Physics Duo 发现二维魔法

超导性的关键是引导通常相互排斥的电子配对并形成称为玻色子的实体。然后玻色子可以共同融合成无摩擦的量子流体。产生玻色子的吸引力，例如原子振动，通常只能在低温或高压下才能克服电子的排斥。但对这些极端条件的需求阻止了超导性进入日常设备。铜酸盐的发现带来了希望，即正确的原子晶格可以将电子牢固地“粘合”在一起，即使在室温下它们也能保持粘连。

在 Bednorz 和 Müller 的发现之后的 40 年里，理论家们仍然不能完全确定铜酸盐中的胶水是如何起作用的，更不用说如何调整材料来加强它了。因此，凝聚态物理学的许多研究都是对晶体的反复试验，寻找可以保持电子配对或以其他奇妙方式引导电子的晶体。 “凝聚态物质是物理学的一个分支，它允许意外发现，”金说。这就是 2004 年发现的二维材料。

在英国曼彻斯特大学研究石墨的Andre Geim和Konstantin Novoselov发现了这种材料片状的令人震惊的后果。石墨晶体包含排列成松散结合的六边形片的碳原子。理论家早就预测，如果没有堆叠的稳定影响，热引起的振动会破坏一层薄板。但海姆和诺沃肖洛夫发现，他们可以剥离稳定的原子级薄片，只需要透明胶带和持久性。石墨烯是第一种真正平坦的材料——电子可以在其上滑动但不能上下滑动的平面。

哥伦比亚物理学家 Hone 发现世界上最薄的材料在某种程度上也是最强的。对于理论家们认为根本不会粘在一起的材料来说，这是一个了不起的挫折。

物理学家对石墨烯最感兴趣的是碳平地如何转化电子：没有什么可以减慢它们的速度。电子经常被它们移动的原子晶格绊倒，比它们的教科书质量更重（绝缘体的不动电子就像它们具有无限质量一样）。然而，石墨烯的扁平晶格让电子以每秒一百万米的速度飞驰而过——只比光速慢几百倍。在那个恒定的、极快的速度下，电子像没有质量一样飞行，赋予石墨烯极强的（虽然不是超强的）导电性。

神奇的材料周围出现了一个完整的领域。研究人员也开始进行更广泛的思考。其他物质的二维薄片能否拥有自己的超能力？霍恩是那些拓展业务的人之一。 2009 年，他测量了石墨的分身二硫化钼的一些机械性能，然后将晶体交给托尼·海因茨哥伦比亚实验室的两名光学专家。这是一个随意的举动，将改变所有相关人员的职业生涯。

二硫化钼样品落到了她职业生涯早期的客座教授Jie Shan和研究生Kin Fai Mak的手中。这对年轻的二人组正在研究石墨烯如何与光相互作用，但他们已经开始幻想其他材料。石墨烯的快速电子使其成为一种奇妙的导体，但他们想要的是一种二维半导体——一种可以打开和关闭电子流的材料，因此可以用作晶体管。

众所周知，二硫化钼是一种半导体。 Shan 和 Mak 很快发现，就像石墨一样，它在 2D 中获得了额外的能力。当他们将激光对准“二硫化钼”的 3D 晶体（他们亲切地称之为）时，晶体保持黑暗。但是，当 Shan 和 Mak 用透明胶带撕下层，用激光击打它们，并在显微镜下检查它们时，他们看到 2D 薄片闪闪发光。

其他小组的研究后来证实，制作精良的密切相关材料薄片可以反射每一个撞击它们的最后一个光子。 “这有点令人难以置信，”最近，当我在康奈尔大学的共用办公室见到他和 Shan 时，Mak 说道。 “你只有一张原子片，它可以像一面完美的镜子一样反射 100% 的光。”他们意识到这种特性可能会导致壮观的光学设备。

独立地，加州大学伯克利分校的物理学家王峰也做出了同样的发现。一种高反射率的二维材料和一种可引导的半导体引起了社区的关注。两个小组都在 2010 年发表了他们的研究结果；此后，这些论文已被引用超过 16,000 次。 “每个拥有激光的人都开始对二维材料非常感兴趣，”Hone 说。

