接测量表征石墨烯基莫尔系统中不同候选不稳定性的关键对称性。我们进一步表明，沿扫描方向的量子度量分量也可以被提取；如果可以使用多于一种子晶格极化，则完整的量子几何张量也是可访问的。我们的工作展示了QTM方法的潜力并扩展了其多功能性。如果在未来的实验中实施，这将为扭曲双层石墨烯及相关系统中相关相的对称性特征和底层量子几何提供前所未有的访问途径。
英文摘要
In two-dimensional (2D) flat-band systems, as engineered, for instance, by stacking and twisting van der Waals materials, the momentum dependence of the Bloch states is a key factor in determining the interaction-induced emergence of different phases. Hence, methods of probing this form of ''quantum geometry'' are crucial to understanding these systems. Yet, extracting the momentum dependence of the underlying quantum geometric tensor from measurements is challenging in 2D. Here, we propose employing a quantum twisting microscope (QTM) with a sublattice-polarized tip to fill this gap. We show how expectation values of sublattice Pauli matrices can be probed across the scanned momentum path. This allows for the direct measurement of crucial symmetries characterizing the different candidate instabilities in graphene-based moiré systems. We furthermore show that the quantum metric component along the scan direction can also be extracted; the full quantum geometric tensor is also accessible, given that more than one sublattice polarization can be used. Our work illustrates the potential and extends the versatility of the QTM approach. If implemented in future experiments, this would provide unprecedented access to the symmetry signatures of the correlated phases and to the underlying quantum geometry in twisted bilayer graphene and related systems.
Comments21 pages, 7 figures
