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Energy Shifts and Broadening of Excitonic Resonances in Electrostatically Doped Semiconductors

Hanan Dery1,2,*, Cedric Robert3, Scott A. Crooker4, Xavier Marie3, and Dinh Van Tuan1

  • *Contact author: hanan.dery@rochester.edu
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Phys. Rev. X 15, 031049 – Published 21 August, 2025

DOI: https://doi.org/10.1103/ddn8-d8bs

Abstract

Tuning the density of resident electrons or holes in semiconductors through electrostatic doping provides crucial insight into the composition of the many excitonic complexes that are routinely observed as absorption or photoluminescence resonances in optical studies. Moreover, we can change the way these resonances shift and broaden in energy by controlling the quantum numbers (e.g., spin and valley) of the resident carriers with applied magnetic fields and doping levels, as well as by selecting the quantum numbers of the photoexcited or recombining electron-hole (e−h) pair through optical polarization. Here, we discuss the roles of distinguishability and optimality of excitonic complexes, showing them to be key ingredients that determine the energy shifts and broadening of optical resonances in charge-tunable semiconductors. A distinguishable e−h pair means that the electron and hole undergoing photoexcitation or recombination have quantum numbers that are not shared by any of the resident carriers. An optimal excitonic complex refers to a complex whose particles come with all available quantum numbers of the resident carriers. Based on the carrier density, magnetic field, and light polarization, all optical resonances may be classified as either distinct or indistinct depending on the distinguishability of the e−h pair, and the underlying excitonic complex can be classified as either optimal or suboptimal. The universality of these classifications, inherited from the fundamental Pauli exclusion principle, allows us to understand how optical resonances shift in energy and whether they should broaden as doping is increased. This understanding is supported by conclusive evidence that the broadening and decay of optical resonances cannot be simply attributed to enhanced screening when resident carriers are added to a semiconductor. Finally, applying the classification scheme in either monolayer or moiré heterobilayer semiconductor systems, we relate the energy shift and amplitude of the neutral-exciton resonance to the compressibility of the resident carrier gas.

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Popular Summary

Electrostatic doping—tuning the density of resident electrons or holes—offers key insights into the structure of excitonic complexes (such as neutral excitons, charged excitons or trions, and more complex many-body composite excitons) commonly observed in optical absorption and photoluminescence spectra. By controlling the quantum numbers (such as spin and/or valley) of resident carriers using magnetic fields and doping levels, and selecting the quantum numbers of photoexcited or recombining electron-hole pairs via optical polarization, researchers can systematically influence how these resonances shift and broaden in energy. In this work, we highlight two fundamental concepts—distinguishability and optimality—as primary factors that govern the behavior of optical resonances in charge-tunable semiconductors.

A distinguishable electron-hole pair refers to a photoexcited or recombining pair whose quantum numbers are not shared by any resident carriers. An optimal excitonic complex is one that incorporates particles representing all available quantum numbers of the background carrier population. Using these criteria, we classify all optical resonances as either distinct or indistinct and all excitonic complexes as optimal or suboptimal. This classification is universal—stemming directly from the Pauli exclusion principle—and provides a predictive framework for understanding how energy shifts and linewidth broadening evolve with increasing charge density.

Making use of the classification scheme in low-dimensional quantum systems, we identify two additional powerful consequences. First, we provide strong evidence that the decay and broadening of optical resonances cannot be explained by enhanced screening due to added carriers. Instead, these effects follow from the quantum statistical structure of the system. Second, we identify a direct relationship between the energy shift and amplitude of neutral exciton resonances and the compressibility of the resident carrier gas in monolayer and moiré heterobilayer semiconductors.

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Phys. Rev. X 15, 031049– Published 21 August, 2025
  • Received 29 November 2024
  • Revised 29 April 2025
  • Accepted 22 July 2025
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