The interplay between topology, geometry and correlations in novel materials

新型材料中拓扑、几何和相关性之间的相互作用

• 批准号: 2594335
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2594335
• 关键词: interplay; between; topology; geometry; correlations

In this project we will consider hydrodynamic electron transport in various strongly-correlated 2Dmaterials. The goal is to derive equations describing the motion of electrons in these systems andsolve them for certain simple geometries. An intriguing possibility is to combine the somewhat"semiclassical" hydrodynamic description with the quantum nature of particles, which are in factcharacterized by discrete spin, pseudospin, valley, layer degrees of freedom. These are, quitegenerally, coupled to the particle kinetic momentum and endow electrons with non-trivial Berryphases. In turn, when the electron momentum varies (as a consequence of external potentials orcollisions), particles "skew" in the orthogonal direction, producing measurable effects. The interplaybetween strong correlations, hydrodynamic transport and the Berry phases of particles in twisted 2Dmaterials is a new and unexplored field.In this project we will:- derive equations of motions for electron in twisted bilayer graphene, both in flat and upper bands,where mobility is very high, accounting for the role of strong interactions, band renormalization,and the coupling between pseudospin/layer/valley indices with kinetic momentum;- solve the above-derived equations in simple but experimentally relevant geometries (channels,constrictions, etc.), addressing a wide range of densities and temperatures - from Fermi liquid toelectron-hole-plasma regime;- understand how Berry phases impact on the collision integral and therefore on viscositiesappearing in electrons' hydrodynamic equations. We will therefore study the emergence of "twobodyside jump" phenomena and calculate transport coefficients and relaxation times;- extend these results to other flat-band materials, such as transition-metal dichalcogenides, whereelectrons feature spin-orbit coupling and describe a new regime for spintronics.During this project the student will gain a knowledge of 2D materials, modern theory of transport andhydrodynamics, all of them hot research topics at the moment. Moreover, he/she will learn how toemploy modern field theoretical methods (Green functions, perturbation theory, Keldysh) to tacklemany-body transport problems in condensed matter physics. Finally, he/she will also develop and/orenhance computational skills by using Mathematica/Python to solve some of the problem numerically.

在这个项目中，我们将考虑各种强相关二维材料中的流体动力电子传输。目标是推导出描述这些系统中电子运动的方程，并求解某些简单的几何形状。一种有趣的可能性是将有点“半经典”的流体动力学描述与粒子的量子性质结合起来，粒子的量子性质实际上以离散自旋、赝自旋、谷、层自由度为特征。一般来说，这些与粒子动量耦合并赋予电子非平凡的浆果相。反过来，当电子动量变化时（由于外部电势或碰撞），粒子在正交方向上“倾斜”，产生可测量的效应。扭曲二维材料中粒子的强相关性、流体动力输运和浆果相之间的相互作用是一个新的、未经探索的领域。在这个项目中，我们将：-推导扭曲双层石墨烯中电子的运动方程，包括平带和上带，其中迁移率非常高，解释了强相互作用、能带重整化以及赝自旋/层/谷指数与动量之间的耦合的作用；-以简单但实验相关的方式求解上述导出的方程几何形状（通道、收缩等），解决各种密度和温度 - 从费米液体到电子-空穴-等离子体体系；- 了解贝里相如何影响碰撞积分，从而影响电子流体动力学方程中出现的粘度。因此，我们将研究“双体跳跃”现象的出现，并计算输运系数和弛豫时间；-将这些结果扩展到其他平带材料，例如过渡金属二硫化物，其中电子具有自旋轨道耦合特征，并描述了一种新的平带材料自旋电子学。在这个项目中，学生将获得二维材料、现代输运理论和流体动力学的知识，这些都是目前的热门研究课题。此外，他/她将学习如何采用现代场论方法（格林函数、微扰理论、凯尔迪什）来解决凝聚态物理中的多体输运问题。最后，他/她还将通过使用 Mathematica/Python 以数值方式解决一些问题来开发和/或增强计算技能。