Abstract: Van der Waals quantum wells, naturally formed in two-dimensional layered materials with nanoscale thickness, possess many inherent advantages over conventional molecular beam epitaxy grown counterparts, and could bring up intriguing physics and applications. However, optical transitions originated from the series of quantized states in these emerging quantum wells are still elusive. Here, we show that multilayer black phosphorus appears to be an excellent candidate for van der Waals quantum wells with well-defined subbands and high optical quality. Using infrared absorption spectroscopy, we probe subband structures of multilayer black phosphorus with tens of atomic layers, revealing clear signatures for optical transitions with subband index as high as 10, far from what was attainable previously. Surprisingly, in addition to allowed transitions, an unexpected series of “forbidden” transitions is also evidently observed, which enables us to determine energy spacings separately for conduction and valence subbands. Furthermore, the linear tunability of subband spacings by temperature and strain is demonstrated. Our results are expected to facilitate potential applications for infrared optoelectronics based on tunable van der Waals quantum wells.

Abstract: Chiroptically active, hierarchically structured materials are difficult to accurately characterize due to linear anisotropic contributions (i.e., linear dichroism (LD) and linear birefringence (LB)) and parasitic ellipticities that produce artifactual circular dichroism (CD) signals, in addition to chiral analyte contributions ranging from molecular-scale clusters to micron-sized assemblies. Recently, we have shown that CdS magic-sized clusters (MSC) can self-assemble into ordered films that have a hierarchical structure spanning seven orders of length-scale. These films have a strong CD response, but the chiral origins are obfuscated by the hierarchical architecture and LDLB contributions. Here, we derive and demonstrate a method for extracting the “pure” CD signal (CD generated by structural dissymmetry) from hierarchical MSC films and identified the chiral origin. The theory behind the method is derived using Mueller matrix and Stokes vector conventions and verified experimentally before being applied to hierarchical MSC and nanoparticle films with varying macroscopic orderings. Each film's extracted “true CD” shares a bisignate profile aligned with the exciton peak, indicating the assemblies adopt a chiral arrangement and form an exciton coupled system. Interestingly, the linearly aligned MSC film possesses one of the highest g-factors (0.05) among semiconducting nanostructures reported. Additionally, we find that films with similar electronic transition dipole alignment can possess greatly different g-factors, indicating chirality change rather than anisotropy is the cause of the difference in the CD signal. The difference in g-factor is controllable via film evaporation geometry. This study provides a simple means to measure “true” CD and presents an example of experimentally understanding chiroptic interactions in hierarchical nanostructures.