Landau levels
E243121
Landau levels are the quantized energy levels of charged particles in a uniform magnetic field, fundamental to understanding quantum Hall effects and magnetic oscillation phenomena in solids.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Landau quantization | 4 |
| Landau levels canonical | 2 |
| Landau level | 1 |
| Landau level theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2173677 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Landau levels Context triple: [de Haas–van Alphen effect, relatedTo, Landau levels]
-
A.
Bloch waves
Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
-
B.
Sommerfeld quantization rules
Sommerfeld quantization rules are an early quantum theory refinement of Bohr’s model that quantize electron motion in elliptical orbits using action integrals, helping to explain fine-structure details in atomic spectra.
-
C.
London equations
The London equations are fundamental relations in superconductivity that describe how magnetic fields behave inside superconductors, capturing key features like the Meissner effect and zero electrical resistance.
-
D.
Fermi surface
The Fermi surface is the boundary in momentum space separating occupied from unoccupied electron states at zero temperature, crucial for determining a metal’s electronic and superconducting properties.
-
E.
Peierls substitution
Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Landau levels Target entity description: Landau levels are the quantized energy levels of charged particles in a uniform magnetic field, fundamental to understanding quantum Hall effects and magnetic oscillation phenomena in solids.
-
A.
Bloch waves
Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
-
B.
Sommerfeld quantization rules
Sommerfeld quantization rules are an early quantum theory refinement of Bohr’s model that quantize electron motion in elliptical orbits using action integrals, helping to explain fine-structure details in atomic spectra.
-
C.
London equations
The London equations are fundamental relations in superconductivity that describe how magnetic fields behave inside superconductors, capturing key features like the Meissner effect and zero electrical resistance.
-
D.
Fermi surface
The Fermi surface is the boundary in momentum space separating occupied from unoccupied electron states at zero temperature, crucial for determining a metal’s electronic and superconducting properties.
-
E.
Peierls substitution
Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
energy level spectrum
ⓘ
quantum mechanical phenomenon ⓘ |
| appliesTo | charged particles in a magnetic field ⓘ |
| are |
discrete energy levels
ⓘ
quantized energy levels ⓘ |
| areDescribedBy |
Landau quantization
ⓘ
linked to:
Landau levels
|
| areFundamentalTo |
Shubnikov–de Haas effect
ⓘ
de Haas–van Alphen effect ⓘ fractional quantum Hall effect ⓘ
linked to:
quantum Hall effect
integer quantum Hall effect ⓘ magnetic oscillation phenomena ⓘ magnetotransport in solids ⓘ quantum Hall effect ⓘ quantum magnetoresistance ⓘ |
| areKeyConceptIn |
condensed matter physics
ⓘ
mesoscopic physics ⓘ quantum Hall physics ⓘ quantum transport theory ⓘ |
| areModifiedBy |
disorder and impurities
ⓘ
electron–electron interactions ⓘ spin Zeeman splitting ⓘ spin–orbit coupling ⓘ |
| areObservedBy |
cyclotron resonance
ⓘ
magneto-optical spectroscopy ⓘ magnetotransport measurements ⓘ scanning tunneling spectroscopy ⓘ |
| areSolutionOf |
Dirac equation in a magnetic field for relativistic particles
ⓘ
linked to:
Dirac equation
Schrödinger equation in a uniform magnetic field ⓘ |
| areUsedToDetermine |
Fermi surface properties
ⓘ
carrier density ⓘ effective mass of charge carriers ⓘ g-factor of electrons ⓘ |
| ariseFrom | motion of charged particles in a uniform magnetic field ⓘ |
| degeneracyProportionalTo |
magnetic flux through the sample
ⓘ
sample area ⓘ |
| dependOn |
charge of the particle
ⓘ
effective mass of the particle ⓘ magnetic field strength ⓘ |
| energySeparationProportionalTo |
cyclotron frequency
ⓘ
magnetic field magnitude ⓘ |
| exhibit | macroscopic degeneracy ⓘ |
| haveCharacteristic |
equally spaced energies for nonrelativistic electrons
ⓘ
non-equidistant spectrum in graphene ⓘ |
| namedAfter | Lev Landau ⓘ |
| occurIn |
bulk metals
ⓘ
graphene ⓘ semiconductor heterostructures ⓘ two-dimensional electron gas ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Landau levels Description of subject: Landau levels are the quantized energy levels of charged particles in a uniform magnetic field, fundamental to understanding quantum Hall effects and magnetic oscillation phenomena in solids.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Landau levels
linked to: Landau levels
linked to: Landau levels
linked to: Landau levels
linked to: Landau levels
linked to: Landau levels