内容来源：https://www.quantamagazine.org/physicists-make-electrons-flow-like-water-20260211/

内容总结：

物理学家实现电子“类流体”运动，为新型电子器件研发开辟新路径

长期以来，电子在导线中的运动被理解为彼此独立、相互碰撞的分散式流动，这与水流那种具有集体协同性的流动模式截然不同。然而，自20世纪60年代起，理论物理学家便预言，在特定条件下电子可表现出类似液体的集体流动行为，即形成“电子流体”。近年来，随着石墨烯等超纯净材料的出现，这一预言正逐步被实验证实。

2017年，诺贝尔奖得主安德烈·海姆团队在石墨烯中首次观测到“古尔吉效应”——随着温度升高，材料电阻反而下降，这标志着电子开始像黏性流体一样保存动量协同运动。2022年，以色列魏茨曼研究所的科学家更直接观测到电子在钨二硒烯材料中形成涡旋，宛如水流在河道转弯处产生的漩涡。

突破性进展出现在2025年。哥伦比亚大学科里·迪恩实验室的研究人员利用两层石墨烯构建出类似火箭发动机喷管的“拉瓦尔喷嘴”结构，将电子加速至每秒数百公里，超越了电子流体中的“声速”。当这些超速电子与下游低速电子相遇时，产生了清晰的激波现象，首次实现了电子流体的“超音速流动”。

这些实验不仅验证了深奥的理论预测，更蕴含着实际应用潜力。当电子以流体模式运动时，其行为会受到流通通道形状的显著影响，这为通过设计微纳结构来调控电子器件性能提供了全新思路。此外，该研究领域有望架起流体力学与量子物理之间的桥梁，帮助科学家用流体方程描述复杂量子系统的宏观行为，从而理解更多尚未破解的凝聚态物理谜题。

目前，探索电子流体的奇异特性已成为凝聚态物理的前沿方向之一。正如加州大学欧文分校物理学家托马斯·斯卡菲迪所言：“这为我们理解电子开辟了一种全新的方式。”

中文翻译：

物理学家让电子如水流般运动

引言

倘若让你描绘电子的运动方式，你脑海中浮现出粒子如溪流般沿导线奔涌、仿佛水流穿过管道的画面，这完全可以理解。毕竟，我们常将电子描述为在"电流"中"流动"。

但实际上，水与电的流动方式截然不同。水分子会共同运动形成涡旋连贯的流体，而电子往往彼此擦身而过。"水流中只有水分子相互作用，"哥伦比亚大学物理学家科里·迪恩解释道，"但在导线这样的电子系统中，情况显然不同。"水分子团结协作形成流动，每个电子却各自为政。

这种"各自为战"的运动模式构成了整个电子理论的基础。它解释了为何热导线比冷导线电阻更大，也说明了圆形导线与方形导线的导电能力相当。

但自20世纪60年代以来，理论物理学家们始终推测：电子或许能被诱导出类似流体的行为特性，从而形成"电子流体"。

近年来，一系列实验证实了这一预言。去年秋天，迪恩团队通过最引人注目的实验演示，成功让电子形成了高速流体撞击低速流体时产生的那种激波。这确凿无疑地证明电子正以极高速度流动。"这确实是当前的前沿领域，"加州大学欧文分校物理学家托马斯·斯卡菲迪评价道，他并未参与该项实验。

让电子表现出类流体特性，未来或许能催生新型电子器件。而将成熟的水流理论拓展至电子领域，可能为量子材料研究开辟全新思路。

碰撞式流动与连贯式流动

科罗拉多大学博尔德分校理论物理学家安德鲁·卢卡斯将导线中的电子运动比作弹珠在弹珠机中的穿梭。弹珠进入游戏区域后，会在挡板与缓冲器间四处弹跳，上下翻飞。类似地，当铜线中的电子与振动的铜原子或金属"杂质"（其他原子取代铜原子的位点）碰撞时，也会朝各个方向散射。

平均而言，弹珠向下运动的趋势确实更强，这种统计意义上的倾向可称为"流动"。同理，电子的"流动"也仅体现在统计平均中——由电池等建立的电场在导线中设定了极其微弱的优先方向。

