Phonons play a significant role in the thermal properties of a material, interact closely with other quasiparticles or collective excitations, and are responsible for extraordinary effects (such as superconductivity). Phonons 1–5 are bosonic excitations in crystals they denote the collective vibrations of the atomic lattice. Our work paves the way for new advancements in topological phononics comprising gapless and gapped topological phonons. Our study not only promotes 2D Kekulé-order graphene as a concrete material platform for exploring the intriguing physics of phononic second-order topology but also proposes the coexistence of different categories of Weyl phonons, i.e., a Weyl complex that comprises two LWPs and one QNP, in two dimensions. Moreover, the difference between the phononic Weyl pair and the phononic Weyl complex was investigated in detail. For the gapless topological phonons, 2D Kekulé-order graphene hosts a phononic Weyl pair and a phononic Weyl complex around 7.54 and 47.3 THz (39.2 THz), respectively.
For the gapped topological phonons, 2D Kekulé-order graphene hosts phononic real Chern insulator states, i.e., second-order topological states, and corner vibrational modes inside frequency gaps at 27.96 and 37.065 THz.
This is the first work to investigate rich gapped and gapless topological phonon states in experimentally feasible 2D materials. In this work, we chose the recently experimentally prepared two-dimensional (2D) Kekulé-order graphene as a target to propose the coexistence of gapless and gapped topological phonon states in its phonon curves. Speedster Erin Naden scored a hat-trick of tries for Player of the Match.The conceptual framework of topological states has recently been extended to bosonic systems, particularly phononic systems. In a massive day of football in Dubbo, Bathurst St Pat's won the Blues Tag Grand Final when scoring a dominant 32-8 victory over Dubbo Macquarie Raiders. Powyer was a deserved winner of the Scott-Weir Medal as best-on-ground in the grand final. With two minutes left on the clock, Thurston put the exclamation mark on the result, slotting a field goal to round out the 25-12 victory. Mudgee scored the next two tries, with Pacey Stockton putting Jack Durrant over to the left of the posts before a Hayden Carpenter kick was caught and grounded by Joshwa Wilson-Tuckey inside the right touchline.īoth tries went unconverted and Mudgee trailed 24-12. Scooting from acting-half, the fullback went 70 metres fending and twisting his way to an entertaining try inside the left touchline. Minutes later, Thurston scored the try of the match. Thurston was on target again, and Dubbo led 20-4. Trailing 14-4 the Dragons at last had a sniff, but the CYMS class prevailed in a telling five-minute period.Īgain, it was Madden in the thick of the action, and playing to his left, he delivered an inch-perfect pass to Thomas Hughes, who cut back inside and beat two players to score to the left of the posts. Needing to score first in the second half, Mudgee responded quickly, with Jack Littlejohn putting up a well-placed kick from 15 metres out.ĭubbo teammates Jeremy Thurston and Jyie Chapman both went for the ball, which led to a mistake and there to pounce on the Steeden and score the try was Mugdee centre David West. Still, the Fishies battled on, and Thurston kicked a penalty for 14-0, which remained the half-time score. The Dubbo outfit lost inspirational hooker Alex Bonham late in the first half. Thurston made no mistake with the kick and CYMS led 12-0 after 23 minutes. In a sight to be seen, the CYMS captain and front rower out-sprinted Mudgee's defence to the try line, going over untouched to the right of the posts. He set up Dubbo's second try when a barnstorming Jarryn Powyer charged through a gap from 25 metres out. Madden was pulling all the right strings in the first half. Jeremy Thurston potted the difficult conversion attempt and CYMS led 6-0 after just five minutes. The popular Fijian flyer had the crowd cheering in delight as he grounded the ball inside the left touchline and just millimetres before the dead-ball line. Gifted good field position early, it didn't take long for Dubbo to strike, with clever half Jordi Madden taking the ball to the line before grubbering for his winger Ratu Roko. Still, Mudgee matched motors with them for most parts, with bookends Cody Godden and Casey Burgess putting in significant time in the Dragons engine room. Jarryn Powyer, Billy Sing, and Ben Marlin led the way for the Fishies. In an absorbing 80-minute fixture, two physical packs engaged in a slog-fest typical of any good grand final.
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