Interface Coupling in Twisted Multilayer Graphene by Resonant Raman Spectroscopy of Layer Breathing Modes.

Raman spectroscopy is the prime nondestructive characterization tool for graphene and related layered materials. The shear (C) and layer breathing modes (LBMs) are due to relative motions of the planes, either perpendicular or parallel to their normal. This allows one to directly probe the interlayer interactions in multilayer samples. Graphene and other two-dimensional (2d) crystals can be combined to form various hybrids and heterostructures, creating materials on demand with properties determined by the interlayer interaction. This is the case even for a single material, where multilayer stacks with different relative orientations have different optical and electronic properties. In twisted multilayer graphene there is a significant enhancement of the C modes due to resonance with new optically allowed electronic transitions, determined by the relative orientation of the layers. Here we show that this applies also to the LBMs, which can be now directly measured at room temperature. We find that twisting has a small effect on LBMs, quite different from the case of the C modes. This implies that the periodicity mismatch between two twisted layers mostly affects shear interactions. Our work shows that ultralow-frequency Raman spectroscopy is an ideal tool to uncover the interface coupling of 2d hybrids and heterostructures.

[1]  Jun Lou,et al.  Vertical and in-plane heterostructures from WS2/MoS2 monolayers. , 2014, Nature materials.

[2]  A. Neto,et al.  Two-dimensional crystals-based heterostructures: materials with tailored properties , 2012 .

[3]  J. Robertson,et al.  Raman spectroscopy of amorphous, nanostructured, diamond–like carbon, and nanodiamond , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[4]  M. Moutinho,et al.  Resonance effects on the Raman spectra of graphene superlattices , 2013 .

[5]  H. Takagi,et al.  Fermi Surface Sheet-Dependent Superconductivity in 2H-NbSe2 , 2001, Science.

[6]  G. Dolling,et al.  LATTICE VIBRATIONS IN PYROLITIC GRAPHITE , 1962 .

[7]  M. Lazzeri,et al.  Phonon surface mapping of graphite: Disentangling quasi-degenerate phonon dispersions , 2009, Physical Review B.

[8]  K. Novoselov,et al.  Rayleigh imaging of graphene and graphene layers. , 2007, Nano letters.

[9]  S. V. Morozov,et al.  Tunable metal-insulator transition in double-layer graphene heterostructures , 2011, 1107.0115.

[10]  D. Mayou,et al.  Localization of dirac electrons in rotated graphene bilayers. , 2009, Nano letters.

[11]  Y. Wang,et al.  The shear mode of multilayer graphene. , 2011, Nature materials.

[12]  Wei Shi,et al.  Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material. , 2015, Chemical Society reviews.

[13]  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.

[14]  M. Prato,et al.  Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. , 2015, Nanoscale.

[15]  D. Basko,et al.  Raman spectroscopy as a versatile tool for studying the properties of graphene. , 2013, Nature nanotechnology.

[16]  Jun Zhang,et al.  Charge transfer and optical phonon mixing in few-layer graphene chemically doped with sulfuric acid , 2010 .

[17]  Enhanced ultra-low-frequency interlayer shear modes in folded graphene layers. , 2013, Nature communications.

[18]  Wei Ji,et al.  Role of the dispersion force in modeling the interfacial properties of molecule-metal interfaces: adsorption of thiophene on copper surfaces , 2012, Scientific Reports.

[19]  Y. Wang,et al.  The shear mode of multi-layer graphene , 2011 .

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

[21]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

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

[23]  R. S. Krishnan.  Raman Spectrum of Quartz , 1945, Nature.

[24]  K. S. Krishnan,et al.  The Raman Effect in Crystals , 1928, Nature.

[25]  A Gholinia,et al.  Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices. , 2012, Nature materials.

[26]  R. Saito,et al.  Observation of layer-breathing mode vibrations in few-layer graphene through combination Raman scattering. , 2012, Nano letters.

[27]  Andre K. Geim,et al.  Two-dimensional atomic crystals. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[28]  R. Saito,et al.  Observation of out-of-plane vibrations in few-layer graphene using combination and overtone Raman modes , 2011 .

[29]  Francesco Mauri,et al.  Kohn anomalies and electron-phonon interactions in graphite. , 2004, Physical review letters.

[30]  N. Peres,et al.  Graphene bilayer with a twist: electronic structure. , 2007, Physical review letters.

[31]  Jin Sung Park,et al.  Raman spectra of out-of-plane phonons in bilayer graphene , 2011 .

[32]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[33]  M. Dresselhaus,et al.  Large Variations of the Raman Signal in the Spectra of Twisted Bilayer Graphene on a BN Substrate. , 2012, The journal of physical chemistry letters.

[34]  R. Hennig,et al.  Angle-resolved Raman imaging of interlayer rotations and interactions in twisted bilayer graphene. , 2012, Nano letters.

[35]  M. Dresselhaus,et al.  Zone folding effect in Raman G-band intensity of twisted bilayer graphene , 2012 .

[36]  Francesco Mauri,et al.  Impact of the electron-electron correlation on phonon dispersion:Failure of LDA and GGA DFT functionals in graphene and graphite. , 2008, 0808.2285.

[37]  A. Jorio,et al.  Raman spectroscopy of twisted bilayer graphene , 2013 .

[38]  S. Haigh,et al.  Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics. , 2012, Nature nanotechnology.

[39]  Temperature-activated layer-breathing vibrations in few-layer graphene. , 2014, Nano letters.

[40]  S. Louie,et al.  Raman spectroscopy study of rotated double-layer graphene: misorientation-angle dependence of electronic structure. , 2012, Physical review letters.

[41]  A. Ferrari,et al.  Raman spectroscopy of shear and layer breathing modes in multilayer MoS2 , 2012, 1212.6796.

[42]  A. Oshiyama,et al.  Atomic corrugation and electron localization due to Moiré patterns in twisted bilayer graphenes , 2014 .

[43]  Jun Zhang,et al.  Interlayer breathing and shear modes in few-trilayer MoS2 and WSe2. , 2013, Nano letters.

[44]  M. Dion,et al.  van der Waals density functional for general geometries. , 2004, Physical review letters.

[45]  K. Shepard,et al.  Boron nitride substrates for high-quality graphene electronics. , 2010, Nature nanotechnology.

[46]  Wei Ji,et al.  High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus , 2014, Nature communications.

[47]  S. Louie,et al.  Evolution of interlayer coupling in twisted molybdenum disulfide bilayers , 2014, Nature Communications.

[48]  Andre K. Geim,et al.  Raman spectrum of graphene and graphene layers. , 2006, Physical review letters.

[49]  A. Shukla,et al.  Anharmonic phonons in few-layer MoS2: Raman spectroscopy of ultralow energy compression and shear modes , 2013, 1304.4122.

[50]  Andrea C. Ferrari,et al.  Resonant Raman spectroscopy of twisted multilayer graphene , 2014, Nature Communications.

[51]  E. G. STEWARD,et al.  Structure of Graphite , 1947, Nature.

[52]  Lin-wang Wang,et al.  Electronic structural Moiré pattern effects on MoS2/MoSe2 2D heterostructures. , 2013, Nano letters.

[53]  C. Cheng,et al.  Van der Waals interaction in a boron nitride bilayer , 2014 .

[54]  A. Ferrari,et al.  Production and processing of graphene and 2d crystals , 2012 .

[55]  F. Tuinstra,et al.  Raman Spectrum of Graphite , 1970 .

[56]  D. Bowler,et al.  Van der Waals density functionals applied to solids , 2011, 1102.1358.