论文标题
非周期性系统的广义瓦尼尔函数的存在和计算在两个维度和较高方面
Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher
论文作者
论文摘要
指数定位的Wannier函数（ELWF）是Fermi投影的正顺序基础，该材料由函数组成，这些功能逐渐衰减的最大值。当材料是绝缘和结晶时，确保ELWF在维度上存在的条件一，二和三是众所周知的，并且用于数值构造ELWF的方法是良好的。我们考虑材料是绝缘但不一定是晶体的情况，在这些情况下，少得多。在一个空间维度中，Kivelson和Nenciu-nenciu已证明可以将ELWF构建为作用于Fermi投影的自动接合操作员的本征函数。在这项工作中，我们确定了一个假设，在该假设下，我们可以将Kivelson-Nenciu-Nenciu结果推广到两个维度且更高。在这个假设下，我们证明可以将ELWF构造为作用于Fermi投影的一系列自动接合操作员的特征函数。我们猜想我们所做的假设等于在材料是晶体的特殊情况下，拓扑障碍物消失了ELWF的存在。我们在数值上验证我们的构建是否在我们的假设成立并为我们的猜想提供数值证据的各种情况下产生ELWF。
Exponentially-localized Wannier functions (ELWFs) are an orthonormal basis of the Fermi projection of a material consisting of functions which decay exponentially fast away from their maxima. When the material is insulating and crystalline, conditions which guarantee existence of ELWFs in dimensions one, two, and three are well-known, and methods for constructing the ELWFs numerically are well-developed. We consider the case where the material is insulating but not necessarily crystalline, where much less is known. In one spatial dimension, Kivelson and Nenciu-Nenciu have proved ELWFs can be constructed as the eigenfunctions of a self-adjoint operator acting on the Fermi projection. In this work, we identify an assumption under which we can generalize the Kivelson-Nenciu-Nenciu result to two dimensions and higher. Under this assumption, we prove that ELWFs can be constructed as the eigenfunctions of a sequence of self-adjoint operators acting on the Fermi projection. We conjecture that the assumption we make is equivalent to vanishing of topological obstructions to the existence of ELWFs in the special case where the material is crystalline. We numerically verify that our construction yields ELWFs in various cases where our assumption holds and provide numerical evidence for our conjecture.