但这是一种特殊的流动。电子与杂质的碰撞方式，很像沙包撞击地面：更多是沉闷的撞击而非弹性反弹。杂质会消耗电子能量，阻碍其积累动量。因此电子在导线中的运动，犹如水流渗过压实沙地，被物理学家称为"弥散流"。

相比之下，水管中的水分子几乎只相互碰撞。这种碰撞如同台球撞击：它们共享动量并持续运动。

水分子这种"保持"动量的能力定义了流体特性。由于与障碍物的碰撞不会损耗动量，水分子能进行复杂的集体运动，形成快慢交替的流区与旋涡。

1963年，苏联物理学家拉季·古尔日首次精确计算出：如果电子仅能相互碰撞并像水分子那样保持动量，将会发生什么。

古尔日发现关键差异在于电流对热的响应。加热铜线通常会阻碍电流，因为铜原子振动加剧会更大程度干扰电子。但他计算出：若动量守恒，热量反而会促进电子运动——就像温热的蜂蜜比冷蜂蜜更易流动。

这项发现后被称作古尔日效应，但当时未受重视。卢卡斯指出，这更像是理论奇想，与现实世界中"充满杂质"的导线里的电子关联甚微。

五十年后，转机来临。

石墨烯登场

2004年，安德烈·海姆与康斯坦丁·诺沃肖洛夫宣布发现石墨烯——他们仅用透明胶带就从铅笔芯中剥离出的碳原子蜂窝状薄层。这项成就为他们赢得了诺贝尔奖。

单层石墨烯如同没有缓冲器的弹珠机：几乎所有原子都排列有序。"这是热力学意义上完美的晶体，天然形成且杂质极少，"专攻石墨烯实验的迪恩解释道。

物理学家花费约十年时间才掌握无干扰研究石墨烯的方法。而当他们成功时，终于观测到真正的电子流体。

2017年的早期实验中，海姆团队在石墨烯条上制造狭窄通道，通入电子并测量电阻。他们发现随着温度升高，电阻反而下降——这正是古尔日效应的体现。

2022年，以色列魏茨曼科学研究所的物理学家首次直接观测到电子流动。他们用类石墨烯材料二硒化钨制成垂直导线，并在中段设计两个米老鼠耳朵状的圆环。当电子沿导线流入"耳朵"区域时，团队通过测量电子运动产生的磁场监控其轨迹，首次观测到电子涡流——流体状电流回旋涌入"耳朵"区域，宛如河水遇弯道时形成的逆流漩涡。

"他们真切看到了这些涡旋，"斯卡菲迪说道。他曾在2022年与海姆团队合作进行另一项电子流体实验。

突破超音速

2025年，迪恩实验室的博士后约翰内斯·格尔斯决定将电子流体研究"推向极致"。

缓流与急流的特性差异在空气中同样显著（空气分子碰撞时也保持动量）。当飞机突破音障时，会产生被称为音爆的激波。格尔斯思考：电子是否也能突破类似的"声音屏障"，产生超音速激波？

为创造最快电子流体，他将双层石墨烯条雕刻成火箭发动机加速尾流的拉瓦尔喷嘴形状。当电子穿过喷嘴形成的收缩通道时，其速度被提升至超越电子流体中波纹传播的速度——即电子流体的"声速"（每秒数百公里）。加速电子撞击喷嘴下游开阔区域的低速电子时，亚音速电子来不及避让，导致流体压缩。研究人员用金属探针在样品上来回扫描，通过测量电场的细微变化检测到堆积效应。激波的出现证实他们确实突破了电子流体的声障。

电子驯术

此类实验让研究者得以拓展对电子的操控能力。这种全新掌控水平可能催生新型电子元件。斯卡菲迪指出："通过设计不同形状的器件通道（无论是米老鼠耳朵还是喷嘴），可以实现截然不同的物理效应。"

