CND-01

Drude conductivity

Free-electron metal.

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CondensedDrude

Governing equation

\sigma=ne^2\tau/m

$\tau \in \left[1, 100\right]$

where

n: Density (1/m³)
\tau: τ (fs)
\sigma: σ (MS/m)

The figure, part by part

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①

Governing law — red

\sigma=ne^2\tau/m

$\tau \in \left[1, 100\right]$

$\tau = 1$ $\sigma = 2.389$

Along the curve

②

Domain of the variable — blue

\tau_{\min} = 1,\quad \tau_{\max} = 100

$\tau \in \left[1, 100\right]$

$\tau = 1$ $\tau = 1$

Along the curve

③

Response curve — green

\sigma=ne^2\tau/m

$\tau \in \left[1, 100\right]$

$\tau = 1$ $\sigma = 2.389$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\sigma}{\mathrm{d}\tau}

$\tau \in \left[1, 100\right]$

$\tau = 1.623$ $\sigma^{\prime} = 2.389$

Along the curve

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-01 — Drude conductivity) is the form associated with Drude. Working symbols: $n$ , $\tau$ $\rightarrow$ $\sigma$ . Free-electron metal.

Purpose

Purpose: compute

\sigma

from

n

\tau

in Condensed matter via

\sigma=ne^2\tau/m

Free-electron metal. 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

n = 8.500e+28\,\mathrm{1/m^{3}}

\tau = 20.000\,\mathrm{fs}

, the governing relation

\sigma=ne^2\tau/m

yields

\sigma = 47.77\,\mathrm{MS/m}

. Free-electron metal. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Density n8.5e+28 1/m³τ \tau20 fs

Outputs

σ \sigma47.77 MS/m

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Narration of this film

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