Probing three-state Potts nematic fluctuations by ultrasound attenuation

Abstract

Motivated by recent studies of three-state Potts nematic states in magic-angle twisted bilayer graphene and doped-Bi${}_2$Se${}_3$, we analyze the impact of critical nematic fluctuations on the low energy properties of phonons. In this study we propose how to identify the three-state Potts nematic fluctuations by ultrasound attenuation. The Gaussian fluctuation analysis shows that the Landau damping term becomes isotropic due to fluctuations of the $C_3$-breaking bond-order, and the nemato-elastic coupling is also shown to be isotropic. These two features lead to an isotropic divergence of the transverse sound attenuation coefficient and an isotropic lattice softening, in contrast to the case of the $C_4$-breaking bond-order which shows the strong anisotropy. Moreover, we use a mean-field approximation and discuss the impurity effects. The transition temperature takes its maximum near the filling of the van-Hove singularity, and the large density of states favors the nematic phase transition. It turns out that the phase transition is of weak first-order in the wide range of filling and, with increasing the impurity scattering, the first order transition line at low temperatures gradually shifts towards the second-order line, rendering the transition a weak first-order in a wider range of parameters. Furthermore, it is confirmed that the enhancement of the ultrasound attenuation coefficient will be clearly observed in experiments in the case of a weak first-order phase transition.

17 pages, 6 figures,

References in corpus (10)

• The electronic properties of graphene
• Fermi-liquid instabilities at magnetic quantum phase transitions
• Theory of Intertwined Orders in High Temperature Superconductors
• Strain-induced quantum phase transitions in magic angle graphene
• Nematic superconductivity in doped Bi2Se3 topological superconductors
• Formation of Electronic Nematic Phase in Interacting Systems
• Charge-$4e$ superconductivity from multi-component nematic pairing: Application to twisted bilayer graphene
• Competition of Fermi surface symmetry breaking and superconductivity
• Pomeranchuk instability in doped graphene
• Quasi-particle evidence for the nematic state above $T_{\mathrm{c}}$ in Sr${}_x$Bi${}_2$Se${}_3$

Cited by in corpus (5)

• Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
• Strain-tuned quantum criticality in electronic Potts-nematic systems
• Classification of electronic nematicity in three-dimensional crystals and quasicrystals
• Phonon-induced rotation of the electronic nematic director in superconducting Bi${}_2$Se${}_3$
• Theories for charge-driven nematicity in kagome metals