In the 1950s, Pomeranchuk¹ predicted that, counterintuitively, liquid ³He may solidify on heating. This effect arises owing to high excess nuclear spin entropy in the solid phase, where the atoms are spatially localized. Here we find that an analogous effect occurs in magic-angle twisted bilayer graphene^2,3,4,5,6. Using both local and global electronic entropy measurements, we show that near a filling of one electron per moiré unit cell, there is a marked increase in the electronic entropy to about 1k_B per unit cell (k_B is the Boltzmann constant). This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons—such as the absence of a thermodynamic gap, metallicity and a Dirac-like compressibility—and others associated with localized moments, such as a large entropy and its disappearance under a magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump has an onset at a temperature of about 30 kelvin, the bandwidth of magnetic excitations is about 3 kelvin or smaller. The hybrid nature of the present correlated state and the large separation of energy scales have implications for the thermodynamic and transport properties of the correlated states in twisted bilayer graphene.

在 1950 年代，Pomeranchuk ¹预测，与直觉相反，液体³ He 可能会在加热时凝固。这种效应是由于固相中的高过量核自旋熵而产生的，其中原子在空间上是局部的。在这里，我们发现在魔角扭曲双层石墨烯^2,3,4,5,6中发生了类似的效果。使用局部和全局电子熵测量，我们表明，在每个莫尔晶胞填充一个电子附近，电子熵显着增加到每个晶胞约 1 k _{B (} k _B是玻尔兹曼常数）。这种巨大的过剩熵被平面内磁场淬灭，指向其磁源。作为电子密度函数的可压缩性急剧下降，与费米能级重新回到狄拉克点附近有关，标志着两相之间的清晰边界。我们将这种跳跃映射为电子密度、温度和磁场的函数。这揭示了一个相图，该相图与从低熵电子液体到具有几乎自由磁矩的高熵相关态的类似波美兰丘克的温度和场驱动转变一致。相关状态具有看似矛盾的属性的不寻常组合，其中一些与巡回电子相关 - 例如没有热力学间隙，金属丰度和类似狄拉克的可压缩性——以及与局部矩相关的其他内容，例如大熵及其在磁场下的消失。此外，表征这两组特性的能量尺度非常不同：压缩性跳跃在大约 30 开尔文的温度下开始，而磁激发的带宽约为 3 开尔文或更小。目前相关态的混合性质和能量尺度的大分离对扭曲双层石墨烯中相关态的热力学和传输特性有影响。而压缩性跳跃在大约 30 开尔文的温度下开始，磁激发的带宽约为 3 开尔文或更小。目前相关态的混合性质和能量尺度的大分离对扭曲双层石墨烯中相关态的热力学和传输特性有影响。而压缩性跳跃在大约 30 开尔文的温度下开始，磁激发的带宽约为 3 开尔文或更小。目前相关态的混合性质和能量尺度的大分离对扭曲双层石墨烯中相关态的热力学和传输特性有影响。