While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a continuous "algebraic deformation" of Hamiltonians, which generates lattice models with the generalized chiral symmetry from those with the conventional chiral symmetry. This enables us to explicitly express zero modes of the deformed Hamiltonian in terms of that of the original Hamiltonian. Another virtue is that the deformation can be extended to non-uniform systems, such as fermion-vortex systems and disordered systems. Application to fermion vortices in a deformed system shows how the zero modes for the conventional Dirac fermions with vortices can be extended to the tilted case.
Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac Cones
众所周知，手征性是狄拉克-费米子系统的一个重要对称性，它导致了石墨烯中的零模朗道能级，在这里，我们探讨这个概念是否可以扩展到有机金属中遇到的倾斜狄拉克锥。我们发现存在一种“广义手征对称性“，它包含倾斜狄拉克锥，其中广义手征算符$γ$，满足$γ^{\dagger} H + Hγ=0$的哈密顿量$H$，保护零模。我们可以利用这一点来证明$n=0$朗道能级是类似δ函数的（没有加宽），这是通过扩展阿哈罗诺夫-卡舍的论证来实现的。数值计算证实了具有广义手征的晶格模型具有非常尖锐的空间关联随机朗道能级。
Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院吴文裕量子中心）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Shanghai Branch, Hefei National Laboratory（合肥国家实验室上海分部）
Topological features of ground states and topological solitons in generalized Su-Schrieffer-Heeger models using generalized time-reversal, particle-hole, and chiral symmetries
