Band Nesting in Two-Dimensional Crystals: An Exceptionally Sensitive Probe of Strain.

Lukas Mennel,Valerie Smejkal,Lukas Linhart,Joachim Burgdörfer,Florian Libisch,Thomas Mueller

doi:10.1021/acs.nanolett.0c00694

Abstract

Band nesting occurs when conduction and valence bands are approximately equispaced over regions in the Brillouin zone. In two-dimensional materials, band nesting results in singularities of the joint density of states and thus in a strongly enhanced optical response at resonant frequencies. We exploit the high sensitivity of such resonances to small changes in the band structure to sensitively probe strain in semiconducting transition metal dichalcogenides (TMDs). We measure and calculate the polarization-resolved optical second harmonic generation (SHG) at the band nesting energies and present the first measurements of the energy-dependent nonlinear photoelastic effect in atomically thin TMDs (MoS2, MoSe2, WS2, and WSe2) combined with a theoretical analysis of the underlying processes. Experiment and theory are found to be in good qualitative agreement displaying a strong energy dependence of the SHG, which can be exploited to achieve exceptionally strong modulation of the SHG under strain. We attribute this sensitivity to a redistribution of the joint density of states for the optical response in the band nesting region. We predict that this exceptional strain sensitivity is a general property of all 2D materials with band nesting.

Highlights

The unique electronic, optical, and mechanical properties of atomically thin crystals continue to attract considerable interest motivated in part by both fundamental aspects of lowdimensional physics and future technological applications
One of their outstanding physical properties is the strong electron− photon interaction: a single transition metal dichalcogenide (TMD) monolayer can absorb up to 20% of light in the spectral region of the so-called C-exciton.[1]. This strong absorption is attributed to singularities at critical points in the joint density of states (JDOS) whose signatures are nearly constant energy spacings between the conduction and the valence bands that vary little over extended regions of the Brillouin zone, an effect known as band nesting.[2,3]
Our results demonstrate that the impact of band nesting on the light−matter interaction in two-dimensional materials can be of similar importance as the well-known enhanced excitonic interaction

Summary

Introduction

The unique electronic, optical, and mechanical properties of atomically thin crystals continue to attract considerable interest motivated in part by both fundamental aspects of lowdimensional physics and future technological applications. The novel properties of these two-dimensional (2D) materials constitute a versatile playground for material science and provide new opportunities for device development. One of their outstanding physical properties is the strong electron− photon interaction: a single transition metal dichalcogenide (TMD) monolayer can absorb up to 20% of light in the spectral region of the so-called C-exciton.[1] This strong absorption is attributed to singularities at critical points in the joint density of states (JDOS) whose signatures are nearly constant energy spacings between the conduction and the valence bands that vary little over extended regions of the Brillouin zone, an effect known as band nesting.[2,3]. Strain strongly changes material properties enabling strain engineering to tailor device properties:[6] homogeneous strain in TMDs modulates the bandgap,[7] softens or hardens phononic modes,[8] and changes the electron−

Methods

Results

Conclusion