Observation of the Breakdown of Optical Phonon Splitting in a Two-dimensional Polar Monolayer

Phonon splitting of the longitudinal optical and transverse optical modes (LO-TO splitting), a ubiquitous phenomenon in three-dimensional (3D) polar materials, is essential for the formation of the 3D phonon polaritons. Theories predict that the LO-TO splitting will break down in two-dimensional (2D) polar systems, but direct experimental verification is still missing. Here, using monolayer hexagonal boron nitride (h-BN) as a prototypical example, we report the direct observation of the breakdown of LO-TO splitting and the finite slope of the LO phonons at the center of the Brillouin zone in 2D polar materials by inelastic electron scattering spectroscopy. Interestingly, the slope of the LO phonon in our measurements is lower than the theoretically predicted value for a freestanding monolayer due to the screening of the Cu foil substrate. This enables the phonon polaritons (PhPs) in monolayer h-BN/Cu foil to exhibit ultra-slow group velocity (~ 5 x 10^-6 c, c is the speed of light) and ultra-high confinement (~ 4000 times smaller wavelength than that of light). Our work reveals the universal law of the LO phonons in 2D polar materials and lays a physical foundation for future research on 2D PhPs.

[1]  F. Mauri,et al.  Electron-phonon interaction and phonon frequencies in two-dimensional doped semiconductors , 2022, Physical Review B.

[2]  S. Louie,et al.  Intervalley Excitonic Hybridization, Optical Selection Rules, and Imperfect Circular Dichroism in Monolayer h-BN. , 2022, Physical review letters.

[3]  M. Stengel,et al.  Exact Long-Range Dielectric Screening and Interatomic Force Constants in Quasi-Two-Dimensional Crystals , 2021, Physical Review X.

[4]  Dominik M. Juraschek,et al.  Highly Confined Phonon Polaritons in Monolayers of Perovskite Oxides. , 2021, Nano letters.

[5]  F. J. García de abajo,et al.  Direct observation of highly confined phonon polaritons in suspended monolayer hexagonal boron nitride , 2020, Nature Materials.

[6]  F. Maia,et al.  Acceleration of Subwavelength Polaritons by Engineering Dielectric-Metallic Substrates , 2020 .

[7]  K. Thygesen,et al.  Efficient Ab Initio Modeling of Dielectric Screening in 2D van der Waals Materials: Including Phonons, Substrates, and Doping , 2020, The Journal of Physical Chemistry C.

[8]  Sang Uck Lee,et al.  Strain-induced work function in h-BN and BCN monolayers , 2020 .

[9]  J. Zhang,et al.  Optical lattice vibrations in monolayer hexagonal boron nitride from macroscopic equations , 2019, Journal of physics. Condensed matter : an Institute of Physics journal.

[10]  S. De Liberato,et al.  Optical Nonlocality in Polar Dielectrics , 2019, Physical Review X.

[11]  J. Kong,et al.  Phonon Polaritons in Monolayers of Hexagonal Boron Nitride , 2019, Advanced materials.

[12]  P. Narang,et al.  Phonon Polaritonics in Two-Dimensional Materials. , 2019, Nano letters (Print).

[13]  F. Mauri,et al.  Position and momentum mapping of vibrations in graphene nanostructures , 2018, Nature.

[14]  S. Bhattacharya,et al.  Giant exciton-phonon coupling and zero-point renormalization in hexagonal monolayer boron nitride , 2018, Physical Review B.

[15]  N. Pryds,et al.  Electron mobility in oxide heterostructures , 2018, Journal of Physics D: Applied Physics.

[16]  V. Giliberti,et al.  Observation of phonon-polaritons in thin flakes of hexagonal boron nitride on gold , 2018 .

[17]  Xiaobo Yin,et al.  Phononic thermal properties of two-dimensional materials , 2018 .

[18]  F. Capasso,et al.  Selective excitation and imaging of ultraslow phonon polaritons in thin hexagonal boron nitride crystals , 2017, Light: Science & Applications.

[19]  Stefano de Gironcoli,et al.  Advanced capabilities for materials modelling with Quantum ESPRESSO , 2017, Journal of physics. Condensed matter : an Institute of Physics journal.

