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Established forms of electromagnetic coupling are usually conservative (in insulators) or dissipative (in metals and semiconductors). Here we point out the possibility of nondissipative electric driving of magnetization dynamics, if the valence electronic states have nontrivial topology in the combined space of crystal momentum and magnetization configuration. We provide a hybrid insulator system to demonstrate that the topology-based nonconservative electrical generalized force is capable of supporting sustained magnetization motion in the presence of Gilbert damping, with quantized and steady energy pumping into magnetization motion from the electric field. We also generalize our results to magnetic textures, and discuss electric field induced Dzyaloshinskii-Moriya interaction which can be nonconservative.
The modern theory of electric polarization has recently been extended to higher multipole moments, such as quadrupole and octupole moments. The higher electric multipole insulators are essentially topological crystalline phases protected by underlyin
We investigate disorder-driven topological phase transitions in quantized electric quadrupole insulators. We show that chiral symmetry can protect the quantization of the quadrupole moment $q_{xy}$, such that the higher-order topological invariant is
Quantized Hall conductance is a generic feature of two dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is believed t
We study theoretically a chain of precessing classical magnetic impurities in an $s$-wave superconductor. Utilizing a rotating wave description, we derive an effective Hamiltonian that describes the emergent Shiba band. We find that this Hamiltonian
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 th