由于温度升高而冻结电子的石墨烯系统

诸平

This visualisation exhibits layers of graphene used for membranes. Credit score: College of Manchester

之前曾经介绍过魔角可以使石墨烯在特定条件下变成超导体（哈佛科学家用三层石墨烯观察更稳健的超导性），新研究发现魔角也可以使石墨烯在特定条件下成为绝缘体（A graphene system that freezes electrons because the temperature rises）。两组研究人员分别发现存在一种固定的石墨烯体系，由于温度升高，电子会冻结。虽然是两组研究人员，但是他们都是由来自美国、以色列和日本的研究人员组成，仅仅是参与研究单位有所不同。其中一组研究团队发现，将一层石墨烯插入另一层石墨烯之上，然后扭曲基本层上的一层，就会产生一种石墨烯新状态，在这种状态下，电子会随着温度升高而冻结。

研究者在试图澄清他们所注意到的问题时，他们发现近乎绝缘部分的熵大约是自由电子自旋所能预期的熵的一半。熵测量揭示了“魔角”石墨烯的独特影响（Entropy measurements reveal unique impact in ‘magic-angle’ graphene）。

第二组研究团队的成员他们发现了相同的石墨烯体系，并进行了研究以领悟了所观察到的结果，他们以绝缘体内二次出现了一个很大的磁性而出名。每个小组都于2021年4月7日在《自然》（Nature）杂志网站上发表了他们的研究结果。详见Asaf Rozen, Jeong Min Park, Uri Zondiner, Yuan Cao, Daniel Rodan-Legrain, Takashi Taniguchi, Kenji Watanabe, Yuval Oreg, Ady Stern, Erez Berg, Pablo Jarillo-Herrero, Shahal Ilani. Entropic evidence for a Pomeranchuk effect in magic-angle graphene. Nature, Published: 07 April 2021, volume 592, pages 214–219. https://doi.org/10.1038/s41586-021-03409-2. 以色列魏茨曼科学研究院（Weizmann Institute of Science）、美国麻省理工学院（Massachusetts Institute of Technology）以及日本国立材料科学研究所（National Institute for Materials Science）参与上述研究。紧跟其后的是另一个研究团队的研究结果——Yu Saito, Fangyuan Yang, Jingyuan Ge, Xiaoxue Liu, Takashi Taniguchi, Kenji Watanabe, J. I. A. Li, Erez Berg, Andrea F. Young. Isospin Pomeranchuk effect in twisted bilayer graphene. Nature, Published: 07 April 2021, volume 592, pages 220–224. https://doi.org/10.1038/s41586-021-03409-2. 参与此项研究的有来自美国加州大学圣巴巴拉分校（University of California at Santa Barbara）、美国布朗大学（Brown University）、日本国立材料科学研究所（National Institute for Materials Science）以及以色列魏茨曼科学研究院（Weizmann Institute of Science）的研究人员。此外，美国普林斯顿大学物理系(Princeton University's Department of Physics)的连彪(Biao Lian)同样是在2021年4月7日，也在《自然》（Nature）杂志网站上发表了关于这两项研究的评述文章——Biao Lian. Heating freezes electrons in twisted bilayer graphene. Nature, Published: 07 April 2021, volume 592, pages 191-193. doi: https://doi.org/10.1038/d41586-021-00843-0. https://www.nature.com/articles/d41586-021-00843-0

随着温度的升高，大多数物质产生的粒子被激发。这将导致固体熔化为液体，液体变成燃料。这是由热力学定义的温度升高导致额外的熵，这是功能紊乱的一个轮廓。在这项新研究中，每个小组都发现了一个例外，即石墨烯系统，由于温度升高，电子会冻结。

石墨烯体系非常简单。每个组仅仅是将一张石墨烯薄片放在另一张作为底质的石墨烯之上，然后将最上层的石墨烯薄片微微扭曲。尽管如此，它还是需要被扭曲以满足神奇的角度为宜。莫尔样品导致系统内电子速度下降，从而导致额外的电阻，使系统几乎成为绝缘体。

然后，每个小组都要特别仔细地研究这些观察结果。他们各自通过测量扭曲晶格的熵来做到这一点，并确定高温部分的熵大于低温部分的熵。因此，他们都发现扭曲层中的电子都有自旋，并且自由度很低，众所周知，这很可能被称为同位自旋（isospin）。因此，他们都建议，因为系统内的温度升高，所以它变得更接近于变成铁磁体。除了关于近绝缘部分的熵的发现外，主要成员还观察到电子可压缩性突然出现过大的峰值。另外，第二组研究人员还发现，在相同的时间内，当系统使用磁场区域时，占据活力范围（vitality ranges）的电子可能会更少。上述介绍仅供参考，更多信息敬请注意浏览原文或者相关报道。

Magic-Angle Twisted Graphene Could Play Host to New Phases of Matter

Abstract (Nature, 2021, volume 592, pages 220–224)

In condensed-matter systems, higher temperatures typically disfavour ordered phases, leading to an upper critical temperature for magnetism, superconductivity and other phenomena. An exception is the Pomeranchuk effect in ³He, in which the liquid ground state freezes upon increasing the temperature¹, owing to the large entropy of the paramagnetic solid phase. Here we show that a similar mechanism describes the finite-temperature dynamics of spin and valley isospins in magic-angle twisted bilayer graphene². Notably, a resistivity peak appears at high temperatures near a superlattice filling factor of −1, despite no signs of a commensurate correlated phase appearing in the low-temperature limit. Tilted-field magnetotransport and thermodynamic measurements of the in-plane magnetic moment show that the resistivity peak is connected to a finite-field magnetic phase transition³ at which the system develops finite isospin polarization. These data are suggestive of a Pomeranchuk-type mechanism, in which the entropy of disordered isospin moments in the ferromagnetic phase stabilizes the phase relative to an isospin-unpolarized Fermi liquid phase at higher temperatures. We find the entropy, in units of Boltzmann’s constant, to be of the order of unity per unit cell area, with a measurable fraction that is suppressed by an in-plane magnetic field consistent with a contribution from disordered spins. In contrast to ³He, however, no discontinuities are observed in the thermodynamic quantities across this transition. Our findings imply a small isospin stiffness^4,5, with implications for the nature of finite-temperature electron transport^6,7,8, as well as for the mechanisms underlying isospin ordering and superconductivity^9,10 in twisted bilayer graphene and related systems.

Abstract（Nature, 2021, volume 592, pages 214–219）

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.