CND-17

Orbital magnetoresistance

Δρ/ρ = (μ B)² for a simple two-carrier sketch at low field.

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Electrons in solidsMagnetoresistance

Governing equation

\Delta\rho/\rho=(\mu B)^2

$B \in \left[0, 30\right]$

where

\mu: Mobility (cm²/V/s)
B: Field (T)
\Delta\rho/\rho: Magnetoresistance (%)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Delta\rho/\rho=(\mu B)^2

$B \in \left[0, 30\right]$

$B = 0$ $\Delta\rho/\rho = 0$

Along the curve

②

Domain of the variable — blue

B_{\min} = 0,\quad B_{\max} = 30

$B \in \left[0, 30\right]$

$B = 0$ $B = 0$

Along the curve

③

Response curve — green

\Delta\rho/\rho=(\mu B)^2

$B \in \left[0, 30\right]$

$B = 0$ $\Delta\rho/\rho = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta\rho/\rho}{\mathrm{d}B}

$B \in \left[0, 30\right]$

$B = 0.189$ $\Delta\rho/\rho^{\prime} = 0.377$

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-17 — Orbital magnetoresistance) is the form associated with Magnetoresistance. Working symbols: $\mu$ , $B$ $\rightarrow$ $\Delta\rho/\rho$ . Kohler's rule: the MR is a function of B/ρ. Open orbits can give linear MR.

Purpose

Purpose: compute

\Delta\rho/\rho

from

\mu

B

in Condensed matter via

\Delta\rho/\rho=(\mu B)^2

Δρ/ρ = (μ B)² for a simple two-carrier sketch at low field. 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

\mu = 1000.000\,\mathrm{cm^{2}/V/s}

B = 1.000\,\mathrm{T}

, the governing relation

\Delta\rho/\rho=(\mu B)^2

yields

\Delta\rho/\rho = 1.00\,\mathrm{%}

. A bar, a perpendicular B, a rising R. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mobility \mu1000 cm²/V/sField B1 T

Outputs

Magnetoresistance \Delta\rho/\rho1.00 %

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Narration of this film

A bar, a perpendicular B, a rising R.

Kohler's rule: the MR is a function of B/ρ. Open orbits can give linear MR.

Reading speed

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