通过将二硫化钼确定为第二种二维神奇材料，这两个小组已经登陆了整个二维材料大陆。二硫化钼属于称为过渡金属二硫属化物 (TMD) 的物质家族，其中来自元素周期表金属中间区域的原子（例如钼）与称为硫属化物的化学化合物对（例如硫）连接。二硫化钼是唯一天然存在的 TMD，但研究人员可以在实验室中制造出更多的 TMD——二硫化钨、二碲化钼等。大多数形成薄弱结合的纸张，使它们容易受到胶带的商业方面的影响。

然而，最初的兴奋浪潮很快就消退了，因为研究人员努力让 TMD 做得不仅仅是发光。王的团队，其中之一，在发现他们不能轻易地将金属电极连接到二硫化钼后，又重新选择了石墨烯。 “多年来，这一直是我们团队的绊脚石，”他说。 “即使是现在，我们也不太擅长接触。”似乎 TMD 相对于石墨烯的主要优势也是它们最大的弱点：为了研究材料的电子特性，研究人员必须经常将电子推入其中并测量产生的电流的电阻。但由于半导体是不良导体，因此很难让电子进出。

Mak 和 Shan 最初感到矛盾。 “目前还不清楚我们是应该继续研究石墨烯还是开始研究这种新材料，”Mak 说。 “但既然我们发现它有这个很好的特性，我们就继续做更多的实验。”

随着他们的工作，这两位研究人员越来越着迷于二硫化钼，并且彼此着迷。最初，他们的联系是专业的，主要限于以研究为重点的电子邮件。 “Fai 经常问，‘那件设备在哪里？你把那个放在哪里了？’”单说。但最终他们的关系，在长时间的培养和实验成功的推动下，变得浪漫起来。 “我们只是经常见面，实际上是在同一个实验室从事同一个项目，”Mak 说。 “这个项目运行得很好也让我们很高兴。”

一直都是物理学

这将需要两位具有铁学科的忠诚物理学家之间的合作，才能解决麻烦的 TMD。

学者总是很​​容易来到掸邦。她在 1970 年代在沿海省份浙江长大，是一名明星学生，在数学、科学和语言方面都表现出色，并在合肥的中国科技大学获得了梦寐以求的学位。在那里，她获得了中苏文化交流项目的资格，并抓住了在莫斯科国立大学学习俄语和物理的机会。 “当你还是个青少年的时候，你渴望探索这个世界，”她说。 “我没有犹豫。”

马上，她看到的世界比她想象的要多。签证问题将她抵达俄罗斯的时间推迟了几个月，她失去了语言课程的席位。当局为她找到了另一条路线，在抵达莫斯科后不久，她登上了一列火车，向东行驶了 5000 公里。三天后，她抵达西伯利亚中部的伊尔库茨克市。 “我得到的建议是，‘永远不要在没有手套的情况下触摸任何东西，’”以免她被卡住，她说。 

珊戴上手套，一个学期就学会了俄语，开始欣赏寒冷风景的绝美之美。课程结束，雪融化后，她回到首都开始攻读物理学学位，并于 1990 年春天抵达莫斯科，当时正值苏联解体。

那是混乱的岁月。当共产党试图重新控制政府时，Shan 看到坦克在大学附近的街道上滚动。还有一次，就在期末考试之后，爆发了战斗。 “我们能听到枪声，我们被告知要关掉宿舍的灯，”她说。从食物到卫生纸，一切都是通过优惠券系统配给的。尽管如此，她的教授们坚韧不拔的精神让珊感到鼓舞，尽管动荡不安，他们仍继续他们的研究。 “条件很艰苦，但许多科学家都有这种态度。尽管发生了什么事，他们真的很喜欢他们所做的事情，”她说。

随着世界秩序的崩溃，Shan 脱颖而出，发表了一篇光学理论论文，引起了 Heinz 在哥伦比亚大学的注意。他鼓励她申请，然后她搬到了纽约，在那里她偶尔帮助其他国际学生在国外站稳脚跟。例如，她招募王在 Heinz 的实验室工作，并分享实验技巧。 “她教会了我如何保持耐心，”他说，“如何避免对激光感到沮丧。”

