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Exciton Binding Energies in 2D Materials: Insights from Braneworld Physics

Antoine Honet, Michaël Sarrazin

TL;DR

The paper addresses exciton binding energies in 2D materials where the standard Coulomb potential fails due to screening. It adapts the Dvali-Gabadadze-Porrati-Shifman (DGPS) mechanism to a (2+1)-D brane in a (3+1)-D spacetime, deriving an effective on-brane potential that matches the Rytova-Keldysh form $V(r)=\frac{1}{8 r_0 M_P^2}[ H_0(r/r_0) - Y_0(r/r_0) ]$. Using a two-step variational hydrogenic model for electron-hole bound states, the authors compute exciton binding energies in WS$_2$ and find close agreement with experimental data, outperforming conventional 3D/2D Coulomb-based predictions. The work forges a cross-disciplinary link between brane-world physics and condensed-matter excitonics and points to extensions involving finite-size or dynamic branes for more complex 2D materials.

Abstract

In the present work, we introduce a new interpretation of exciton binding energies in two-dimensional (2D) materials using concepts from brane physics. We adapt the Dvali-Gabadadze-Porrati-Shifman mechanism to a (2+1)-dimensional brane in a (3+1)-D spacetime, deriving an effective electromagnetic potential on the brane. Using this potential, we develop a hydrogenic model for exciton binding energies in 2D materials, applying it to s-type excitons and comparing theoretical predictions with experimental results on WS$_{2}$ monolayers. This interdisciplinary approach bridges high-energy and condensed matter physics, offering a new didactic representation of excitons in low-dimensional systems.

Exciton Binding Energies in 2D Materials: Insights from Braneworld Physics

TL;DR

The paper addresses exciton binding energies in 2D materials where the standard Coulomb potential fails due to screening. It adapts the Dvali-Gabadadze-Porrati-Shifman (DGPS) mechanism to a (2+1)-D brane in a (3+1)-D spacetime, deriving an effective on-brane potential that matches the Rytova-Keldysh form . Using a two-step variational hydrogenic model for electron-hole bound states, the authors compute exciton binding energies in WS and find close agreement with experimental data, outperforming conventional 3D/2D Coulomb-based predictions. The work forges a cross-disciplinary link between brane-world physics and condensed-matter excitonics and points to extensions involving finite-size or dynamic branes for more complex 2D materials.

Abstract

In the present work, we introduce a new interpretation of exciton binding energies in two-dimensional (2D) materials using concepts from brane physics. We adapt the Dvali-Gabadadze-Porrati-Shifman mechanism to a (2+1)-dimensional brane in a (3+1)-D spacetime, deriving an effective electromagnetic potential on the brane. Using this potential, we develop a hydrogenic model for exciton binding energies in 2D materials, applying it to s-type excitons and comparing theoretical predictions with experimental results on WS monolayers. This interdisciplinary approach bridges high-energy and condensed matter physics, offering a new didactic representation of excitons in low-dimensional systems.

Paper Structure

This paper contains 14 sections, 37 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. DGPS mechanism for a (4+1)-D space-time
  3. DGPS mechanism for a 2-brane in a (3+1)-D space-time
  4. Derivation of the effective potential on the 2-brane from a scalar field
  5. Definition of the action and Green's function formulation
  6. Derivation of the potential
  7. Limiting case: $r>>r_0$
  8. Limiting case: $r<<r_0$
  9. Application to excitons of 2D materials
  10. Hydrogenic model for excitons through variational principle
  11. Application: Excitons of a WS$_{2}$ monolayer
  12. Conclusion
  13. Green's function in momentum space
  14. Energy levels of an hydrogen atom on a 2-brane

Figures (2)

  • Figure 1: Diagram of the one-loop correction to a gauge boson propagator. The wavy lines represent the bare propagator of the boson and the full lines composing the loop represent a fermion propagator.
  • Figure 2: Electron energy of an hydrogen atom (1s to 5s) in a 2-brane embedded in a (3+1)-D space-time using the Rytova-Keldysh potential obtained via the adapted DGPS mechanism, combined with a variational principle. The energies depends on the $r_0$ parameter which is defined in the main text after eq. (\ref{['eq:potential_electrostatic']}) as the ratio between coupling constants in the bulk and on the brane.