Frustration and reduced dimensionality as routes to new forms of quantum order

当蒸汽冷却下来时，快速运动的水分子凝结成水。如果水进一步冷却，水分子就完全停止运动，并自行组织成美丽的晶体结构，我们称之为冰。我们用来制造电子设备的所有材料——例如你现在使用的计算机的半导体大脑——都含有液态或气态的移动电子。那么这些电子冷却后会发生什么呢？答案取决于它们所生活的物质的化学结构。在一些物质中，电子形成固体，很像冰中的水分子。有些会变得有磁性。有些会变成超导体”——一种电阻率为零的非凡金属。这样的系统被称为“表现出不同形式的秩序”，也就是说，它们所包含的电子在冷却时以不同的方式组织自己。21世纪材料科学最重要的主题之一是寻找电子表现出全新秩序形式的材料。这是一个与寻找新型基本粒子一样重要的问题。但它也具有深远的技术意义，因为这些新材料有一天可能被用来制造新型电子设备。这个提议结合了最先进的理论和实验，目的是探索新形式的量子秩序是如何在系统中出现的，在这个系统中，没有简单的秩序形式完全获胜，电子（就像人一样）被他们面临的一系列令人困惑的选择所挫败。我们考虑的实验系统处于现代材料科学的前沿，并且在物理行为上是独一无二的。在LiV2O4中，钒的d电子变得和μ子一样大。在Na4Ir3O8中，磁性Ir离子在任何温度下都不能磁性有序。PrBa2Cu4O8是已知存在的最一维的金属，而有机化合物kappa-(ET)2Cu2(CN)3和kappa-(ET)2Cu[N(CN)2]Cl，在高度受挫的三角形晶格上提供了长期寻求的量子自旋实现。我们的主要实验方法将是测量这些系统如何传输热量和电力。在一定温度范围内测量的导热系数和导电性的比值，是对给定材料中电子组织方式的一种非常敏感的测试。测量这个比率将使我们能够确定这些材料完全不同于传统的金属和绝缘体。我们还将研究它们的电子特性，如质量，如何随着系统变得更加受挫而演变。与此同时，我们将使用超级计算机来解决数学模型，以说明非常规秩序如何在这些材料中发挥作用。特别是，我们试图理解电子是如何一起工作以形成新型的“基本激发”，例如具有电子一半电荷的粒子！如果成功，这项工作有可能永远改变我们对金属的看法……

When steam cools down, fast-moving water molecules condense into water. And if this water is cooled further, the watermolecules stop moving altogether, and organize themselves into the beautiful crystal structures we know as ice. All ofthe materials we use to make electronic devices --- for example the semi-conductor brain'' of the computer you arenow using - contain mobile electrons in a liquid or gas-like state. So what happens to these electrons when they cooldown ? The answer depends on the chemical structure of material in which they live.In some materials the electrons form a solid, rather like the water molecules in ice. Some become magnetic. And somebecome superconductors'' - a remarkable type of metal whose electrical resistivity is exactly zero. Such systemsare said to exhibit different forms of order'', which is to say that the electrons they contain organize themselvesin different ways when they are cooled down. One of the most important themes in 21st century materials science is thesearch for materials whose electrons exhibit completely new forms of order. This is a problem as fundamental as thesearch for new types of elementary particle. But it is also one of profound technological significance, since thesenew materials may one day be used to build new forms of electronic device.This proposal combines state-of-the-art theory and experiment, with the goal of exploring how new forms of quantumorder can arise in systems where no simple form of order wins outright, and the electrons are frustrated (muchlike people) by the bewildering array of choices which they face. The experimental systems we consider are at the forefront of modern materials science, and are unique in their physical behaviour. In LiV2O4, vanadium d-electrons become as massive as muons.In Na4Ir3O8, magnetic Ir ions fail to order magnetically at any temperature. PrBa2Cu4O8 is the most one-dimensional metal known to exist, whilst the organic compounds kappa-(ET)2Cu2(CN)3 and kappa-(ET)2Cu[N(CN)2]Cl, provide a long-sought realization of quantum spins on a highly-frustrated triangular lattice.Our main experimental approach will be to measure how these systems transport heat and electricity. The ratio of thermal and electrical conductivities, measured over a range of temperatures, is a very sensitive test of the way in which the electrons in a given material have organized themselves. Measuring this ratio will enable us to establish that these materials are completely unlike conventional metals and insulators. We will also study how their electronic characteristics, such as mass, evolve as the systems become more frustrated. At the same time, we will use super-computers to solve mathematical models of how unconventional order might work in these and materials. In particular we try to understand how electrons work together to form new types of elementary excitation'', for example particles with half the charge of an electron ! If successful, this work has the potential to change how we think about metals forever...