Thermal Hall effect

Key takeaways

Thermal Hall effect belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Thermal Hall effect to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Thermal Hall effect from memory before moving on to harder problems.

Reference excerpt

In solid-state physics, the thermal Hall effect, also known as the Righi–Leduc effect, named after independent co-discoverers Augusto Righi and Sylvestre Anatole Leduc, is the thermal analog of the Hall effect. Given a thermal gradient across a solid, this effect describes the appearance of an orthogonal temperature gradient when a magnetic field is applied. For conductors, a significant portion of the thermal current is carried by the electrons. In particular, the Righi–Leduc effect describes the heat flow resulting from a perpendicular temperature gradient and vice versa. The Maggi–Righi–Leduc effect, named after Gian Antonio Maggi, describes changes in thermal conductivity when placing a conductor in a magnetic field. A thermal Hall effect has also been measured in a paramagnetic insulators, called the "phonon Hall effect". In this case, there are no charged currents in the solid, so the magnetic field cannot exert a Lorentz force. Phonon thermal Hall effects have been measured in various classes of non-magnetic insulating solids, but the exact mechanism giving rise to this phenomenon is largely unknown. An analogous thermal Hall effect for neutral particles exists in polyatomic gases, known as the Senftleben–Beenakker effect. Measurements of the thermal Hall conductivity are used to distinguish between the electronic and lattice contributions to thermal conductivity. These measurements are especially useful when studying superconductors.

Description Given a conductor or semiconductor with a temperature difference in the x-direction and a magnetic field B perpendicular to it in the z-direction, then a temperature difference can occur in the transverse y-direction,

∂ T ∂ y = R T H B ∂ T ∂ x {\displaystyle {\frac {\partial T}{\partial y}}=R_{\mathrm {TH} }B{\frac {\partial T}{\partial x}}}

The Righi–Leduc effect is a thermal analogue of the Hall effect. With the Hall effect, an externally applied electrical voltage causes an electrical current to flow. The mobile charge carriers (usually electrons) are transversely deflected by the magnetic field due to the Lorentz force. In the Righi–Leduc effect, the temperature difference causes the mobile charge carriers to flow from the warmer end to the cooler end. Here, too, the Lorentz force causes a transverse deflection. Since the electrons transport heat, one side is heated more than the other. The thermal Hall coefficient R T H {\displaystyle R_{\mathrm {TH} }} (sometimes also called the Righi–Leduc coefficient) depends on the material and has units of tesla−1. It is related to the Hall coefficient R H {\displaystyle R_{\mathrm {H} }} by the electrical conductivity σ {\displaystyle \sigma } , as

R T H = σ R H {\displaystyle R_{\rm {TH}}=\sigma R_{\rm {H}}} .

Worked examples

Example 1 — a first encounter with Thermal Hall effect

Start with the simplest possible case. Write down what Thermal Hall effect claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Thermal Hall effect before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Thermal Hall effect ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Thermal Hall effect

In research: Thermal Hall effect appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Thermal Hall effect in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Thermal Hall effect is common in secondary-school and first-year university syllabi. It links to neighbouring topics Condensed matter stubs, Hall effect, Superconductivity, so understanding it makes those chapters shorter.
In everyday life: Look for Thermal Hall effect outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Thermal Hall effect in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Thermal Hall effect means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Thermal Hall effect out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Thermal Hall effect in simple terms?

In solid-state physics, the thermal Hall effect, also known as the Righi–Leduc effect, named after independent co-discoverers Augusto Righi and Sylvestre Anatole Leduc, is the thermal analog of the Hall effect. Given a thermal gradient across a solid, this effect describes the appearance of an orth…

Why does Thermal Hall effect matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Thermal Hall effect?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Thermal Hall effect.