Two-dimensional system (physics)

A physical system whose relevant degrees of freedom or motion are confined to two spatial dimensions. Its behavior can differ sharply from that of a three-dimensional system because geometry changes interactions and fluctuations.

Quantum confinement: Restriction of particle motion to a small region that quantizes motion in confined directions. Confining carriers perpendicular to a plane produces effectively two-dimensional electronic states.
Graphene: A single layer of carbon atoms arranged in a honeycomb lattice. Its carriers behave as massless Dirac fermions in an atomically thin plane.
Degrees of freedom: Independent variables needed to specify the state of a physical system. Two-dimensionality concerns which spatial degrees of freedom remain dynamically relevant.
One-dimensional system: A physical system whose relevant motion or degrees of freedom are confined to one spatial dimension. Its stronger fluctuation effects and restricted scattering differ from planar systems.
Two-dimensional electron gas: An electron system free to move in two dimensions but confined in the third. It is the canonical electronic realization of a two-dimensional system.
Transition metal dichalcogenide monolayers: Single layers of compounds such as MoS₂, with a transition metal between two chalcogen layers. They provide direct-gap semiconductors whose valley and spin properties can be controlled.
Dimensionality: The number of independent spatial or mathematical coordinates needed to describe a system. It supplies the broader framework for comparing one-, two-, and three-dimensional physics.
Three-dimensional system: A physical system whose relevant motion or degrees of freedom extend through three spatial dimensions. The extra spatial direction can permit forms of order forbidden in two dimensions.
Mermin–Wagner theorem: A theorem forbidding spontaneous breaking of continuous symmetries at finite temperature in systems with sufficiently short-range interactions in one or two dimensions. It explains why thermal fluctuations obstruct conventional continuous-symmetry order in two dimensions.
Quantum Hall effect: Quantization of Hall conductance in a two-dimensional electron system under a strong magnetic field. It is a hallmark phenomenon enabled by two-dimensional motion and magnetic quantization.

Linked from 1 page

1-dimensional systems (physics)Compared with: Two dimensions can support finite-temperature ordering and topological phenomena unavailable in one dimension.