[20]  Zhigang Sun,et al.  Launching Phonon Polaritons by Natural Boron Nitride Wrinkles with Modifiable Dispersion by Dielectric Environments , 2017, Advanced materials.

[21]  R. Hillenbrand,et al.  Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas , 2017, Nature Communications.

[22]  I. Vurgaftman,et al.  Ultralow-loss polaritons in isotopically pure boron nitride. , 2017, Nature materials.

[23]  Xiaobo Yin,et al.  Colloquium: Phononic thermal properties of two-dimensional materials , 2017, Reviews of Modern Physics.

[24]  M. Calandra,et al.  Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene , 2017, 1705.04973.

[25]  Kenji Watanabe,et al.  Tuning quantum nonlocal effects in graphene plasmonics , 2017, Science.

[26]  E. Yablonovitch,et al.  Goos-Hänchen Shift and Even-Odd Peak Oscillations in Edge-Reflections of Surface Polaritons in Atomically Thin Crystals. , 2017, Nano letters.

[27]  M. Gibertini,et al.  Breakdown of Optical Phonons' Splitting in Two-Dimensional Materials. , 2016, Nano letters.

[28]  S. Soubatch,et al.  Electron energy loss spectroscopy with parallel readout of energy and momentum. , 2016, The Review of scientific instruments.

[29]  J. Aizpurua,et al.  Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope , 2016, Nature Communications.

[30]  F. Guinea,et al.  Polaritons in layered two-dimensional materials. , 2016, Nature materials.

[31]  D. N. Basov,et al.  Polaritons in van der Waals materials , 2016, Science.

[32]  M. Calandra,et al.  Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: Theoretical modeling and first-principles calculations , 2016, 1605.08207.

[33]  Feliciano Giustino,et al.  Electron-phonon interactions from first principles , 2016, 1603.06965.

[34]  F. de Juan,et al.  Emergence of an Out-of-Plane Optical Phonon (ZO) Kohn Anomaly in Quasifreestanding Epitaxial Graphene. , 2015, Physical review letters.

[35]  E. W. Plummer,et al.  High resolution electron energy loss spectroscopy with two-dimensional energy and momentum mapping. , 2015, The Review of scientific instruments.

[36]  F. D. Juan,et al.  Symmetries and selection rules in the measurement of the phonon spectrum of graphene and related materials , 2014, 1405.1467.

[37]  A. H. Castro Neto,et al.  Tunable Phonon Polaritons in Atomically Thin van der Waals Crystals of Boron Nitride , 2014, Science.

[38]  K. Michel,et al.  Theory of elastic and piezoelectric effects in two-dimensional hexagonal boron nitride , 2009 .

[39]  Stefano de Gironcoli,et al.  QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[40]  D. Sánchez-Portal,et al.  Vibrational properties of single-wall nanotubes and monolayers of hexagonal BN , 2002, cond-mat/0211173.

[41]  Stefano de Gironcoli,et al.  Phonons and related crystal properties from density-functional perturbation theory , 2000, cond-mat/0012092.

[42]  G. Kresse,et al.  From ultrasoft pseudopotentials to the projector augmented-wave method , 1999 .

[43]  C. Oshima,et al.  PHONON DISPERSION OF AN EPITAXIAL MONOLAYER FILM OF HEXAGONAL BORON NITRIDE ON NI(111) , 1997 .

[44]  Xavier Gonze,et al.  Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory , 1997 .

[45]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[46]  W. Mönch,et al.  Phonons in 3C-, 4H-, and 6H-SiC , 1995 .

[47]  Hiroshi Iwasaki.  Angle Resolved Electron Energy Loss Spectroscopy , 1982 .

[48]  D. Mills,et al.  Electron Energy Loss Spectroscopy and Surface Vibrations , 1982 .

[49]  D. Mills,et al.  Polaritons: the electromagnetic modes of media , 1974 .

[50]  A. Pinczuk,et al.  Raman scattering by polaritons , 1968 .

[51]  C. H. Perry,et al.  Normal Modes in Hexagonal Boron Nitride , 1966 .