Interlayer resistance of misoriented MoS₂

Abstract

Interlayer misorientation in transition metal dichalcogenides alters the interlayer distance, the electronic bandstructure, and the vibrational modes, but, its effect on the interlayer resistance is not known. This work analyzes the coherent interlayer resistance of misoriented 2H-MoS2 for low energy electrons and holes as a function of the misorientation angle. The electronic interlayer resistance monotonically increases with the supercell lattice constant by several orders of magnitude similar to that of misoriented bilayer graphene. The large hole coupling gives low interlayer hole resistance that weakly depends on the misorientation angle. Interlayer rotation between an n-type region and a p-type region will suppress the electron current with little effect on the hole current. We estimate numerical bounds and explain the results in terms of the orbital composition of the bands at high symmetry points. Density functional theory calculations provide the interlayer coupling used in both a tunneling Hamiltonian and a non-equilibrium Green function calculation of the resistivity.Introduction: There is tremondous interest in multilayer and heterostructure stacks of transition metal dichalcogenides (TMDs) . They exhibit strong spin orbit coupling and non-trivial topology [3][4][5] [14,17,20], and rectifying pn junctions [7,14,20]. Multilayer and heterostructure growth with stacking control have been demonstrated [20][21][22][23]. Recent reviews provide an overview of the state of the art [24,[27][28][29].For TMD misoriented bilayers, both experiments and simulations show that the interlayer coupling and the interlayer distance are sensitive to the rotation angle, and that the sensitivity of the coupling is very different for different valleys [11-13, 16, 25]. A small rotation angle in hetero-bilayers alters the inter-layer exciton dynamics [30,31]. While the effects of misorientation on the geometry, electronic bandstructure, and vibrational modes of bilayer TMDs have received significant attention, the effect of misorientation on the interlayer resistivity of TMDs has not yet been studied. Recent work considered the effect of misorientation on the in-plane transport [32]. In this work, we theoretically determine the coherent electron and hole interlayer (vertical) conductance of a misoriented MoS 2 interface as illustrated in Fig. 1(a).In MoS 2 bilayers, the low-energy electron transport takes place at the K valley, and the low-energy hole transport takes place at the Γ valley. This results in an extremely asymmetric response of the electron and

Stacking and interlayer electron transport in MoS2

“…Table I also includes the interlayer coupling quantities for the CBM at K C point and VBM at K V and Γ V points. The results for the AA' (2H phase) are in agreement with the values reported in ref 22 . Here, what is to be noted is that AB' stacking presents the highest interlayer coupling for the VBM at Γ V and the lowest K V hinting at the specific difference of this phase as discussed below.…”

“…From Figure 3 and Figure S2 of the Supplemental Material 28 in tune with the discussion in Ref. 22 , the predominant contribution to the conduction band at K is due to d z 2 orbital of Mo atoms, while the valence band is principally made of d x 2 −y 2 and d xy orbitals at K V 6 and p z orbitals of S atoms and d z 2 orbitals of Mo atoms at Γ V . The interlayer coupling at K C for AA' stacking is then an order of magnitude smaller than at K V .…”

“…[34][35][36] Spinorbit coupling has not been taken into account, because of its small effect on the band structure. 22,23 For more details about calculations, see Supplemental Material. 28 Table I reports the electronic properties (valence band maximum (VBM), conduction band minimum (CBM), direct and indirect band gaps and relative energy with respect to the AA' stacking) of extended bilayer MoS 2 systems for the different stacking configurations.…”

Precise control of the interlayer twist angle in large scale MoS2 homostructures

“…We attribute the electron mobility of 30°bilayer higher than that of (30°,0°) and (0°, 30°) trilayer to the screen of the electric field by the bottom MoS 2 layers and the enhanced scattering effect of by trapped interlayer bubbles in trilayer samples. The higher mobility of 30°twist angle may be due to the interlayer decoupling by incommensurate structure or smaller interlayer resistance 47 . For more information, please refer to Supplementary Notes 7.…”

Site-specific electrical contacts with the two-dimensional materials

“…The exchange-correlation functions are described with the generalized gradient approximation (GGA) in the form of the Perdew, Burke, and Ernzernhof (PBE) functional 59 . The DFT-D3 scheme of Grimme for the vdW correction 60 is applied on multiple layers of MoS 2 . The whole systems contain 71-432 atoms.…”