Scanning Tunneling Microscopy of Atomic Scale Phonon Standing Waves in Quasi-freestanding WSe 2 Monolayers
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Scanning Tunneling Microscopy of Atomic Scale Phonon Standing Waves in Quasi-freestanding WSe2 Monolayers Igor Altfeder1*, Sarah M. Eichfeld2, Rachel D. Naguy1, Joshua A. Robinson2 and Andrey A. Voevodin1 1
Nanoelectronic Materials Branch, Air Force Research Laboratory, Wright Patterson AFB, OH
45433, USA 2
Department of Materials Science and Engineering and The Center for Two-Dimensional and
Layered Materials, The Pennsylvania State University, University Park, PA 16802, USA
ABSTRACT Using scanning tunneling microscopy (STM) we observed atomic scale interference patterns on quasi-freestanding WSe2 islands grown on top of graphene. The bias-independent double atomic size periodicity of these patterns and the sharp Brillouin zone edge revealed by 2D STM Fourier analysis indicate formation of optical phonon standing waves due to scattering on intercalating defects supporting these islands. Standing wave patterns of both synchronized and non-synchronized optical phonons, corresponding to resonant and non-resonant phonon scattering regimes, were experimentally observed. We also found the symmetry breaking effect for individual phonon wave packets, one of the unique features distinguishing phonon standing waves. We show that vibrational and electronic anharmonicities are responsible for STM detection of these patterns. A significant contribution to the interference contrast arises from quantum zero-point oscillations. INTRODUCTION The unusual behavior of phonons in nanomaterials manifests in such phenomena as spontaneous ripples on graphene [1], inelastic Friedel oscillations [2], phonon tunneling in subnanometer gaps [3], and phonon interference in quantum wells [4]. Experimental observation of atomic scale phonon standing waves that will be described here opens new page in this rapidly developing research field. A large number of theoretical and experimental publications [5, 6] have confirmed that phonons can be efficiently scattered by individual lattice defects and
Figure 1. Simulated interference pattern for dispersionless 1D optical phonons. The scattering center is located at x = 0. The pattern profile: , where k0=π/a. Vertical axis periodically reverses sign because of oscillations.
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individual intercalating atoms. To understand what periodicities are anticipated from defectinduced phonon standing wave patterns, in the Figure 1 we show the simulated interference wave packet for a simplest case of nearly-dispersionless one-dimensional optical phonons. The construction of this curve takes into account (a) significant phonon scattering probability and (b) summation over all Brillouin zone (BZ). In addition, due to narrow oscillator frequency distribution, phase synchronization of all Z k modes caused by defect-induced coupling between them has to be taken into account [7, 8].
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