Cross-dimensional electron-phonon coupling in van der Waals heterostructures

Abstract

The electron-phonon coupling (EPC) in a material is at the frontier of the fundamental research, underlying many quantum behaviors. van der Waals heterostructures (vdWHs) provide an ideal platform to reveal the intrinsic interaction between their electrons and phonons. In particular, the flexible van der Waals stacking of different atomic crystals leads to multiple opportunities to engineer the interlayer phonon modes for EPC. Here, in hBN/WS₂ vdWH, we report the strong cross-dimensional coupling between the layer-breathing phonons well extended over tens to hundreds of layer thick vdWH and the electrons localized within the few-layer WS₂ constituent. The strength of such cross-dimensional EPC can be well reproduced by a microscopic picture through the mediation by the interfacial coupling and also the interlayer bond polarizability model in vdWHs. The study on cross-dimensional EPC paves the way to manipulate the interaction between electrons and phonons in various vdWHs by interfacial engineering for possible interesting physical phenomena.

Fig. 1

Characterizations and Raman spectra of the 3LW flake and hBN/3LW vdWHs. a Optical images of 2LW, 3LW, 39L-hBN/2LW and 39L-hBN/3LW. b AFM image of the hBN flake with thickness of 12.9 nm in pink box of a. The atomic lattice images of c 3LW and d 39L-hBN flakes. The dashed white lines in c, d represent the lattice orientations of 3LW and 39L-hBN are 125.9° and 136.2°, respectively. The scanning angles are 60° and 70° for 3LW and 39L-hBN, respectively. The twist angle θ_t between the 39L-hBN and 3LW flakes is 0.3°. e Raman spectra of 39L-hBN, 3LW and 39L-hBN/3LW. The green dash profile depicts the LB_3,2 mode in 3LW while the pink dash profile represents the S_3,1 mode. The spectra are scaled and offset for clarify and the scale factors are shown. f The polarized (VV) and depolarized (HV) Raman spectra of 39L-hBN/3LW

Fig. 2

Raman spectra of hBN/WS₂ and WS₂/hBN with different numbers of WS₂ and hBN layers in vdWHs. a Raman spectra of 13L-hBN/1LW (θ_t = 17.4°), 39L-hBN/2LW (θ_t = 0.3°) and 39L-hBN/3LW (θ_t = 0.3°) along with the corresponding WS₂ flakes. The dark red and dash profile depicts the LB_3,2 mode in 3LW while the gray dash profile represents the S_3,1 mode. b Raman spectra of 3LW/32L-hBN (θ_t = 23.5°), 3LW/44L-hBN (θ_t = 23.5°) and 3LW/224L-hBN (θ_t = 17.2°) along with the standalone 3LW flake. The spectra are scaled and offset for clarify. The stars represent the two prime LB modes in vdWHs. The inset in b shows the schematic diagram of the linear chain model for the LB modes in nL-hBN/3LW

Fig. 3

Intensity resonances of the S and LB modes in 39L-hBN/mLW and corresponding mLW. Raman spectra of a 39L-hBN/3LW and b 3LW excited by E_ex in the range of 2.41–2.81 eV. The diamonds and circles represent the two prime LB modes in 39L-hBN/3LW. The crosses show TA phonons resonant with the B exciton. The resonant profiles of c the LB_42,36 (red diamonds), LB_42,37 (blue circles) and S_3,1 (gray stars) in 39L-hBN/3LW, d the LB_41,33 (red diamonds), LB_41,34 (blue circles) and S_2,1 (gray stars) modes in 39L-hBN/2LW, e the S_3,1 (gray stars) and LB_3,2 (red diamonds) modes in 3LW flake, f the S_2,1 (gray stars) and LB_2,1 (red diamonds) modes in 2LW flake. The diamonds, circles, and stars represent the experimental data while the red and blue solid lines are the fitting results. The Raman intensity is normalized by the E₁ mode of quartz at ~127 cm⁻¹ to eliminate the different efficiencies of charge-coupled device at different E_ex

Fig. 4

Schematic diagram for constituent-vdWH EPC of the LB modes in hBN/WS₂ vdWHs. a Raman spectrum of a 39L-hBN/3LW in the region of 5~50 cm⁻¹ and the normal mode displacements (red arrows) of the LB_42,37, LB_42,36, LB_42,32, and LB_42,29 modes in a 39L-hBN/3LW and the LB_3,2 in a standalone 3LW flake. The triangles represent the representative expected LB modes in the 39L-hBN/3LW based on the LCM. In the nL-hBN/3LW (n = 39), ${\alpha }_i^{\prime }$(BN) (i = 1, 2, …, n) and ${\alpha }_j^{\prime }$(W) (j = 1, 2, 3) are the polarizability derivative of the entire layer i from hBN constituents and layer j from WS₂ constituents with respective to the displacement in the z direction. b The modulus square of the projection from wavefunction of different LB modes in 39L-hBN/3LW vdWH onto the wavefunction of the LB_3,2 mode in a standalone 3LW flake. c The relative intensity of LB modes in 39L-hBN/3LW vdWH based on the interlayer bond polarizability model