CND-19

Meissner exponential

B(x) = B₀ e^{−x/λ}. Field expulsion at a superconducting surface.

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SuperconductivityMeissner

Governing equation

B(x)=B_0 e^{-x/\lambda}

where

B_0: External field (mT)
x: Depth (nm)
\lambda: Penetration (nm)
B: Field (mT)

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-19 — Meissner exponential) is the form associated with Meissner. Working symbols: $B_0$ , $x$ , $\lambda$ $\rightarrow$ $B$ . Perfect diamagnetism, not merely perfect conductivity. The hallmark of the Meissner state.

Purpose

Purpose: compute

B

from

B_0

x

\lambda

in Condensed matter via

B(x)=B_0 e^{-x/\lambda}

B(x) = B₀ e^{−x/λ}. Field expulsion at a superconducting surface. Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

B_0 = 10.000\,\mathrm{mT}

x = 50.000\,\mathrm{nm}

\lambda = 80.000\,\mathrm{nm}

, the governing relation

B(x)=B_0 e^{-x/\lambda}

yields

B = 5.353\,\mathrm{mT}

. A surface, a dying B, a λ mark. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

External field B_010 mTDepth x50 nmPenetration \lambda80 nm

Outputs

Field B5.353 mT

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Narration of this film

A surface, a dying B, a λ mark.

Perfect diamagnetism, not merely perfect conductivity. The hallmark of the Meissner state.

Reading speed

Watch on YouTube