Phonon dynamics and chiral modes in the two-dimensional square-octagon lattice

Abstract: Chiral phonons, originally identified in two-dimensional hexagonal lattices and later extended to kagome, square, and other lattices, have been extensively studied as manifestations of broken inversion and time-reversal symmetries in vibrational dynamics. In this work, we investigate the vibrational dynamics of the two-dimensional square-octagon lattice using a spring-mass model with central-force interactions. The model incorporates mass contrast and variable coupling strengths among nearest, next-nearest, and third-nearest neighbors. From the dynamical matrix, we obtain the phonon dispersion relations and identify tunable phononic band gaps governed by both mass and spring-constant ratios. The angular dependence of phase and group velocities is analyzed to reveal the pronounced anisotropy inherent to this lattice geometry. We also examine the distinctive features of the square-octagon geometry, including flat-band anomalies in the density of states and anisotropic sound propagation induced by longer-range couplings. In addition, we explore the emergence of chiral phonons by introducing a time reversal symmetry-breaking term in the dynamical matrix, and to elucidate their optical signatures, we construct a minimal model to study infrared circular dichroism arising from chiral phonon modes.