Van der Waals moiré materials have emerged as a highly controllable platform to study electronic correlation phenomena^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}. Robust correlated insulating states have recently been discovered at both integer and fractional filling factors of semiconductor moiré systems^{10,11,12,13,14,15,16,17}. In this study we explored the thermodynamic properties of these states by measuring the gate capacitance of MoSe₂/WS₂ moiré superlattices. We observed a series of incompressible states for filling factors 0–8 and anomalously large capacitance in the intervening compressible regions. The anomalously large capacitance, which was nearly 60% above the device’s geometrical capacitance, was most pronounced at small filling factors, below the melting temperature of the charge-ordered states, and for small sample–gate separation. It is a manifestation of the device-geometry-dependent Coulomb interaction between electrons and phase mixing of the charge-ordered states. Based on these results, we were able to extract the thermodynamic gap of the correlated insulating states and the device’s electronic entropy and specific heat capacity. Our findings establish capacitance as a powerful probe of the correlated states in semiconductor moiré systems and demonstrate control of these states via sample–gate coupling.

范德华云纹材料已成为研究电子相关现象的高度可控平台^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17} . 最近在半导体莫尔系统的整数和分数填充因子中发现了稳健的相关绝缘状态^{10,11,12,13,14,15,16,17}。_{在这项研究中，我们通过测量 MoSe 2} /WS ₂的栅极电容来探索这些状态的热力学性质莫尔超晶格。我们观察到填充因子 0-8 的一系列不可压缩状态和中间可压缩区域中异常大的电容。异常大的电容，比器件的几何电容高出近 60%，在小的填充因子、低于电荷有序态的熔化温度以及小的样品-栅极分离时最为明显。它是电子与电荷有序态的相混合与器件几何相关的库仑相互作用的表现。基于这些结果，我们能够提取相关绝缘状态的热力学间隙以及器件的电子熵和比热容。