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Correlations and impurities in topological insulators

拓扑绝缘体中的相关性和杂质

基本信息

批准号：
193069739
负责人：
Professor Dr. Christoph Karrasch
金额：
--
依托单位：
Institut für Mathematische Physik
依托单位国家：
德国
项目类别：
Research Fellowships
财政年份：
2011
资助国家：
德国
起止时间：
2010-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/193069739?language=en
关键词：
Correlations impurities topological insulators

项目摘要

Topological insulators are fundamentally different from ordinary insulating materials in that they feature an insulating gap in the bulk but exhibit robust metallic surface states. The latter can be attributed to topological properties of the bulk wave functions and can be observed experimentally. Most theoretical approaches to describe topological insulators ignore the Coulomb interactions between electrons. Adding such terms to the tight-binding model of graphene with spin-orbit couplings -- which is a paradigm in the field as it describes the most simple realization of topological order -- yields a two-band Hubbard model. Hubbard models, however, are well-know to exhibit a variety of strongly-correlated phases ranging from magnetic types of order to Mott insulating behavior. The honeycomb geometry was addressed in a few works, but a complete picture of how the different (conventional) kinds of order evolve out of the topological phase (persisting in absence of Coulomb interactions) is yet missing. As the first part of this proposal, I want to study this problem using a framework which provides an unbiased approach to the various instabilities of the Hubbard model -- the functional renormalization group.The low-energy physics of a normal metal is drastically modified by the addition of even a few magnetic impurities. A single spin degree of freedom can be screened completely by the conduction electrons by virtue of the Kondo effect. The surface of topological insulators represents a helical metal, but it is not obvious whether the Kondo effect persists. I want to study this problem of impurities on top of topological insulators using two complementary renormalization group frameworks - the functional and real-time renormalization group. Moreover, I want to investigate the real-time and steady state dynamics of a two-terminal transport geometry in a quantum dot setup.

拓扑绝缘体从根本上不同于普通的绝缘材料，因为它们在本体中具有绝缘间隙，但表现出稳健的金属表面状态。后者可以归因于体波函数的拓扑性质，并且可以在实验中观察到。大多数描述拓扑绝缘体的理论方法忽略了电子之间的库仑相互作用。将这些项添加到具有自旋轨道耦合的石墨烯的紧束缚模型中-这是该领域的一个范例，因为它描述了拓扑顺序的最简单实现-产生了一个双带哈伯德模型。然而，哈伯德模型是众所周知的，表现出各种强相关的阶段，从磁类型的秩序莫特绝缘行为。蜂窝状的几何结构在一些著作中得到了讨论，但是关于不同的（传统的）有序是如何从拓扑相（在没有库仑相互作用的情况下持续存在）演化出来的，还没有一个完整的图景。作为这个提议的第一部分，我想用一个框架来研究这个问题，这个框架提供了一个无偏的方法来处理哈伯德模型的各种不稳定性--泛函重整化群。正常金属的低能物理被加入甚至一些磁性杂质所彻底改变。单自旋自由度可以完全屏蔽的传导电子凭借近藤效应。拓扑绝缘体的表面代表螺旋金属，但近藤效应是否持续并不明显。我想用两个互补的重整化群框架--泛函重整化群和实时重整化群来研究拓扑绝缘体上的杂质问题。此外，我想调查的实时和稳态动力学的双终端输运几何量子点设置。