Excitons in Momentum Space

THE CHALLENGE AND THE SOLUTION

Nearly a century ago, in the 1930s, Frenkel and Wannier postulated that when a semiconductor or insulator absorbed light, it created an exciton – a composite particle made up of the photoexcited electron bound to the oppositely charged hole. Over the ensuing decades, excitons were extensively studied and shown to play a critical role in the opto-electronic properties of materials and devices. Nonetheless, the vast majority of these studies used optical techniques, and couldn’t resolve the momentum coordinate of excitons and the associated rich physics.

To resolve the momentum-coordinate of excitons, one expects to utilize a technique like time- and angle-resolved photoemission spectroscopy (TR-ARPES). However, for decades, this hadn’t been experimentally feasible: Known semiconductors were three-dimensional, possessing excitons with low binding energy. In contrast, TR-ARPES measurements are typically surface sensitive, and lack the needed energy resolution.

In 2010, the discovery of atomically thin transition metal dichalcogenides (TMDC) – two-dimensional (2D) semiconductors possessing excitons with large binding energies, brought new hope. They also brought their own set of experimental challenges:

(i) The band extrema and excitons in TMDCs lie at the edge of the BZ, thus requiring XUV photons to probe excitonic states. (ii) The high-quality samples of 2D semiconductors came in micron scale sizes, thus requiring micron-scale resolution to the ARPES experiments. (iii) The tightly bound excitons have short radiative lifetimes, thus requiring temporal resolution in sub-picosecond range. Together, one needed ultrafast TR-XUV-µ-ARPES capabilities, which weren’t plausible in existing experimental platforms. Typical table-top systems easily offered the required time-resolution but were bogged down with inadequate XUV flux, or space charge due to low repetition rates. Synchrotron or XFEL sources provided suitable XUV flux, but relevant time-resolution was challenging. Furthermore, µ-ARPES capabilities were available only in a few synchrotron sources in the world, with none of those capable of the needed time-resolution.

Over the course of a decade, we developed an experimental platform capable of TR-XUV-µ-ARPES capabilities in mind. In our platform – a photoemission electron microscope (PEEM) or a Momentum Microscope (MM) enables energy-resolved images of momentum-space, obtained from selected micron sized regions of the sample (µ-ARPES). Combining this with a patented technique from my lab to generate 100fs XUV pulses with a high flux, we were able to perform very high-quality TR-XUV-µ-ARPES measurements. With this, we achieved three important breakthroughs summarized below.