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

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 (MoS 2 , MoSe 2 , WS 2 , and WSe 2 ) 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.

Optical Harmonic Generation in 2D Materials

“…For instance, a considerable enhancement is found for the 12th order harmonic. In various other studies, [ 54,210,272 ] a large SHG enhancement with high values of conversion efficiency in the band nesting region are achieved in 1L TMDs. The peaks of A and B excitons are labelled A and B, respectively.…”

“…[ 45 ] This highly sensitive strain dependent SHG behavior at the band nesting region has been proven through simulations [ 209 ] and experiments. [ 210 ]…”

Strongly Anisotropic Strain‐Tunability of Excitons in Exfoliated ZrSe3

“…Among the different strategies to strain engineer 2D materials, the application of uniaxial strain through bending flexible substrates with a bending jig apparatus is one of the most popular approaches. [1,11,12,[15][16][17][18] This method presents some issues when applied to 2D materials with in-plane anisotropic properties. Indeed, the effect of uniaxial strain along different crystal orientations is expected to modify the properties of these anisotropic 2Ds differently.…”

All-optical polarization and amplitude modulation of second-harmonic generation in atomically thin semiconductors

“…In contrast to thin films, where surface SHG is allowed due to an out-of-plane component of the second-order susceptibility [6,35], TMDs belong to the D 3h symmetry group and thus have only one non-vanishing in-plane component of the nonlinear optical susceptibility (see Methods) [35][36][37][38][39][40].…”