Umklappung

Umklappung, in solid-state physics often called Umklapp process or Umklapp scattering, refers to a type of scattering event in crystalline solids in which crystal momentum is conserved only up to a reciprocal lattice vector. In such processes the total momentum of interacting quasiparticles (for example phonons or electrons) is not conserved within the first Brillouin zone, but is redirected by a reciprocal lattice vector, effectively folding momentum back into the zone.

In phonon-phonon Umklapp processes, two incoming phonons with wave vectors k1 and k2 scatter to produce an outgoing phonon with wave vector k3 such that k1 + k2 = k3 + G, where G is a reciprocal-lattice vector. If G is nonzero, the resulting phonon is mapped back into the first Brillouin zone. This mechanism changes the net crystal momentum and acts as a resistive channel for heat flow, contributing to finite lattice thermal conductivity at finite temperatures.

Normal (N) processes conserve crystal momentum within the first Brillouin zone and satisfy k1 + k2 = k3 (G = 0). Umklapp processes become more probable as temperature rises because higher-energy phonons are populated, increasing scattering events that involve a reciprocal lattice vector. Consequently, Umklapp scattering strongly influences the temperature dependence of thermal conductivity in crystals.

Electronic Umklapp scattering plays a similar role for electrons, allowing momentum transfer to the lattice via a reciprocal lattice vector, and can affect electrical resistivity, particularly at higher temperatures or in materials with strong interactions.

Etymology-wise, "Umklappen" is German for "to fold back," reflecting the folding of momentum back into the Brillouin zone.