Quantum mechanics is the field of physics governing the behavior of things on atomic scales, where things work very differently from our everyday world.
One of the most direct manifestations of quantum mechanics is quantization. Quantization results in the discrete character of physical properties at small scales, which could be the radius of an atomic orbit or the resistance of a molecular wire. The most famous one, which won Albert Einstein the Nobel Prize, is the quantization of the photon energy in the photoelectric effect-- the observation that many metals emit electrons when light shines upon them.
Quantization occurs when a quantum particle is confined to a small space. Its wave function develops a standing wave pattern, like waves in a small puddle. Physicists then speak of size quantization: the energy of the particle may only take those values where the nodal pattern of the standing wave matches the system boundary.
A striking consequence of size quantization is quantized conductance: the number of particles that can simultaneously traverse a narrow corridor, a so-called nanoconstriction, become discrete. As a result the current through such a constriction is an integer multiple of the quantum of conductance.
In a recent joint experimental and theoretical work, an international group of physicists demonstrated size quantization of charge carriers, i.e. quantized conductance in nanoscale samples of graphene. The results have been published in an article called "Size quantization of Dirac fermions in graphene constrictions" in Nature Communications.
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