Resistivity near a nematic quantum critical point: Impact of acoustic phonons

• Published in: arXiv.org
• Main Authors: de Carvalho, V S, Fernandes, R M
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 04.09.2019
• Subjects: Acoustic coupling; Boltzmann transport equation; Coupling; Critical point; Distribution functions; Electrical resistivity; Fermi liquids; Impurities; Lattice strain; Order parameters; Phonons; Physics - Strongly Correlated Electrons; Scattering; Temperature; Temperature dependence; Trigonometric functions; Variations
• DOI: 10.48550/arxiv.1906.03205

We revisit the issue of the resistivity of a two-dimensional electronic system tuned to a nematic quantum critical point (QCP), focusing on the non-trivial impact of the coupling to the acoustic phonons. Due to the unavoidable linear coupling between the electronic nematic order parameter and the lattice strain fields, long-range nematic interactions mediated by the phonons emerge in the problem. By solving the semi-classical Boltzmann equation in the presence of scattering by impurities and nematic fluctuations, we determine the temperature-dependence of the resistivity as the nematic QCP is approached. One of the main effects of the nemato-elastic coupling is to smooth the electronic non-equilibrium distribution function, making it approach the simple cosine angular dependence even when the impurity scattering is not too strong. We find that at temperatures lower than a temperature scale set by the nemato-elastic coupling, the resistivity shows the \(T^2\) behavior characteristic of a Fermi liquid. This is in contrast to the \(T^{4/3}\) low-temperature behavior expected for a lattice-free nematic quantum critical point. More importantly, we show that the effective resistivity exponent \(\alpha_\text{eff}(T)\) in \(\rho(T)-\rho_0\sim T^{\alpha_\text{eff}(T)}\) displays a pronounced temperature dependence, implying that a nematic QCP cannot generally be characterized by a simple resistivity exponent. We discuss the implications of our results to the interpretation of experimental data, particularly in the nematic superconductor FeSe\(_{1-x}\)S\(_x\).