Electron-Photon Chern Number in Cavity-Embedded 2D Moir\'e Materials

Electron-Photon Chern Number in Cavity-Embedded 2D Moiré Materials

Danh-Phuong Nguyen, Geva Arwas, Zuzhang Lin, Wang Yao, and Cristiano Ciuti

Phys. Rev. Lett. 131, 176602 – Published 25 October 2023

Abstract

We explore theoretically how the topological properties of 2D materials can be manipulated by cavity quantum electromagnetic fields for both resonant and off-resonant electron-photon coupling, with a focus on van der Waals moiré superlattices. We investigate an electron-photon topological Chern number for the cavity-dressed energy minibands that is well defined for any degree of hybridization and entanglement of the electron and photon states. While an off-resonant cavity mode can renormalize electronic topological phases that exist without cavity coupling, we show that when the cavity mode is resonant to electronic miniband transitions, new and higher electron-photon Chern numbers can emerge.

Received 28 March 2023
Revised 11 September 2023
Accepted 25 September 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.176602

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Quantum description of light-matter interaction Topological phase transition

Quantum cavities Topological materials Twisted heterostructures

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Danh-Phuong Nguyen ¹, Geva Arwas¹, Zuzhang Lin ^2,3, Wang Yao^2,3, and Cristiano Ciuti ¹

¹Université Paris Cité, CNRS, Matériaux et Phénomènes Quantiques, 75013 Paris, France
²Department of Physics, The University of Hong Kong, Hong Kong, China
³HKU-UCAS Joint Institute of Theoretical and Computational Physics at Hong Kong, China

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Vol. 131, Iss. 17 — 27 October 2023

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Figure 1
Top: sketch of a twisted bilayer system with its moiré pattern inside the gap region of a split-ring resonator. Bottom: on the left, the first Brillouin zone with Dirac points of the bottom layer and corresponding wave vectors; on the right, the Brillouin zones of both the bottom and rotated top layer together with the moiré mini Brillouin zone (shown in red) for the corresponding moiré superlattice.
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Figure 2
Electron-photon Chern numbers of the first three (top) and two (bottom) moiré minibands of the twisted TMD bilayer system ( ${MoTe}_{2}$ parameters). The dashed lines depict the phase boundary predicted by an effective electronic Hamiltonian obtained by adiabatically eliminating the photonic degrees of freedom [21] and calculating the electron Chern number. Top: Chern numbers versus the twisting angle $θ$ and the dimensionless cavity coupling $g$ (see definition in the text), with no interlayer bias ( $V_{z} = 0$ ). Bottom: Chern numbers versus $V_{z}$ and the dimensionless cavity coupling $g$ for a fixed angle $θ = 1.2 °$ . Parameters: cavity photon energy $ℏ ω_{c} = 20 meV$ (top) and 6 meV (bottom), cavity mode polarization vector $u = (1, 0, 0)$ .
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Figure 3
Electron-photon energy-momentum dispersions $E_{n k}^{(e - p)}$ for $g = 0.0$ (left) and 0.05 (right) for a ribbon geometry (periodic boundary conditions along the long direction). Parameters: cavity photon energy $ℏ ω_{c} = 6 meV$ , $V_{z} = 0.5 meV$ , $θ = 1.2 °$ , ribbon width $D_{1} / a_{M} = 10$ , and cavity mode polarization vector $u = (1, 0, 0)$ . Here, the photonic component of the electron-photon eigenstates is small (see text).
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Figure 4
Electron-photon Chern numbers of the first four moiré minibands for the considered cavity-embedded twisted TMD bilayer system. Note that this topological diagram cannot be predicted by the effective electronic model used in Fig. 2. Other parameters: cavity photon energy $ℏ ω_{c} = 10 meV$ , $V_{z} = 0 meV$ , and cavity mode polarization $u = (0, 0, 1)$ .
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Figure 5
Top panels: electron-photon miniband dispersions $E_{n k}^{(e - p)}$ for $g_{⊥} = 0$ (left panel) and 0.35 (right panel), where three edge states emerge (thicker red lines). Bottom panels: electronic purity (left panel) and electronic spectral function (right panel, normalized by its maximum value) for $g_{⊥} = 0.35$ . We have considered a ribbon geometry with width $D_{1} / a_{M} = 10$ and periodic boundary conditions along the long direction. Other parameters: cavity photon energy $ℏ ω_{c} = 10 meV$ , $V_{z} = 0 meV$ , $θ = 1.8 °$ , cavity mode polarization $u = (0, 0, 1)$ .
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Physical Review Letters

Electron-Photon Chern Number in Cavity-Embedded 2D Moiré Materials

Danh-Phuong Nguyen, Geva Arwas, Zuzhang Lin, Wang Yao, and Cristiano Ciuti

Phys. Rev. Lett. 131, 176602 – Published 25 October 2023

Abstract

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