412 research outputs found
Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry
The quantum geometry has significant consequences in determining transport
and optical properties in quantum materials. Here, we use a semiclassical
formalism coupled with perturbative corrections unifying the nonlinear
anomalous Hall effect (NLAHE) and nonreciprocal magnetoresistance (NMR,
longitudinal resistance) from the quantum geometry. In the dc limit, both
transverse and longitudinal nonlinear conductivities include a term due to the
normalized quantum metric dipole. The quantum metric contribution is intrinsic
and does not scale with the quasiparticle lifetime. We demonstrate the
coexistence of a NLAHE and NMR in films of the doped antiferromagentic
topological insulator MnBiTe. Our work indicates that both longitudinal
and transverse nonlinear transport provide a sensitive probe of the quantum
geometry in solids.Comment: 4.5 pages; 2 figures. SI. Comments welcome
General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
Can a generic magnetic insulator exhibit a Hall current? The quantum
anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a
quantized Hall conductivity and other insulators (with zero Chern number)
present zero Hall conductance in the linear response regime. Here, we find that
a general magnetic insulator possesses a nonlinear Hall conductivity quadratic
to the electric field if the system breaks inversion symmetry. This
conductivity originates from an induced orbital magnetization due to virtual
interband transitions. We identify three contributions to the wavepacket
motion, a velocity shift, a positional shift, and a Berry curvature
renormalization. In contrast to the crystalline solid, we find that this
nonlinear Hall conductivity vanishes for Landau levels of a 2D electron gas,
indicating a fundamental difference between the QAHE and the Integer quantum
Hall effect
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