论文标题
二维中带横求点的波功能几何形状
Wave-function geometry of band crossing points in two-dimensions
论文作者
论文摘要
波功能的几何形状是现代固态物理学的中心支柱。在这项工作中，我们揭示了带有带交叉点（BCP）的二维半学的波功能几何形状。我们表明，BCP的浆果阶段受描述量子状态之间无限距离的量子度量的控制。对于通用线性BCP，我们表明相应的浆果相是由量子公制的角积分确定的，或者通过Bloch状态的最大量子距离来确定。这自然地解释了线性BCP的$π$ - 莓相位的起源。在二次BCP的情况下，浆果阶段的任意值在0到$2π$之间。我们在两种情况下发现浆果相，最大量子距离和量子度量之间的简单关系：（i）当两个交叉带中的一个是平坦的； （ii）当系统具有旋转和/或时间反转对称时。为了证明连续模型分析在晶格系统中的含义，我们研究了描述二次BCP的紧密结合的哈密顿量。我们表明，当不存在浆果曲率时，具有任意浆果相的二次BCP总是伴随着另一个二次BCP，以使周期系统的总浆果相变为零。这项工作表明，量子公制在理解拓扑半学的几何特性中起着至关重要的作用。
Geometry of the wave function is a central pillar of modern solid state physics. In this work, we unveil the wave-function geometry of two-dimensional semimetals with band crossing points (BCPs). We show that the Berry phase of BCPs are governed by the quantum metric describing the infinitesimal distance between quantum states. For generic linear BCPs, we show that the corresponding Berry phase is determined either by an angular integral of the quantum metric, or equivalently, by the maximum quantum distance of Bloch states. This naturally explains the origin of the $π$-Berry phase of a linear BCP. In the case of quadratic BCPs, the Berry phase can take an arbitrary value between 0 and $2π$. We find simple relations between the Berry phase, maximum quantum distance, and the quantum metric in two cases: (i) when one of the two crossing bands is flat; (ii) when the system has rotation and/or time-reversal symmetries. To demonstrate the implication of the continuum model analysis in lattice systems, we study tight-binding Hamiltonians describing quadratic BCPs. We show that, when the Berry curvature is absent, a quadratic BCP with an arbitrary Berry phase always accompanies another quadratic BCP so that the total Berry phase of the periodic system becomes zero. This work demonstrates that the quantum metric plays a critical role in understanding the geometric properties of topological semimetals.