这些实验也有助于理论家建立描述电子与亚原子系统的全新范式。斯卡菲迪认为，这是"运用流体运动知识理解量子系统的一小步"。

当电子如流体般运动时，会形成连贯图案。一旦掌握流体的密度、粘度等宏观特性，就能用标准方程预测流体行为，无需追踪每个电子的运动轨迹。

理论家希望在其他复杂量子或半量子系统中，也能像2024年某团队对特定混沌量子电路所做的那样，通过识别守恒定律来把握宏观流动规律。

曾为哥伦比亚大学实验提供理论计算的卢卡斯表示，或许通过持续在实验室培育电子流体、运用流体力学描述其旋涡运动，理论家终将找到描述电子"消融"等更神秘现象的方法。"这是教科书范式无法解释现象的绝佳展示，"他总结道。

英文来源：

Physicists Make Electrons Flow Like Water
Introduction
If you were asked to picture how electrons move, you could be forgiven for imagining a stream of particles sluicing down a wire like water rushing through a pipe. After all, we often describe electrons as “flowing” in an “electric current.”
In reality, water and electricity flow in completely different ways. Whereas water molecules move together to form a swirly, coherent substance, electrons tend to fly past one another. “Water is seeing nothing but other water,” said Cory Dean, a physicist at Columbia University, “but in an electronic system, in a wire, that’s manifestly not the case.” Water molecules unite to flow, but each electron acts on its own.
This every-particle-for-itself movement serves as the foundation for all of electronic theory. It explains why a warm wire resists more than a cold wire, and why a round wire conducts as well as a square wire.
But since the 1960s, theorists have suspected that electrons can be coaxed to act more like their watery counterparts, and to form an electron fluid.
In recent years, a string of experiments has confirmed that prediction. Last fall, in the most dramatic demonstration yet, Dean and his collaborators arranged for electrons to form a type of shock wave that occurs when a quickly flowing fluid crashes into a slowly flowing fluid. It was a surefire sign that electrons were flowing at extremely high speeds. “That’s really the frontier right now,” said Thomas Scaffidi, a physicist at the University of California, Irvine who was not involved in the experiment.
Making electrons behave like water might someday lead to the development of new kinds of electronic devices. And extending the familiar theory of water to electrons could spawn a new way of thinking about quantum materials.
Thudding vs. Flowing
Andrew Lucas, a theoretical physicist at the University of Colorado, Boulder, compares electrons traveling down a wire to pinballs traveling around a pinball machine. Once they enter the playing field, pinballs bounce around in every direction, flying off flippers and bumpers. They travel up the machine, down the machine, and all around it. Similarly, when electrons in a copper wire collide with vibrating copper atoms or with “impurities” in the metal — spots where some other atom has usurped an atom of copper — they ricochet in all directions.
On average, pinballs do tend to travel farther down than up; in this sense they “flow” downward. Analogously, the “flow” of electrons emerges only in an average sense; an electric field, perhaps generated by a battery, establishes an ever-so-slightly preferred direction in the wire.
But this is a peculiar type of flow. An electron collides with an impurity much in the same way a hacky sack collides with the floor: It thuds more than it bounces. The impurity saps the electron’s energy, preventing it from building up much momentum. Consequently, electrons move through a wire a bit like water seeping through packed sand, a motion physicists describe as a “dispersive” flow.
In contrast, water molecules flowing down a pipe collide almost exclusively off each other. And when they collide, they bounce like billiard balls: They share their momentum and keep on moving.
This ability of water molecules to “conserve” their momentum defines the nature of liquidity. Since collisions with obstacles don’t drain their momentum, water molecules can engage in complicated collective motions, flowing in faster- and slower-moving zones and in swirling eddies.
In 1963 Radii Gurzhi, a Soviet physicist, was the first to calculate exactly what would happen if electrons found themselves in a situation where they could only knock into each other, conserving momentum like water molecules.
Gurzhi found that the difference would lie in how the electric current reacted to heat. Warming a copper wire typically impedes electric current, since vibrations in the copper atoms intensify and more greatly impede electrons. But Gurzhi calculated that if momentum were conserved, heat would make electrons move more readily — similar to the way warm honey is runnier than cool honey.
His observation became known as the Gurzhi effect, but it didn’t attract much attention at the time. It seemed like a theoretical curiosity, with little relevance to real electrons, trapped as they were in real-world wires “full of dirt and impurities,” Lucas said.
Fifty years later, that would change.
Enter Graphene
