Momentum space valleys in WS2 monolayer, schematic and observation

A visualization of momentum space in ultrathin semiconductor materials. Two, topography-like 3D renderings are seen, one above the other, with a hexagonal prism in between showing how valleys in the top ‘landscape’ correspond to peaks in the bottom. Each valley-peak pair is denoted with a “K”. The landscapes are colored blue and red depending on spin-configuration. An inserted image shows a hexagonal outline with shining stars of electrons imaged at alternating points along the 2D hexagon.

The atomic structure of ultrathin semiconductors like TMDs is hexagonal, and this symmetry is reflected in momentum space, where the conduction (top) and valence (bottom) bands each have local energy minima and maxima at specific points (K), which can be visualized as valleys in a momentum landscape. Time-reversal symmetry in quantum mechanics dictates that what happens in one valley is mirrored in the opposite valley: if the conduction band at K has spin-down (red), then K’ must have spin-up (blue), leading to an alternating pattern along the edge of the hexagon. Bright excitons form when the electron rests in the same valley and has the same spin as the corresponding hole. By using either left- or right-circularly polarized light, one can selectively populate bright exciton in a specific valley. The insert shows energy measurements of bright excitons, showing the contrast in valleys K and K’.

Date:
22 September 2025
Credit:
Momentum landscape figure adapted Bussolotti et al., (2018) Nano Futures 2 032001. Insert adapted from Zhu et al., (2025) Nature Communications 16 6385

Copyright OIST (Okinawa Institute of Science and Technology Graduate University, 沖縄科学技術大学院大学). Creative Commons Attribution 4.0 International License (CC BY 4.0).

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