---
title: "Mott’s insulating states: counting bands was not enough"
description: "Why can electrons fail to conduct when a simple independent-electron picture suggests a metal?"
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[Magnetism, disorder and topological response](https://sandboxphysics.com/stories/condensed-matter/#magnetism)

Materials · Measurements · Explanation

# Mott’s insulating states: counting bands was not enough

Why can electrons fail to conduct when a simple independent-electron picture suggests a metal?

Sandbox Physics · 2026-10-23

Nobel contribution: 1977-1

1. Compare the band expectation with transport
2. Include the cost of local charge change
3. Separate disorder and interactions
4. Test temperature and density dependence

Interaction-driven Mott insulation, disorder localization and variable-range hopping are related topics with different assumptions.

## Local charge can cost energy

Mott emphasized that moving an electron between nearly localized ions can require a substantial Coulomb energy. An independent-electron band count may then predict conduction where correlated electrons instead resist charge rearrangement.

This line of reasoning emerged in the 1930s and developed alongside work on disordered and amorphous materials. The 1977 award recognizes that broader electronic-structure contribution.

Sources: [1] [2]

## An interaction gap differs from a mobility edge

A correlation-induced charge gap concerns the energy needed to change occupations. A mobility edge separates localized from extended states in an energy spectrum. An insulator can involve either mechanism or a combination, so the term insulating does not identify the cause.

Sources: [2] [1]

## Hopping has a different temperature signature

Localized electrons can conduct at finite temperature by phonon-assisted hopping. The preferred hop balances distance against the energy difference between sites. A stretched-exponential temperature law needs its dimensionality, density-of-states assumptions and competing processes checked before interpretation.

Sources: [2]

## The disorder Lab supplies one comparison

The existing coherent disorder model illustrates localization without electron–electron interactions. It cannot generate a Mott charge gap. Reading the two articles together makes the distinction explicit, instead of assigning the same animation to every poorly conducting material.

Sources: [2] [1] [3]

Continue with the physics

## Try the related models

### [Disorder and wave transport](https://sandboxphysics.com/labs/anderson-localization-transport/)

Change disorder and compare transmission and spatial localization.

The single-particle model omits electron interactions and cannot produce a Mott transition.

### [Pairing across the crossover](https://sandboxphysics.com/labs/bec-bcs-crossover/)

Compare weak pairs with tightly bound pairs.

The teaching crossover does not predict a cuprate mechanism or helium-three order parameter.

## Sources and reading notes

1. [Anderson: Local moments and localized states (1977)](https://www.nobelprize.org/uploads/2018/06/anderson-lecture-1.pdf)

   The local-moment and disorder-localization problems are related contributions with different Hamiltonians.

2. [Mott: Electrons in glass (1977)](https://www.nobelprize.org/uploads/2018/06/mott-lecture.pdf)

   Mobility edges, amorphous semiconductors and hopping; do not merge these with interaction-driven Mott localization.

3. [Nobel Prize in Physics 1977: official award](https://www.nobelprize.org/prizes/physics/1977/summary/)

   Official attribution and award year. The observation or theoretical paper may be much earlier.

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