In 2004, Andre Geim and Konstantin Novoselov announced the discovery of graphene, a honeycomb sheet of carbon atoms they could peel off a block of pencil lead using only Scotch tape. The effort earned them a Nobel Prize.
A layer of graphene was like a pinball machine with no bumpers; almost every atom was in its place. “It’s just a thermodynamically beautiful crystal. It comes out of the earth well formed, with very few impurities,” said Dean, who specializes in graphene experiments.
It took physicists about a decade to figure out how to study graphene without interference from other materials. But when they did, they detected electrons truly flowing.
In one early experiment, in 2017, Geim and his collaborators carved a choke point into a strip of graphene, poured electrons through, and measured the resistance. They found that as they turned up the temperature, the resistance fell — the Gurzhi effect in action.
And in 2022, physicists at the Weizmann Institute of Science in Israel managed to directly watch electrons flowing. They shaped a material with some similarities to graphene, called tungsten diselenide, into a vertical wire flanked halfway down by two circles resembling Mickey Mouse ears. As electrons flowed into the ears on their way down the wire, the group monitored their motion by measuring the magnetic field the electrons generated when moving around the wire. In doing so, they saw fluidic electric currents swirling backward into the ears — electron whirlpools. The whirlpools resembled the eddies that form when part of a river’s current runs into a bend and turns upstream.
“They can really see these vortices,” said Scaffidi, who collaborated with Geim’s group on another electron fluid experiment, also in 2022.
Going Supersonic
In 2025, Johannes Geurs, a postdoc in Dean’s lab, decided to push the idea of electron fluids “to the extreme,” Dean said.
Slowly moving fluids act differently from quickly moving fluids. We can see this in the air, which is as much a fluid as water, because air molecules conserve momentum when they collide. When a plane accelerates past the sound barrier in the air, it generates a shock wave known as a sonic boom. Geurs wondered if it was possible to break an analogous sound barrier with electrons themselves, which would lead to another sort of supersonic shock wave.
To produce the speediest electron fluid possible, he carved a strip made from two sheets of graphene into a sleek shape known as a de Laval nozzle — a shape that rocket engines use to accelerate their exhaust.
Then he sent electrons through the constriction formed by the nozzle, which boosted their speed beyond the rate at which ripples travel through the electron fluid. That’s the “speed of sound” for an electron fluid, a few hundred kilometers per second. When the accelerated electrons crashed into other electrons lingering in an open region downstream of the nozzle, the slower, subsonic electrons couldn’t get out of the way fast enough, and the liquid compressed. The researchers swept a metallic tip back and forth over the sample, measuring minute changes in the electric field, and detected the pileup. The shock wave indicated that they had in fact broken the electron fluid’s sound barrier.
Electron Whisperers
Experiments like these allow researchers to flex and extend their control over electrons. This new level of mastery could lead to novel electronics components. For example, when electrons move like fluids, they start to respond to the shape of the channel through which they’re moving, whether it’s Mickey Mouse ears or a nozzle. “By using different shapes for your device, you can realize very different physics,” Scaffidi said.
These experiments could also help theorists develop an entirely new way of talking and thinking about electrons and subatomic systems. It’s “a baby step” toward using what we know about the movement of liquids to understand quantum systems, Scaffidi said.
When electrons flow like fluids, they form coherent patterns. Once you know some high-level properties of the fluid, such as density and viscosity, you can use standard equations to find out what the fluid will do, without needing to keep track of the motion of every last electron.
The hope is that in other complicated quantum or semi-quantum systems, theorists might, for instance, be able to identify conservation laws that will help them recognize similar large-scale flow behavior, as one group was able to do for certain chaotic quantum circuits in 2024.
Perhaps by continuing to cook up electron fluids in the lab, and by using hydrodynamics to describe the way they swirl, theorists will find a way to describe other, more enigmatic situations where electrons seem to melt away, said Lucas, who helped with some of the theory calculations for the Columbia experiment. “It’s a very appealing showcase of something that can’t be explained in any textbook paradigm,” he said.