耦合六角晶格中的非线性Dirac点和拓扑不变量
Nonlinear Dirac Points and topological invariant in coupled hexagonal lattices
摘要：
近年来，拓扑相和拓扑材料引起了人们的广泛关注。虽然在这方面取得了许多进展，但非线性对这类系统的影响仍未得到解决。本文在玻色子-六角晶格耦合系统中考虑平均场近似，得到了一种不同类型的狄拉克锥。由于其特殊的锥结构，这个新的狄拉克锥的Berry相（二维Zak相）被不同地量子化，即，它由于相互作用而被修改，并且不同拓扑相之间的临界线根据相互作用的类型而移动。此外，新的Berry相位被发现是量化的，提供了一个可能的非线性拓扑不变量，它可以提供作为一个标准的拓扑分类的相互作用系统。根据这个判据，我们还研究了系统的量子相变。
英文摘要：
Topological phases and materials have attracted much attention in recent years. Though many progress has been made, the effect of nonlinearity on such system remains untouched. In this paper, by considering the mean-field approximation in a coupled boson-hexagonal lattice system, we obtain a different type of Dirac cone. Due to its special structure of the cone, the Berry phase (two-dimensional Zak phase) of this new Dirac cone is quantized differently, i.e., it has been modified due to the interactions and the critical line between different topological phases has moved, depending on the type of interactions. Furthermore, the new Berry phase is found to be quantized, offering a possible nonlinear topological invariant which can supply as a criterion of topological classification for that interacting system. The quantum phase transition in terms of this criterion in the system has also been examined.
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