Beyond Luttinger Liquids-spin-charge separation at high excitation energies

一个令人吃惊的事实是，尽管就我们所知，孤立的电子是不可分割的，但被限制只能在一条狭窄的导线中运动的电子集合似乎解离成两种新的粒子。这两种粒子分别携带电子的磁性（或自旋）和电荷，称为自旋子和holon。这些物质构成了一种新的物质状态，称为Tomonaga-Luttinger液体。几十年来，我们对这种Luttinger液体的理解完全是理论上的，依赖于电子行为的简化模型，因为即使是世界上最强大的计算机，我们也无法精确地解决超过少数电子的行为-这就是多电子薛定谔方程的复杂性。近年来，半导体物理学的进步使人们有可能建立必要的条件来创造一种Luttinger液体，并直接观察自旋-电荷分离现象。我们在2009年的一次合作中实现了这一目标，这次合作汇集了实验学家和理论家，他们是这一提议的主要研究者。该实验的工作原理是将电子注入一组导线（通过量子力学隧道效应），并通过改变磁场和电压来绘制出它们随后的去向。虽然实验是成功的，但它提出了许多有趣的问题只有在我们面前的实验结果，我们才能看到当前理论的缺点。最令人惊讶的观察是，虽然预测自旋-电荷分离的近似理论只适用于最低能量的激发，但我们在实验中看到了自旋-电荷分离延伸到更高能量的暗示。关键的问题是：我们能在多高的能量下追踪自旋子和霍隆？如果它们异常稳定，那么是什么导致了这种稳定性，我们能从数学上理解它吗？此外，所有的理论都假设电线是无限长的。我们的建议包括研究一系列的长度，以解决如何激励的影响，当它是短的电线的两端。这可能是解释15年来量子线电导率“0.7”阶跃特征之谜所必需的关键一步。这项提议的核心是一种改进的测量自旋-电荷分离的装置，以及最近的理论思想，这些思想发展了数学机器，使我们能够计算出远离窄线低能极限的性质。这个理论需要与新的隧道实验的建议。我们的新设备也将允许两种新类型的实验进行。我们将测量进入和离开一维导线的隧穿，由此可以理解新的激发是如何弛豫回到平衡的。我们还将测量两条一维线之间的阻力，这将再次帮助我们理解不同的自旋和霍隆性质。这两个实验都有初步的理论预测，我们将加以验证，这个提议的影响超出了Luttinger液体状态的界限。其他类型的金属（所谓的“坏金属”）在高温下也表现出只属于低能量和低温度的性质。如果我们能理解这在一维Luttinger液体中是如何工作的（通常我们有更多的数学技术可以部署），它可能指向那个更难的问题的解决方案。同样，操纵非常窄的导线并稳定其不寻常的量子特性的技术也是制造拟议中的量子计算机所需要的。像Luttinger液体一样，所讨论的线也有非常不寻常的激发，但这些激发在高温下通过一种拓扑保护使人联想到防止莫比乌斯带解开的拓扑保护而变得坚固。

It is an astonishing fact that although an isolated electron is, as far as we can tell, indivisible, a collection of electrons constrained to move only in a narrow wire appear to dissociate into two new types of particle. These two particles carry separately the magnetism (or spin) of the electron and its electric charge and are called spinons and holons. These form the building blocks of a new state of matter known as a Tomonaga-Luttinger liquid. For decades our understanding of this Luttinger liquid has been entirely theoretical, resting on simplified models of how electrons behave, since even with the world's most powerful computers we are unable to solve exactly the behaviour of more than a handful of electrons-such is the complexity of the many-electron Schrödinger equation. Advances in semiconductor physics have made it possible in recent years to set up the necessary conditions to create a Luttinger liquid and observe the phenomenon of spin-charge separation directly. This we achieved in 2009 in a collaboration that brought together the experimentalist and theorist who are the principal investigators on this proposal. The experiment worked by injecting electrons into an array of wires (via quantum mechanical tunnelling) and mapping out where they subsequently go by varying the magnetic field and voltage. Though the experiment was a success, it raised a number of intriguing questions-only with the experimental results in front of us could we see the shortcomings of current theory. It is those questions that underpin this proposal.The most surprising observation is that, while the approximate theories that predict spin-charge separation are only valid for the lowest-energy excitations, we saw hints in the experiment that spin-charge separation extends to higher energies. The key question is: how high in energy can we track the spinon and holon? If they are unusually stable then what causes this stability and can we understand it mathematically? Also, the theories all assume the wires are infinitely long. Our proposal involves studying a range of lengths to address how the excitations are influenced by the ends of the wire when it is short. That may be the vital step necessary to explain a 15 year-old mystery of the "0.7" step-like feature in the conductance of quantum wires. At the heart of this proposal is an improved device for measuring spin-charge separation, and recent theoretical ideas that develop mathematical machinery to allow us to calculate properties away from the low-energy limit of narrow wires. This theory needs to be related to the new tunnelling experiment of the proposal.Our new devices will also allow two new types of experiment to be undertaken. We will measure the tunnelling both into and out of a one-dimensional wire, from which it is possible to understand how the novel excitations relax back to equilibrium. We will also measure the drag forces between two 1D wires, which again will help characterise the distinct spinon and holon properties. There are preliminary theoretical predictions for both experiments, which we will test.The implications of the proposal extend beyond the boundaries of the Luttinger-liquid state. Other types of metal (so called "bad metals") also show, at high temperatures, properties that naively only belong at low energies and temperatures. If we can understand how this works in the one-dimensional Luttinger liquid (where typically we have more mathematical techniques to deploy) it could point to a solution of that much harder problem. Similarly, the techniques of manipulating very narrow wires and stabilising their unusual quantum properties are also what would be required to make a proposed type of quantum computer. Like the Luttinger liquid, the wires in question also have very unusual excitations but these have been constructed to be robust at high temperatures through a type of topological protection reminiscent of that which prevents a Möbius strip from unwinding.