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arXiv 2107.09720cond-mat.mes-hallcond-mat.str-elquant-ph
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具有缺陷和绝热电荷泵的费米子链中的局域态谱

Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping

Filiberto Ares, José G. Esteve, Fernando Falceto

摘要:

在本文中,我们研究了一般的二次费米子链有限范围耦合和跳跃(缺陷)的不均匀性,打破平移不变性的局域态。当跳跃的缺陷消失,这代表了一个开放的链,我们得到一个简单的散装边缘对应:本地化的链的两端的零能量模式有关的多项式的根确定的耦合的哈密顿量的散装。从这个结果中,我们定义了一个指数,该指数表征了系统的不同拓扑相位,并且可以通过计算多项式的根来容易地计算。当缺陷被打开并动态变化时,零能模可以穿过能隙并连接价带和导带。我们分析了对扰动的哈密顿频带之间的连接的鲁棒性。从一个能带到另一个能带的状态泵浦允许在体中产生粒子-空穴对。我们分析的一个重要组成部分是标准离散对称下的哈密顿量的变换,$C$,$P$,$T$,以及第四个,特有的我们的系统,这是与存在的间隙和局域态。

英文摘要:

In this paper, we study the localized states of a generic quadratic fermionic chain with finite-range couplings and an inhomogeneity in the hopping (defect) that breaks translational invariance. When the hopping of the defect vanishes, which represents an open chain, we obtain a simple bulk-edge correspondence: the zero-energy modes localized at the ends of the chain are related to the roots of a polynomial determined by the couplings of the Hamiltonian of the bulk. From this result, we define an index that characterizes the different topological phases of the system and can be easily computed by counting the roots of the polynomial. As the defect is turned on and varied adiabatically, the zero-energy modes may cross the energy gap and connect the valence and conduction bands. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian. The pumping of states from one band to the other allows the creation of particle-hole pairs in the bulk. An important ingredient for our analysis is the transformation of the Hamiltonian under the standard discrete symmetries, $C$, $P$, $T$, as well as a fourth one, peculiar to our system, that is related to the existence of a gap and localized states.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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