大多数研究人员在获得博士学位后担任博士后职位，但单于 2001 年直接加入凯斯西储大学担任副教授。几年后，在休假期间，她回到了亨氏在哥伦比亚的实验室。这一次，她的时机是偶然的。她开始与 Heinz 小组中一位迷人且目光炯炯的研究生 Kin Fai Mak 合作。

Mak 沿着一条不同的、不那么喧嚣的道路前往纽约市。他在香港长大，在学校里挣扎，除了物理对他来说几乎没有意义。 “这是我唯一喜欢并且实际上很擅长的事情，所以我选择了物理，”他说。

他在香港大学的本科研究脱颖而出，亨氏聘请他加入哥伦比亚蓬勃发展的凝聚态物理项目。在那里，他全身心投入研究，除了偶尔的校内足球比赛外，几乎所有醒着的时间都在实验室度过。研究生 Andrea Young（现为加州大学圣巴巴拉分校的助理教授）与 Mak 合租一间位于西 113 街的公寓。 “如果我能在凌晨 2 点赶上他煮意大利面和谈论物理，我就很幸运了。一直都是物理学，”杨说。

在读研究生期间，Mak（左）和他的室友 Andrea Young 去哥伦比亚的亚马逊热带雨林远足。

但好景不长。在与 Young 一起游览哥伦比亚的亚马逊雨林后不久，Mak 病倒了。他的医生不知道如何看待他令人费解的测试结果，他病得更重了。一个幸运的巧合救了他的命。杨向他的医学研究人员父亲描述了这种情况，他立即意识到再生障碍性贫血的迹象——一种不寻常的血液状况，恰好是他自己研究的主题。 “首先，这种疾病实际上非常罕见，”Mak 说。 “更罕见的是，你室友的父亲是专家的疾病。”

Young 的父亲帮助 Mak 参加了实验性治疗。他在研究生院的最后一年大部分时间都在医院度过，并数次濒临死亡。在整个磨难中，麦对物理学的热情驱使他继续工作。 “他在病床上写PRL信，”杨说，指的是《物理评论快报》杂志。 “尽管如此，他是有史以来最有成就的学生之一，”海因茨说。 “这是一个奇迹。”

进一步的治疗最终帮助 Mak 完全康复。杨本人是一位著名的实验家，后来他对他的干预进行了调侃，“在朋友中，我称其为我对物理学的最大贡献。”

进入二维荒野

2012 年，Mak 以博士后研究员的身份来到康奈尔大学，此时 Shan 已经回到凯斯西区。他们用石墨烯和其他材料进行了单独的项目，但他们也继续共同解开 TMD 的更多秘密。

在康奈尔大学，Mak 学习了电子传输测量的艺术——这是除光学之外的另一种预测电子运动的主要方法。在研究人员通常专注于一种或另一种类型的领域，这种专业知识使他和 Shan 成为双重威胁。 “每当我遇到 Fai 和 Jie 时，我都会抱怨，’你们做交通工具是不公平的，’”Kim 说。 “我应该做些什么？”

两人对 TMD 了解得越多，他们就越感兴趣。研究人员通常关注电子的两种特性之一：它们的电荷和自旋（或固有角动量）。控制电荷的流动是现代电子学的基础。翻转电子的自旋可能会导致“自旋电子学”设备将更多信息打包到更小的空间中。 2014 年， Mak 帮助发现二维二硫化钼中的电子可以获得特殊的第三个属性：这些电子必须以特定量的动量移动，这是一种被称为“谷”的可控属性，研究人员推测这可能会催生“谷电子学”的第三个领域“ 技术。

同年，Mak 和 Shan 发现了 TMD 的另一个显着特征。电子不是唯一穿过晶体的实体。物理学家还追踪“空穴”，即电子在别处跳跃时产生的空位。这些孔可以像真正的带正电粒子一样漫游材料。正空穴吸引负电子形成短暂的伙伴关系，称为激子，在电子堵塞空穴之前的那一刻。 Shan 和 Mak测量了 2D 二硒化钨中电子和空穴之间的吸引力，发现它比典型的 3D 半导体强数百倍。这一发现暗示，TMD 中的激子可能特别强大，而且通常电子更有可能做各种奇怪的事情。

