Locally critical resistivities from umklapp scattering

Area of Science:

• Condensed Matter Physics
• Quantum Critical Phenomena
• Materials Science

Background:

• Efficient momentum relaxation via umklapp scattering is crucial for understanding DC resistivity's temperature dependence.
• A significant low-energy spectral weight at finite momentum, often from Fermi surface structure, typically leads to relaxation rates proportional to T^2.

Purpose of the Study:

• To investigate if local criticality, where energies scale but momenta do not, offers an alternative mechanism for efficient umklapp scattering.
• To determine the resulting temperature dependence of resistivity in locally critical theories.

Main Methods:

• Theoretical analysis of umklapp scattering by an ionic lattice within a locally critical theory.
• Holographic computation using Einstein-Maxwell theory in Anti-de Sitter spacetime to model locally critical theories.
• Analysis of scattering by random impurities in these theories.

Main Results:

• Umklapp scattering in locally critical theories leads to a relaxation rate Γ∼T^(2Δ(k(L))), where Δ(k(L)) is the dimension of a charge density operator at lattice momentum k(L).
• Scattering by random impurities in these theories results in a universal relaxation rate Γ∼(log(1/T))^(-1).

Conclusions:

• Local criticality provides a distinct route to efficient umklapp scattering, modifying the expected temperature dependence of resistivity.
• The findings offer new insights into electron scattering mechanisms and their impact on material properties, particularly in systems exhibiting local criticality.