Quantum-mechanical vector property in solid-state physics
There are an infinite number of sinusoidal oscillations that perfectly fit a set of discrete oscillators, making it impossible to define a k-vector unequivocally. This is a relation of inter-oscillator distances to the spatial Nyquist frequency of waves in the lattice.[1] See also Aliasing § Sampling sinusoidal functions for more on the equivalence of k-vectors.
In solid-state physics, crystal momentum or quasimomentum is a momentum-like vector associated with electrons in a crystal lattice.[2] It is defined by the associated wave vectors of this lattice, according to
(where is the reduced Planck's constant).[3]: 139
Frequently[clarification needed], crystal momentum is conserved like mechanical momentum, making it useful to physicists and materials scientists as an analytical tool.
^"Topic 5-2: Nyquist Frequency and Group Velocity" (PDF). Solid State Physics in a Nutshell. Colorado School of Mines. Archived (PDF) from the original on 2015-12-27.
^Gurevich V.L.; Thellung A. (October 1990). "Quasimomentum in the theory of elasticity and its conversion". Physical Review B. 42 (12): 7345–7349. Bibcode:1990PhRvB..42.7345G. doi:10.1103/PhysRevB.42.7345. PMID 9994874.
^Neil Ashcroft; David Mermin (1976). Solid State Physics. Brooks/Cole Thomson Learning. ISBN 0-03-083993-9.
In solid-state physics, crystalmomentum or quasimomentum is a momentum-like vector associated with electrons in a crystal lattice. It is defined by the...
maximal-energy state in the valence band are each characterized by a certain crystalmomentum (k-vector) in the Brillouin zone. If the k-vectors are different, the...
In Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and...
it has a momentum ħk; however, this is not strictly correct, because ħk is not actually a physical momentum; it is called the crystalmomentum or pseudomomentum...
electron (or other particle) in a crystal, its value of k relates almost always to its crystalmomentum, not its normal momentum. Therefore, k and p are not...
of momentum: two wave vectors pointing to the right can combine to create a wave vector that points to the left. This non-conservation is why crystal momentum...
π / d {\displaystyle G=2\pi /d} . As momentum is conserved, the transfer of momentum occurs to crystalmomentum. The presentation in reciprocal space...
the crystalmomentum of conduction electrons. According to the Bloch theorem the conduction of electrons depends on the periodicity of the crystal lattice...
effect which can be described in terms of the Berry phase effect in the crystalmomentum space (k-space). The Hall effect in an ionized gas (plasma) is significantly...
The angular momentum of light is a vector quantity that expresses the amount of dynamical rotation present in the electromagnetic field of the light. While...
linear dispersion relation between energy and the two components of the crystalmomentum kx and ky. However, this concept can be extended to three dimensions...
must conserve quantized energy crystalmomentum, and the vibrating lattice which plays a large role in conserving momentum as in collisions, photons can...
correspondence principle then allows the identification of momentum and angular momentum (called spin), as well as energy, with the photon. The wave...
that the Hamiltonian of an electron in a crystal includes a coupling between the electron crystalmomentum k = p / ℏ {\displaystyle \mathbf {k} =\mathbf...
store the information of 0s and 1s at different discrete values of the crystalmomentum. The Berry curvature is even under spatial inversion (P) and odd under...
information of 0s and 1s would be stored as different discrete values of the crystalmomentum. Valleytronics may refer to other forms of quantum manipulation of...
crystal structure of metals and semiconductors, where electrons in a crystal lattice are substituted by Bloch electrons with a corresponding crystal momentum...
idler frequencies. In this case, the crystal itself provides the additional wavevector k = 2π/Λ (and hence momentum) to satisfy the phase-matching condition...
the momentum difference between incoming and diffracted X-rays of a crystal is a reciprocal lattice vector. The diffraction pattern of a crystal can be...
of a crystal, the dynamics of an electron or other particle in the crystal depend on how it moves relative to the crystal, and particle momentum can change...
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