美林谢尔曼/广达杂志

这对夫妇一起在宾夕法尼亚州立大学获得了职位，并在那里开设了一个实验室。最终确信 TMD 值得在他们的职业生涯上押注，他们将材料作为新团队的重点。他们也结婚了。

与此同时，哥伦比亚的 Hone 团队发现，当他们将石墨烯放置在优质绝缘体氮化硼之上时，其性能变得更加极端。这是二维材料最新颖的方面之一的早期例子：它们的可堆叠性。

将一种 2D 材料放在另一种之上，这些层之间的距离只有几分之一纳米——从电子的角度来看，根本没有距离。结果，堆叠的片材有效地合并为一种物质。 “这不仅仅是两种材料在一起，”王说。 “你真的创造了一种新材料。”

尽管石墨烯完全由碳原子组成，但多样化的 TMD 晶格家族为堆叠游戏带来了数十种额外的元素。每个 TMD 都有自己的内在能力。有些是磁性的；其他超导。研究人员期待着将它们与具有综合能力的时尚材料混合搭配。

但是，当 Hone 的小组将二硫化钼放在绝缘体上时，与他们在石墨烯中看到的相比，堆栈的特性显示出平淡的增益。最终他们意识到他们没有检查过 TMD 晶体的质量。当他们让一些同事将他们的二硫化钼放在能够分辨单个原子的显微镜下时，他们惊呆了。一些原子坐错了位置，而另一些原子则完全消失了。多达百分之一的晶格位点存在问题，阻碍了晶格引导电子的能力。相比之下，石墨烯是完美的形象，大约每百万个原子中就有一个缺陷。 “我们终于意识到我们一直在购买的东西完全是垃圾，”Hone 说。

2016 年左右，他决定涉足研究级 TMD 的增长业务。他招募了一位博士后​​Daniel Rhodes ，他拥有通过在极高温度下熔化原材料粉末然后以极快的速度冷却它们来生长晶体的经验。 “这就像在水中用糖制成冰糖，”Hone 解释道。与商业方法相比，新过程需要一个月的时间。但它生产的 TMD 晶体比化学目录中出售的晶体好数百到数千倍。

在 Shan 和 Mak 能够利用 Hone 日益原始的晶体之前，他们面临着一项乏味的任务，即弄清楚如何处理不喜欢接受电子的微观薄片。为了泵入电子（Mak 在博士后学到的传输技术的基础），这对夫妇痴迷于无数细节：电极使用哪种金属，离 TMD 多远，甚至需要使用哪些化学物质用于清洁触点。尝试无数种设置电极的方法既缓慢又费力——“这是一个耗时的过程，可以一点一点地完善这个或那个，”Mak 说。

他们还花了数年时间研究如何提升和堆叠微观薄片，这些薄片的直径仅为百万分之十分之一米。有了这种能力，再加上 Hone 的晶体和改进的电接触，一切都在 2018 年走到了一起。这对夫妇搬到了纽约的伊萨卡，在康奈尔大学担任新职位，一连串开创性的成果从他们的实验室中涌现出来。

康奈尔大学的突破

“今天，由于某种原因，一切都难以拾起，”Mak 和 Shan 小组的研究生 Zhengchao Xia 说，因为氮化硼薄片的黑色轮廓可能会剥落并落回下方的硅表面。马达加斯加形状的薄片无力地粘在一大块类似沙特阿拉伯的石墨上，就像纸可能粘在最近摩擦过的气球噼啪作响的表面上一样。反过来，石墨被粘在附在载玻片上的粘性塑料露珠上。夏使用计算机界面来指挥一个电动支架夹住载玻片。就像一个玩街机的人可能会用操纵杆操纵爪机一样，她小心翼翼地将堆栈以每点击一次鼠标百万分之一米的速度举到空中，全神贯注地盯着电脑显示器看她是否有成功地抓住了氮化硼薄片。

她有。再点击几下，两层堆栈就自由了，夏迅速但有意地将薄片沉积到嵌入了蔓延金属电极的第三种材料上。再点击几下，她加热了表面，在我们中的任何一个人将微型设备打喷嚏之前融化了载玻片的塑料粘合剂。

