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

一个令人吃惊的事实是，尽管一个孤立的电子，据我们所知，是不可分的，但一群被限制只能在一条狭窄的电线中运动的电子，似乎会分离成两种新的粒子。这两种粒子分别携带电子的磁性（或自旋）及其电荷，被称为自旋子和介子。这些物质构成了一种被称为Tomonaga-Luttinger液体的新物质状态的基石。几十年来，我们对这种卢廷格液体的理解完全是理论上的，基于电子行为的简化模型，因为即使使用世界上最强大的计算机，我们也无法准确地解决几个电子的行为——这就是多电子Schrödinger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制造卢廷格液体，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，这次合作将实验学家和理论家聚集在一起，他们是该提案的主要研究人员。该实验通过将电子注入一组导线（通过量子力学隧道），并通过改变磁场和电压来绘制出它们随后的去向。虽然这个实验是成功的，但它提出了许多有趣的问题——只有在我们面前的实验结果中，我们才能看到当前理论的缺点。正是这些问题支撑了这项提议。最令人惊讶的观察结果是，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-电荷分离扩展到更高能量的迹象。关键的问题是：我们能在多高的能量下追踪到自旋子和黑洞？如果它们异常稳定，那么是什么导致了这种稳定，我们能从数学上理解吗？而且，这些理论都假设电线是无限长的。我们的建议包括研究一系列长度，以解决当导线较短时，激励如何受到导线两端的影响。这可能是解释15年来量子线电导率“0.7”步状特征的关键一步。这个提议的核心是一个改进的测量自旋电荷分离的装置，以及最近的理论思想，这些理论思想发展了数学机制，使我们能够计算出窄线低能量极限以外的特性。这一理论需要结合新的隧道掘进实验提出建议。我们的新设备也将允许进行两种新的实验。我们将测量进入和走出一维导线的隧穿，由此有可能理解新的激发是如何放松到平衡的。我们还将测量两根一维线之间的阻力，这将再次有助于描述自旋子和全息子的独特特性。这两个实验都有初步的理论预测，我们将对其进行测试。该建议的含义超出了卢廷格-液态的边界。其他类型的金属（所谓的“坏金属”）在高温下也表现出一些只属于低能量和低温度的特性。如果我们能理解这在一维卢廷格液体中是如何工作的（通常我们有更多的数学技术来部署），它可能会指向那个更难的问题的解决方案。同样，操纵非常窄的电线并稳定其不寻常的量子特性的技术也是制造一种拟议类型的量子计算机所需要的。就像卢廷格液体一样，这些电线也有非常不寻常的激发，但它们已经通过一种拓扑保护被构造成在高温下坚固耐用，这让人想起了防止Möbius条展开的拓扑保护。

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.