Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model

Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices

In this work we use Floquet theory to theoretically study the influence of monochromatic circularly and linearly polarized light on the Hofstadter butterfly---induced by a uniform perpendicular magnetic field--for both the kagome and triangular lattices. In the absence of the laser light, the butterfly has fractal structure with inversion symmetry about magnetic flux $ϕ=1/4$, and reflection symmetry about $ϕ=1/2$. As the system is exposed to an external laser, we find circularly polarized light deforms the butterfly by breaking the mirror symmetry at flux $ϕ=1/2$. By contrast, linearly polariz…

Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly

We perform an analytical study of the energy and entanglement spectrum of non-interacting fermionic bilayer honeycomb lattices in the presence of trigonal warping in the energy spectrum, on-site energy difference and uniform magnetic field. Employing single particle correlation functions, we present an explicit form for layer-layer entanglement Hamiltonian whose spectrum is entanglement spectrum. We demonstrate that in the absence of trigonal warping, at zero on-site energy difference exact correspondence is established between entanglement spectrum and energy spectrum of monolayer which means…

三角笼目晶格上的脆弱拓扑相及其体边对应

Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence

本文基于紧束缚模型与拓扑量子化学理论，系统研究三角笼目晶格中的脆弱拓扑态、体边对应及磁场诱导的拓扑相变。

Magnetic field effects on two-dimensional Kagome lattices

Magnetic field effects on single-particle energy bands (Hofstadter butterfly), Hall conductance, flat-band ferromagnetism, and magnetoresistance of two-dimensional Kagome lattices are studied. The flat-band ferromagnetism is shown to be broken as the flat-band has finite dispersion in the magnetic field. A metal-insulator transition induced by the magnetic field (giant negative magnetoresistance) is predicted. In the half-filled flat band, the ferromagnetic-paramagnetic transition and the metal-insulator one occur simultaneously at a magnetic field for strongly interacting electrons. All of th…

Orbital magnetization of the electron gas on a two-dimensional kagome lattice under a perpendicular magnetic field

The orbital magnetization of the electron gas on a two-dimensional kagome lattice under a perpendicular magnetic field is theoretically investigated. The interplay between the lattice geometry and magnetic field induce nontrivial $k$-space Chern invariant in the magnetic Brillouin zone, which turns to result in profound effects on the magnetization properties. We show that the Berry-phase term in the magnetization gives a paramagnetic contribution, while the conventional term brought about by the magnetic response of the magnetic Bloch bands produces a diamagnetic contribution. As a result, th…

从(2+1)D可逆费米态与Hofstadter蝴蝶中的部分旋转提取完整晶体拓扑不变量

Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly

本文提出从(2+1)D可逆费米态的部分旋转中提取多体晶体拓扑不变量，结合Chern数等参量实现了对拓扑态的完整表征，并在Hofstadter模型中验证了与场论计算的一致性。