Designing Dirac points in two-dimensional lattices
Designing Dirac points in two-dimensional lattices
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DOI：
10.1103/physrevb.83.245125
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发表时间：
2011-06-27
影响因子：
3.7
通讯作者：
Hotta, Chisa
中科院分区：
文献类型：
--
作者：
Asano, Kenichi;Hotta, Chisa
我们提出了一个框架来阐明偶然接触的能带的存在，特别是那些所谓的狄拉克点，这是在其附近的线性能量色散的点接触。我们在这里提出的广义冯诺伊曼-维格纳定理给出了在不微调晶格参数的情况下具有接触所需的晶格约束的数量。通过计算这个数字，人们可以搜索狄拉克系统的候选人，而无需求解长期方程。约束可以由系统中存在的任何种类的对称性提供。该理论还能够通过选择性地仅拾取长期方程的退化解来分析确定具有偶然接触的k点。通过使用这些框架，我们证明了狄拉克点在各种二维晶格中是可行的，例如，发现在反演对称下的各向异性Kagom ′ e晶格在整个晶格参数空间上具有接触。自旋相关的情况下，如自旋密度波态的反射对称性的LaOFeAs，也处理在本计划。
We present a framework to elucidate the existence of accidental contacts of energy bands, particularly those called Dirac points which are the point contacts with linear energy dispersions in their vicinity. A generalized von Neumann-Wigner theorem we propose here gives the number of constraints on the lattice necessary to have contacts without fine tuning of lattice parameters. By counting this number, one could search for the candidate of Dirac systems without solving the secular equation. The constraints can be provided by any kinds of symmetry present in the system. The theory also enables the analytical determination of a k-point having accidental contact by selectively picking up only the degenerate solution of the secular equation. By using these frameworks, we demonstrate that the Dirac points are feasible in various two-dimensional lattices, e.g., the anisotropic Kagom 'e lattice under inversion symmetry is found to have contacts over the whole lattice parameter space. Spin-dependent cases, such as the spin-density-wave state in LaOFeAs with reflection symmetry, are also dealt with in the present scheme.