Unusual Twisting Phonons and Breathing Modes in Tube‐Terminated Phosphorene Nanoribbons and Their Effects on Thermal Conductivity

Abstract

By studying tube-terminated phosphorene nanoribbons (PNRs), it is found that unusual phonon and thermal properties can emerge from topologically new edges. The lattice dynamics calculations show that in tube-terminated PNRs, the breaking of rotation symmetry suppresses the degeneracy of phonon modes, causing the emergence of twisting mode. An anomalous change of an out-of-plane acoustic mode to breathing modes with nonzero energy at the center of Brillouin zone occurs when the phosphorene sheet is converted into a tube-terminated PNR. These unusual twisting and breathing modes provide a larger phase space for scattering phonons, thus explaining the low thermal conductivity of tube-terminated PNRs revealed by molecular dynamics calculations. Due to the change in the stress field distribution caused by the tube edge, a nearly strain-independent thermal conductivity in tube-terminated PNRs is observed, which is in contrast to the apparent enhancement of thermal conductivity in pristine and dimer-terminated PNRs under tensile strain. The work reveals intriguing phononic and thermal behaviors of tube-terminated 2D materials.

The Ultrahigh Quantum Thermal Conductance of Hydrogenated Boron Nanotubes

“…The fourth one originates from the out‐of‐plane acoustic mode of the 2D sheet, but in the tubular structure, it is becoming a new mode in which all the atoms move radially, thus giving non‐zero energy at the Γ point. The unique 1D characteristic of phonon dispersion relationship is similar to that reported in carbon nanotubes and phosphorene nanotubes …”

“…The unique 1D characteristic of phonon dispersion relationship is similar to that reported in carbon nanotubes [11] and phosphorene nanotubes. [49] From Figure 2, the high frequency optical modes (>1500 cm À1 ) are contributed by the B-H bonds, and the phonon dispersion contributed by boron atoms is mainly from 0 cm À1 to 1100 cm À1 , which is lower than (3,3) CNT (%1450 cm À1 ). However, compared with the cut-off frequency in other 2D materials such as MoS 2 and phosphorene, [50] the cut-off frequency is remarkably higher, indicating high thermal conductance.…”

Thermal transport properties of single-layer black phosphorus from extensive molecular dynamics simulations

“…The in-plane lattice constants are determined automatically using a barostat and the thick-ness of the system is chosen as the conventional value of [8] of 0.525 nm. We only consider heat transport in effectively two-dimensional systems and do not consider edge effects in nanoribbons [24].…”

Computational Understanding of the Growth of 2D Materials

“…That means that the transition time for a pair of edge atoms at room temperature is only about 1 ns. [131] Besides the phosphorene edge reconstruction, ab initio calculations have been employed to explore the reconstruction of zigzag edge of monolayer transition metal dichalcogenides, such as MoS 2 and WSe 2 . Therefore, the configuration of a zigzag edge in freestanding monolayer phosphorene is highly likely to transform into a 1D tubed edge.…”

“…[130] Besides, the tube edge also brings new vibrational modes and thermal transport properties to phosphorene ribbons. [131] Besides the phosphorene edge reconstruction, ab initio calculations have been employed to explore the reconstruction of zigzag edge of monolayer transition metal dichalcogenides, such as MoS 2 and WSe 2 . Theoretical studies predicted that both metal and chalcogen edges of freestanding transition metal dichalcogenides nanoribbons undergo obvious reconstruction.…”