Temperature-dependent layer breathing modes in two-dimensional materials

Abstract

Relative out of plane displacements of the constituent layers of two dimensional materials gives rise to unique low frequency breathing modes. By computing the height-height correlation functions in momentum space, we show that, the layer breathing modes (LBMs) can be mapped consistently to vibrations of a simple linear chain model. Our calculated thickness dependence of LBM frequencies for few layer (FL) graphene and molybdenum disulphide (MoS 2 ) are in excellent agreement with available experiments. Our results show a redshift of LBM frequency with increase in temperature, which is a direct consequence of anharmonicities present in the interlayer interaction. We also predict the thickness and temperature dependence of LBM frequencies for FL hexagonal boron nitride (hBN). Our study provides a simple and efficient way to probe the interlayer interaction for layered materials and their heterostructures, with the inclusion of anharmonic effects. arXiv:1801.01753v1 [cond-mat.mtrl-sci] 5 Jan 2018Two dimensional (2D) materials, for example, graphene, transition metal dichalcogenides, hBN, are being studied extensively for their exciting electronic, thermal, mechanical properties [1,2]. A great deal of effort has also been directed towards understanding hybrid structures of these 2D materials [3]. It is well known that, typically few layers of 2D materials and their hybrid structures are coupled by weak van der Waals (VDW) forces. Such layer-layer couplings give rise to unique low frequency interlayer vibrational modes at finite temperature, namely, shear and layer breathing modes (LBMs). [4,5]. It has been found experimentally that, LBMs are more sensitive to external perturbations than shear modes [6]. These LBMs can be used as direct probe to determine layer thickness, stacking order, effects of external environment, adsorbates etc [6][7][8][9][10][11][12][13][14][15][16][17][18]. Furthermore, LBMs play a crucial role in interlayer electric conductance [19], thermoelectric transport [20]. Understanding the origin and quantification of LBM frequencies is thus of immense practical importance.Three key features emerge from the low frequency Raman spectroscopic measurements of LBMs in 2D materials : (i) A system with n layers will have n − 1 distinct LBMs [21].(ii) LBM frequencies (at the Γ point) are highly sensitive to the thickness of the material i.e. number of layers. For instance, when the number of layers of graphene is increased from 2 to 8, the lowest LBM frequency redshifts from 81 cm −1 to 22 cm −1 [6]. (iii) The lowest LBM frequency also redshifts with increment of temperature (T ), as seen in experiments by controlled laser heating [6,13]. The reported linewidths in Raman spectroscopic measurements for LBMs are typically larger than shear modes [11]. These observations suggest the presence of strong anharmonicity in the interlayer interaction for LBMs. In this work, we address these three key aspects of LBMs.A 2D material embedded in 3D space can have out of plane acoustic phonon modes called flexural mode...

Kolmogorov–Crespi Potential For Multilayer Transition-Metal Dichalcogenides: Capturing Structural Transformations in Moiré Superlattices

“…Figure 6 similarly shows the performance of the KC parameters for bilayer WS 2 and MoSe 2 . Furthermore, the shear and layer breathing modes 66 of the bilayer TMDs computed using SW + KC are in good agreement with experimental measurements (Table 2). See Supporting Information for the performance of the other set of parameters: KC M−M X−X and KC M−X X−X .…”

“…Relaxing these moirépatterns in DFT starting from the rigidly twisted structure leads to significant in-plane and out-of-plane displacements of the atoms. 9 Because of large bending rigidity, 66 the out-of-plane displacements smoothly vary across the MSL surface. The ILS is largest for the AA and B S/S stacking regions, as shown in Figure 9e, for the case of 3.5°twisted bilayer MoS 2 .…”

Evolution of high-frequency Raman modes and their doping dependence in twisted bilayer MoS2

“…37,49,[52][53][54] The low-frequency shear and layer breathing modes originate from the relative displace-ment of the constituent layers in bilayer MoS 2 and provides a non-destructive probe to the interlayer coupling. [55][56][57] Therefore, these low-frequency modes can further provide insights into the evolution of the interlayer coupling strength and can also be used as a sensitive probe for twist angle. 18,19,26 Furthermore, recent computational study also suggests the existence of the phason modes in all twisted bilayer structures.…”

Phonons in twisted transition-metal dichalcogenide bilayers: Ultrasoft phasons and a transition from a superlubric to a pinned phase

“…An important facet of twisting is the evolution of low-frequency vibrational modes, which has largely remained unexplored. Since the low-frequency modes are solely determined by interlayer coupling and are accessible in Raman measurements, they provide a direct nondestructive probe of the interlayer interaction [27][28][29][30]. The existing theoretical reports on the evolution of vibrational modes in twisted structures are restricted to large twist angles and use the Lennard-Jones potential [31] to describe the interlayer interaction, which is insufficient for capturing the stackingdependent energetics [32].…”