The modern theory of orbital magnetization addresses crystalline materials at the noninteracting level: therein the observable is the k-space integral of a geometrical integrand. Alternatively, magnetization admits a local representation in r space, i.e. a "density" which may address noncrystalline and/or inhomogeneous materials as well; the Chern number admits an analogous density. Here we provide the formulation for ribbons, polymers, and layered materials, where both k-space and r-space integrations enter the definition of the two observables.
We investigate possible phase transitions among the different quantum anomalous Hall (QAH) phases in a zigzag graphene ribbon under the influence of the exchange field. The effective tight-binding Hamiltonian for graphene is made up of the hopping term, the Kane-Mele and Rashba spin-orbit couplings as well as the Haldane orbital term. We find that the variation of the exchange field results in bulk gap-closing phenomena and phase transitions occur in the graphene system. If the Haldane orbital coupling is absent, the phase transition between the chiral (anti-chiral) edge state $ν=+2$ ($ν=-2$) …
We studied effects of disorder in a three dimensional layered Chern insulator. By calculating the localization length and density of states numerically, we found two distict types of metallic phases between Anderson insulator and Chern insulator; one is diffusive metallic (DM) phase and the other is renormalized Weyl semimetal (WSM) phase. We show that longitudinal conductivity at the zero energy state remains finite in the renormalizd WSM phase as well as in the DM phase, while goes to zero at a semimetal-metal quantum phase transition point between these two. Based on the Einstein relation c…
Universal magnetotunnel conductance at a Weyl semimetal-layered Chern insulator junction
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础科学国际理论中心）；Technion - Israel Institute of Technology（以色列理工学院）
Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the inter-layer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) ($μ_1,μ_2$) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as…
We proposed a minimal model to describe the Floquet band structure of two-dimensional materials with light-induced resonant inter-band transition. We applied it to graphene to study the band features caused by the light irradiation. Linearly polarized light induces pseudo gaps (gaps are functions of wavevector), and circularly polarized light causes real gaps on the quasi-energy spectrum. If the polarization of light is linear and along the longitudinal direction of zigzag ribbons, flat edge bands appear in the pseudo gaps, and if is in the lateral direction of armchair ribbons, curved edge ba…
We investigate the change in the non-zero Chern number and out-of-plane spin polarization of the edge currents in a honeycomb lattice with the Haldane-Rashba interaction. This interaction breaks the time-reversal symmetry due to the Haldane phase caused by a current loop at site-I and -II atoms and also accounts for the Rashba-type spin-orbit interaction. The Rashba spin-orbit interaction increases the number of Dirac points and the band-touching phenomenon can be generated by tuning the on-site potential in the non-zero Haldane phase. By using the Pontryagin winding number and numerical Berry…
We study topological properties and the topological phase transitions therein for a semi-Dirac Haldane model on a honeycomb lattice in presence of an extended range (third neighbour) hopping. While in the absence of a third neighbour hopping, $t_3$, the system exhibits gapless electronic spectrum, its presence creates an energy gap in the dispersion. However, the nature of the spectral gap, that is, whether it is trivial or topological needs to be ascertained. We find that the answer depends on the value of $t_3$, and its interplay with the value of the onsite potential that breaks the sublatt…
The interplay between band topology and magnetic order plays a key role in quantum states of matter. MnBi2Te4, a van der Waals magnet, has recently emerged as an exciting platform for exploring Chern insulator physics. Its layered antiferromagnetic order was predicted to enable even-odd layer-number dependent topological states, supported by promising edge transport measurements. Furthermore, it becomes a Chern insulator when all spins are aligned by an applied magnetic field. However, the evolution of the bulk electronic structure as the magnetic state is continuously tuned and its dependence…
Topological phases with large Chern numbers have important implications. They were previously predicted to exist by considering fabricated long-range interactions or multi-layered materials. Stimulated by recent wide interests in Floquet topological phases, here we propose a scheme to engineer large-Chern-number phases with ease by periodic quenching. Using a two-band system as an example, we theoretically show how a variety of topological phases with widely tunable Chern numbers can be generated by periodic quenching between two simple Hamiltonians that otherwise give low Chern numbers. The o…
Factors affecting the topological Hall effect in strongly correlated layered magnets: spin of the magnetic atoms, polar and azimuthal angle subtended by the spin texture
We carry out both the tight-binding model and the $ab\ initio$ to study the layered silicene, the spin, valley, sublattice degrees of freedom are taken into consider and the effects of electric field, magnetic field, and even the light in finite frequency together with its interesting optical propertice, which are all closely related to the spin-orbit coupling and Rashba coupling and lead to the tunable phase transitions (between the nontrivial topological phase which has nonzero Chern number or nonzero spin Chern number and the trivial phase). An exotic quantum anomalous Hall insulator phase …
The topology in different dimensions has attracted enormous interests, e.g. the Zak phase in 1D systems, the Chern number in 2D systems and the Weyl points or nodal lines in the systems with higher dimensions. It would be fantastic to find the connection of different topology in different dimensions from one simple model and reveal the deep physical picture behind them. In this work, we propose a new model which starts from a binary-layered 1D photonic crystal, and by introducing synthetic dimensions the topology of higher dimension systems could appear. From this model, we find that the topol…