“我总是做噩梦，它就消失了，”她说。

从开始到结束，夏花了一个多小时组装了一个简单设备的下半部分——相当于一个开放式 PB&J。她向我展示了她最近整理的另一堆材料，并大声说出了一些成分，其中包括 TMDs 二硒化钨和二碲化钼。作为她去年构建和研究的数十种微型三明治之一，这种由 Dagwood 制成的装置有多达 10 层，需要几个小时才能组装起来。

这种二维材料的堆叠，也在哥伦比亚、麻省理工学院、伯克利、哈佛和其他机构的实验室中完成，代表了凝聚态物理学家长期以来的梦想的实现。研究人员不再局限于在地下发现或在实验室中缓慢生长的材料。现在，他们可以玩乐高积木的原子等价物，将片材拼接在一起以构建具有所需特性的定制结构。在组装 TMD 结构方面，很少有人能达到康奈尔集团的水平。

Mak 和 Shan 在康奈尔大学的第一个重大发现涉及激子，这是他们早在 2014 年在 TMD 中看到的强束缚电子-空穴对。激子吸引了物理学家，因为这些“准粒子”可能为实现凝聚态物理学的长期目标提供了一种迂回的方法：室温超导。

激子遵循与电子-电子对相同的时髦规则。这些电子-空穴对也变成了玻色子，这让它们“凝聚”成一个共享的量子态，称为玻色-爱因斯坦凝聚态。这种连贯的准粒子群可以显示出量子特性，例如超流性、无阻力流动的能力。 （当超流体携带电流时，它会超导。）

但与排斥电子不同，电子和空穴喜欢耦合。研究人员说，这可能会使他们的胶水更牢固。基于激子的超导性的挑战在于阻止电子填充空穴，并使电中性对在电流中流动——所有这些都在尽可能温暖的房间里。到目前为止，Mak 和 Shan 已经解决了第一个问题，并计划解决第二个问题。

通过使用强大的激光将它们冷却到绝对零以上的头发，可以将原子云哄骗形成冷凝物。但理论家长期以来一直怀疑激子的凝聚体可能在更高的温度下形成。康奈尔小组通过他们的可堆叠 TMD 实现了这一想法。使用两层三明治，他们将额外的电子放入顶层并从底部移除电子，留下空穴。电子和空穴配对，产生寿命长的激子，因为电子难以跳到对面的层以中和它们的伙伴。 2019 年 10 月，该小组报告了温和 100 开尔文的激子冷凝物的迹象。在这种设置中，激子持续了数十纳秒，这是这种准粒子的寿命。在 2021 年秋天，该小组描述了一种改进的装置，其中激子似乎持续了几毫秒，Mak 称之为“几乎永远”。

该团队现在正在推行一项由理论家在 2008 年炮制的计划，以产生激子电流。德克萨斯大学奥斯汀分校的著名凝聚态理论家艾伦麦克唐纳和他的研究生 Jung-Jung Su 提出通过施加电场来使中性激子流动，该电场以鼓励电子和空穴向同一方向移动的方式进行.为了在实验室中成功，康奈尔小组必须再次与他们的宿敌电触点作斗争。在这种情况下，他们必须将多组电极连接到 TMD 层，其中一些用于制造激子，另一些用于移动它们。

Shan 和 Mak 相信他们很快就能让激子以高达 100 开尔文的速度流动。对于一个人来说，这是一个寒冷的房间（-173 摄氏度或 -280 华氏度），但与大多数玻色子冷凝物所需的纳米开尔文条件相比，这是一个巨大的飞跃。

“That will be by itself a nice achievement,” Mak said with a sly smile, “to warm up the temperature by a billion times.”

Magical Moiré Materials

In 2018, while the Cornell lab ramped up their TMD experiments, another graphene surprise launched a second 2D materials revolution. Pablo Jarillo-Herrero , a researcher at MIT and another Columbia alum, announced that twisting one layer of graphene with respect to the layer below created a magical new 2D material. The secret was to drop the upper layer such that its hexagons landed with a slight “twist,” so that they were rotated exactly 1.1 degrees against the hexagons below. This angle misalignment causes an offset between atoms that grows and shrinks as you move across a material, generating a repeating pattern of large “supercells” known as a moiré superlattice. MacDonald and a colleague had calculated in 2011 that at the “magic angle” of 1.1 degrees, the unique crystal structure of the superlattice would compel graphene’s electrons to slow and sense the repulsion of their neighbors.

