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Register a new userOrbital dynamics in 2D topological and Chern insulators
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Within a relativistic quantum formalism we examine the role of second-order corrections caused by the application of magnetic fields in two-dimensional topological and Chern insulators. This allows to reach analytical expressions for the change of the Berry curvature, orbital magnetic moment, density of states and energy determining their canonical grand potential and transport properties. The present corrections, which become relevant at relatively low fields due to the small gap characterizing these systems, unveil a zero-field diamagnetic susceptibility which can be tuned by the external magnetic field.
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We theoretically study magnon-phonon hybrid excitations (magnon-polarons) in two-dimensional antiferromagnets on a honeycomb lattice. With an in-plane Dzyaloshinskii-Moriya interaction (DMI) allowed from mirror symmetry breaking from phonons, we find non-trivial Berry curvature around the anti-crossing rings among magnon and both optical and acoustic phonon bands, which gives rise to finite Chern numbers. We show that the Chern numbers of the magnon-polaron bands can be manipulated by changing the magnetic field direction or strength. We evaluate the thermal Hall conductivity reflecting the non-trivial Berry curvatures of magnon-polarons and propose a valley Hall effect resulting from spin-induced chiral phonons as a possible experimental signature. Our study complements prior work on magnon-phonon hybridized systems without optical phonons and suggests possible applications in spin caloritronics with topological magnons and chiral phonons.
We theoretically propose a gigantic orbital Edelstein effect in topological insulators and interpret the results in terms of topological surface currents. We numerically calculate the orbital Edelstein effect for a model of a three-dimensional Chern insulator as an example. Furthermore, we calculate the orbital Edelstein effect as a surface quantity using a surface Hamiltonian of a topological insulator, and numerically show that it well describes the results by direct numerical calculation. We find that the orbital Edelstein effect depends on the local crystal structure of the surface, which shows that the orbital Edelstein effect cannot be defined as a bulk quantity. We propose that Chern insulators and Z_2 topological insulators can be a platform with a large orbital Edelstein effect because current flows only along the surface. We also propose candidate topological insulators for this effect. As a result, the orbital magnetization as a response to the current is much larger in topological insulators than that in metals by many orders of magnitude.
We theoretically study the effect of magnetic moire superlattice on the topological surface states by introducing a continuum model of Dirac electrons with a single Dirac cone moving in the time-reversal symmetry breaking periodic pontential. The Zeeman-type moire potentials generically gap out the moire surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $pm1$. This result provides a promising platform for realizing the time-reversal breaking correlated topological phases. In a $C_6$ periodic potential, when the scalar $U_0$ and Zeeman $Delta_1$ moire potential strengths are equal to each other, we find that energetically the first three bands of $Gamma$-valley moire surface electrons are non-degenerate and realize i) an $s$-orbital model on a honeycomb lattice, ii) a degenerate $p_x,p_y$-orbitals model on a honeycomb lattice, and iii) a hybridized $sd^2$-orbital model on a kagome lattice, where moire surface Dirac cones in these bands emerge. When $U_0 eqDelta_1$, the difference between the two moire potential serves as an effective spin-orbit coupling and opens a topological gap in the emergent moire surface Dirac cones.
Robustness against disorder and defects is a pivotal advantage of topological systems, manifested by absence of electronic backscattering in the quantum Hall and spin-Hall effects, and unidirectional waveguiding in their classical analogs. Two-dimensional (2D) topological insulators, in particular, provide unprecedented opportunities in a variety of fields due to their compact planar geometries compatible with the fabrication technologies used in modern electronics and photonics. Among all 2D topological phases, Chern insulators are to date the most reliable designs due to the genuine backscattering immunity of their non-reciprocal edge modes, brought via time-reversal symmetry breaking. Yet, such resistance to fabrication tolerances is limited to fluctuations of the same order of magnitude as their band gap, limiting their resilience to small perturbations only. Here, we tackle this vexing problem by introducing the concept of anomalous non-reciprocal topological networks, that survive disorder levels with strengths arbitrarily larger than their bandgap. We explore the general conditions to obtain such unusual effect in systems made of unitary three-port scattering matrices connected by phase links, and establish the superior robustness of the anomalous edge modes over the Chern ones to phase link disorder of arbitrarily large values. We confirm experimentally the exceptional resilience of the anomalous phase, and demonstrate its operation by building an ideal anomalous topological circulator despite its arbitrary shape and large number of ports. Our results pave the way to efficient, arbitrary planar energy transport on 2D substrates for wave devices with full protection against large fabrication flaws or imperfections.
Magic-angle twisted bilayer graphene (MA-TBG) exhibits intriguing quantum phase transitions triggered by enhanced electron-electron interactions when its flat-bands are partially filled. However, the phases themselves and their connection to the putative non-trivial topology of the flat bands are largely unexplored. Here we report transport measurements revealing a succession of doping-induced Lifshitz transitions that are accompanied by van Hove singularities (VHS) which facilitate the emergence of correlation-induced gaps and topologically non-trivial sub-bands. In the presence of a magnetic field, well quantized Hall plateaus at filling of 1, 2, 3 carriers per moire-cell reveal the sub-band topology and signal the emergence of Chern insulators with Chern-numbers, ! = !, !, !, respectively. Surprisingly, for magnetic fields exceeding 5T we observe a VHS at a filling of 3.5, suggesting the possibility of a fractional Chern insulator. This VHS is accompanied by a crossover from low-temperature metallic, to high-temperature insulating behavior, characteristic of entropically driven Pomeranchuk-like transitions,
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