title: Low-Frequency Interlayer Breathing Modes in Few-Layer Black Phosphorus.
abstract: As a new two-dimensional layered material, black phosphorus (BP) is a very promising material for nanoelectronics and optoelectronics. We use Raman spectroscopy and first-principles theory to characterize and understand the low-frequency (LF) interlayer breathing modes (<100 cm(-1)) in few-layer BP for the first time. Using a laser polarization dependence study and group theory analysis, the breathing modes are assigned to Ag symmetry. Compared to the high-frequency (HF) Raman modes, the LF breathing modes are considerably more sensitive to interlayer coupling and, thus, their frequencies show a stronger dependence on the number of layers. Hence, they constitute an effective means to probe both the crystalline orientation and thickness of few-layer BP. Furthermore, the temperature dependence shows that in the temperature range -150 to 30 °C, the breathing modes have a weak anharmonic behavior, in contrast to the HF Raman modes that exhibit strong anharmonicity.
authors.affiliation: †Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
authors.forename: Xi
authors.initials: X
authors.lastname: Ling
authors.affiliation: ‡Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, United States.
authors.forename: Liangbo
authors.initials: L
authors.lastname: Liang
authors.affiliation: †Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
authors.forename: Shengxi
authors.initials: S
authors.lastname: Huang
authors.affiliation: §Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States.
authors.forename: Alexander A
authors.initials: AA
authors.lastname: Puretzky
authors.affiliation: §Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States.
authors.forename: David B
authors.initials: DB
authors.lastname: Geohegan
authors.affiliation: §Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States.|∥Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States.
authors.forename: Bobby G
authors.initials: BG
authors.lastname: Sumpter
authors.affiliation: †Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
authors.forename: Jing
authors.initials: J
authors.lastname: Kong
authors.affiliation: ‡Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, United States.
authors.forename: Vincent
authors.initials: V
authors.lastname: Meunier
authors.affiliation: †Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.|⊥Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
authors.forename: Mildred S
authors.initials: MS
authors.lastname: Dresselhaus
keywords: Raman spectroscopy; density functional theory; polarization dependence; temperature dependence; thickness dependence