Merrill Sherman/Quanta Magazine

When electrons become aware of each other, weird things happen. In normal insulators, conductors and semiconductors, electrons are thought to interact only with the lattice of atoms; they race around too quickly to notice each other. But slowed to a crawl, electrons can jostle each other and collectively assume an assortment of exotic quantum states. Jarillo-Herrero’s experiments demonstrated that, for poorly understood reasons, this electron-to-electron communication in twisted, magic-angle graphene gives rise to an especially strong form of superconductivity .

The graphene moiré superlattice also introduced researchers to a radical new way of controlling electrons. In the superlattice, electrons become oblivious to the individual atoms and experience the supercells themselves as if they were giant atoms. This makes it easy to populate the supercells with enough electrons to form collective quantum states. Using an electric field to dial up or down the average number of electrons per supercell, Jarillo-Herrero’s group was able to make their twisted bilayer graphene device serve as a superconductor, act as an insulator , or display a raft of other , stranger electron behaviors .

Physicists around the world rushed into the nascent field of “twistronics.” But many have found that twisting is tough. Atoms have no reason to fall neatly into the “magic” 1.1-degree misalignment, so sheets wrinkle in ways that completely change their properties. Xia, the Cornell graduate student, said she has a bunch of friends at other universities working with twisted devices. Creating a working device typically takes them dozens of tries. And even then, each device behaves differently, so specific experiments are almost impossible to repeat.

TMDs present a far easier way to create moiré superlattices. Because different TMDs have hexagonal lattices of different sizes, stacking a lattice of slightly larger hexagons over a smaller lattice creates a moiré pattern just the way angle misalignment does. In this case, because there is no rotation between the layers, the stack is more likely to snap into place and stay still. When Xia sets out to create a TMD moiré device, she said, she generally succeeds four times out of five.

TMD moiré materials make ideal playgrounds for exploring electron interactions. Because the materials are semiconductors, their electrons get heavy as they slog through the materials, unlike the frenetic electrons in graphene. And the gigantic moiré cells slow them down further: Whereas electrons often move between atoms by “tunneling,” a quantum mechanical behavior akin to teleportation, tunneling rarely happens in a moiré lattice, since supercells sit roughly 100 times further apart than the atoms inside them. The distance helps the electrons settle down and gives them a chance to know their neighbors.

Feng Wang studied alongside Jie Shan at Columbia University. Now he runs a competing lab at the University of California, Berkeley, where his group has made parallel discoveries in the expanding world of 2D materials.

Shan and Mak’s friendly rival, Feng Wang, was one of the first to recognize the potential of TMD moiré superlattices. Back-of-the-envelope calculations suggested that these materials should give rise to one of the simplest ways electrons can organize — a state known as a Wigner crystal, where mutual repulsion locks lethargic electrons into place. Wang’s team saw signs of such states in 2020 and published the first image of electrons holding each other at arm’s length in Nature in 2021. By then, word of Wang’s TMD moiré activities had already spread through the tightknit 2D physics community, and the Cornell TMD factory was churning out TMD moiré devices of their own. Shan and Mak also reported evidence for Wigner crystals in TMD superlattices in 2020 and discovered within months that electrons in their devices could crystallize in almost two dozen different Wigner crystal patterns .

At the same time, the Cornell group was also crafting TMD moiré materials into a power tool. MacDonald and collaborators had predicted in 2018 that these devices have the right combination of technical features to make them perfectly represent one of the most important toy models in condensed matter physics. The Hubbard model, as it’s called, is a theorized system used to understand a wide variety of electron behaviors. Independently proposed by Martin Gutzwiller, Junjiro Kanamori and John Hubbard in 1963, the model is physicists’ best attempt to strip the practically infinite variety of crystalline lattices down to their most essential features. Picture a grid of atoms hosting electrons. The Hubbard model assumes that each electron feels two competing forces: It wants to move by tunneling to neighboring atoms, but it’s also repulsed by its neighbors, which makes it want to stay where it is. Different behaviors arise depending on which desire is strongest. The only problem with the Hubbard model is that in all but the simplest case — a 1D string of atoms — it is mathematically unsolvable.

