Skin effect

Abstract: The theory of paramagnetic resonance absorption by the conduction electrons in a metal is worked out, taking into account the diffusion of the electrons in and out of the thin skin into which the radio-frequency field penetrates. Calculations are carried through in detail for the case of a flat metal plate. It is found that the diffusion has no marked effect on the width of the resonance absorption line, but has a radical effect on the shape of the line. In particular, for a piece of metal thick compared to the skin depth and with a relaxation time long compared to the diffusion time, the line is antisymmetrical about its center and has an unusual characteristic shape.

Abstract: Recent experiments have discovered a giant magneto‐impedance (MI) effect in FeCoSiB amorphous wires. This effect includes a sensitive change (as much as 60%) in a high frequency wire voltage by an applied dc magnetic field and is thus a high frequency analog of giant magnetoresistance. We consider this phenomenon in terms of ac complex resistance or impedance. The giant MI effect is demonstrated to arise from a combination of a skin effect and a strong field dependence of the circumferential magnetic permeability associated with circular domain wall movements. The theoretical results agree satisfactorily with the existing experimental data.

Abstract: A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non-Hermitian topology. Such a topological origin not merely explains the universal feature of the known skin effect, but also leads to new types of the skin effects---symmetry-protected skin effects. In particular, we discover the ${\mathbb{Z}}_{2}$ skin effect protected by time-reversal symmetry. On the basis of topological classification, we also discuss possible other skin effects in arbitrary dimensions. Our work provides a unified understanding about the bulk-boundary correspondence and the skin effects in non-Hermitian systems.

Abstract: At radio frequencies, the penetration of currents and magnetic fields into the surface of conductors is governed by the skin effect. Many formulas are simplified if expressed in terms of the "depth of penetration," which has merely the dimension of length but involves the frequency and the conductivity and permeability of the conductive material. Another useful parameter is the "surface resistivity" determined by the skin effect, which has simply the dimension of resistance. These parameters are given for representative metals by a convenient chart covering a wide range of frequency. The "incremental-inductance rule" is given for determining not only the effective resistance of a circuit but also the added resistance caused by conductors in the neighborhood of the circuit. Simple formulas are given for the resistance of wires, transmission lines, and coils; for the shielding effect of sheet metal; for the resistance caused by a plane or cylindrical shield near a coil; and for the properties of a transformer with a laminated iron core.