According to MacDonald and colleagues, TMD moiré materials could act as “simulators” of the Hubbard model, potentially solving some of the field’s deepest mysteries, such as the nature of the glue that binds electrons into superconducting pairs in cuprates. Instead of struggling with an impossible equation, researchers could set electrons loose in a TMD sandwich and see what they did. “We can write down this model, but it’s very difficult to answer lots of important questions,” MacDonald said. “Now we can do it just by doing an experiment. That’s really groundbreaking.”

To build their Hubbard model simulator, Shan and Mak stacked layers of tungsten diselenide and tungsten sulfide to create a moiré superlattice, and they attached electrodes to dial up or down an electric field passing through the TMD sandwich. The electric field controlled how many electrons would fill each supercell. Since the cells act like giant atoms, going from one electron to two electrons per supercell was like transforming a lattice of hydrogen atoms into a lattice of helium atoms. In their initial Hubbard model publication in Nature in March 2020, they reported simulating atoms with up to two electrons; today, they can go up to eight. In some sense, they had realized the ancient aim of turning lead into gold. “It’s like tuning chemistry,” Mak said, “going through the periodic table.” In principle, they can even conjure up a grid of fictitious atoms with, say, 1.38 electrons each.

Next, the group looked to the hearts of the artificial atoms. With more electrodes, they could control the supercells’ “potential” by making changes akin to adding positive protons to the centers of the giant synthetic atoms. The more charge a nucleus has, the harder it is for electrons to tunnel away, so this electric field let them raise and lower the hopping tendency.

Mak and Shan’s control of the giant atoms — and therefore the Hubbard model — was complete. The TMD moiré system lets them summon a grid of ersatz atoms, even ones that don’t exist in nature, and smoothly transform them as they wish. It’s a power that, even to other researchers in the field, borders on magical. “If I were to single out their most exciting and impressive effort, that’s the one,” Kim said.

The Cornell group quickly used their designer atoms to settle a 70-year-old debate. The question was: What if you could take an insulator and tweak its atoms to turn it into a conducting metal? Would the changeover happen gradually or abruptly?

With their moiré alchemy, Shan and Mak carried out the thought experiment in their lab. First they simulated heavy atoms, which trapped electrons so that the TMD superlattice acted like an insulator. Then they shrank the atoms, weakening the trap until electrons became able to hop to freedom, letting the superlattice become a conducting metal. By observing a gradually falling electrical resistance as the superlattice acted increasingly like a metal, they showed that the transition is not abrupt. This finding, which they announced in Nature last year, opens up the possibility that the superlattice’s electrons may be able to achieve a long-sought type of fluidity known as a quantum spin liquid . “That may be the most interesting problem one can tackle,” Mak said.

Almost at the same time, the couple lucked into what some physicists consider their most significant discovery yet. “It was actually a total accident,” Mak said. “Nobody expected it.”

When they started their Hubbard simulator research, the researchers used TMD sandwiches in which the hexagons on the two layers are aligned, with transition metals atop transition metals and chalcogenides atop chalcogenides. (That’s when they discovered the gradual insulator-to-metal transition.) Then, serendipitously, they happened to repeat the experiment with devices in which the top layer had been stacked backward.

As before, the resistance started falling as electrons began to hop. But then it plunged abruptly, going so low that the researchers wondered if the moiré had begun to superconduct. Exploring further, though, they measured a rare pattern of resistance known as the quantum anomalous Hall effect — proof that something even weirder was going on. The effect indicated that the crystal structure of the device was compelling electrons along the edge of the material to act differently from those in the center. In the middle of the device, electrons were trapped in an insulating state. But around the perimeter, they flowed in one direction — explaining the super-low resistance. By accident, the researchers had created an extremely unusual and fragile type of matter known as a Chern insulator.

The quantum anomalous hall effect, first observed in 2013 , usually falls apart if the temperature rises above a few hundredths of a kelvin. In 2019, Young’s group in Santa Barbara had seen it in a one-off twisted graphene sandwich at around 5 kelvins. Now Shan and Mak had achieved the effect at nearly the same temperature, but in a no-twist TMD device that anyone can re-create. “Ours was a higher temperature, but I’ll take theirs any day because they can do it 10 times in a row,” Young said. That means you can understand it “and use it to actually do something.”

Mak and Shan believe that, with some fiddling, they can use TMD moiré materials to build Chern insulators that survive to 50 or 100 kelvin. If they’re successful, the work could lead to another way to get current flowing with no resistance — at least for tiny “nanowires,” which they may even be able to switch on and off at specific places within a device.

Exploration in Flatland

Even as the landmark results pile up, the couple shows no signs of slowing down. On the day I visited, Mak looked on as students tinkered with a towering dilution refrigerator that would let them chill their devices to temperatures a thousand times colder than what they’ve worked with so far. There’s been so much physics to discover at “warmer” conditions that the group hasn’t had a chance to thoroughly search the deeper cryogenic realm for signs of superconductivity. If the super fridge lets the TMDs superconduct, that will answer yet another question, showing that a form of magnetism intrinsic to cuprates (but absent from TMDs) is not an essential ingredient of the electron-binding glue. “That’s like killing one of the important components that theorists really wanted to kill for a long time,” Mak said.

He and Shan and their group haven’t even begun to experiment with some of the funkier TMDs. After spending years inventing the equipment needed to move around the continent of 2D materials, they’re finally gearing up to venture beyond the moly disulfide beachhead they landed on back in 2010.

The two researchers attribute their success to a culture of cooperation that they absorbed at Columbia. The initial collaboration with Hone that introduced them to moly disulfide, they say, was just one of the many opportunities they enjoyed because they were free to follow their curiosity. “We didn’t have to discuss” their plans with Heinz, the head of their lab, Shan said. “We talked to people from other groups. We did the experiments. We even wrapped things up.”

Today they foster a similarly relaxed environment at Cornell, where they oversee a couple dozen postdocs, visiting researchers and students, all of whom are largely free to do their own thing. “Students are very smart and have good ideas,” Mak said. “Sometimes you don’t want to interfere.”

Their marriage also makes their lab unique. The two have learned to lean into their personal strengths. Besides an abundance of creativity as an experimentalist, Shan possesses a careful discipline that makes her a good manager; as the three of us talked, she frequently nudged “Professor Fai” back on track when his enthusiasm for physics pushed him too deep into technicalities. Mak, for his part, enjoys toiling alongside the early-career researchers, both inside and outside the lab. He recently started rock climbing with the group. “It seems like their lab is their family,” said Young. Shan and Mak told me they achieve more together than they could alone. “One plus one is more than two,” Mak said.

The devices they’re building may also stack up to be more than the sum of their parts. As researchers join TMD sheets together to create excitons and moiré superlattices, they speculate about how the new ways of domesticating electrons might supercharge technology. Even if pocket-ready superconductivity remains elusive, Bose-Einstein condensates could lead to ultra-sensitive quantum sensors, and better control of Chern-like insulators could enable powerful quantum computers . And those are just the obvious ideas. Incremental improvements in materials science often add up to radical applications few saw coming. The researchers who developed the transistor, for instance, would have struggled to predict smartphones powered by billions of microscopic switches stuffed into a chip the size of a fingernail. And the scientists who endeavored to fashion glass fibers that could carry light across their lab bench could not have foreseen that 10,000-kilometer undersea optical fibers would someday link continents. Two-dimensional materials may evolve in similarly unpredictable directions. “A really new materials platform generates its own applications as opposed to displacing existing materials,” said Heinz.

While driving me to the Ithaca bus stop, Shan and Mak told me about a recent (and rare) vacation they took to Banff, Canada, where they once again displayed their knack for stumbling onto surprises through a blend of effort and luck. They had spent days trying — in vain — to spot a bear. Then, at the end of the trip, on their way to the airport, they stopped to stretch their legs at a botanical reserve and found themselves face to face with a black bear.

Similarly, with condensed matter physics, their approach is to wander around together in a new landscape and see what shows up. “We don’t have much theoretical guidance, but we just fool around and play with experiments,” Mak said. “It can fail, but sometimes you can bump into something very unexpected.”