Dirac Exciton-Polaritons

• Dirac exciton-polaritons are hybrid quasiparticles formed by strong exciton-photon coupling in engineered photonic environments, exhibiting linear Dirac-like dispersion and topological features.
• They are realized in semiconductor microcavities, metasurfaces, and organic lattices, where experiments reveal Dirac cones, flatbands, and non-Hermitian trapping effects.
• Driven-dissipative dynamics introduce complex potentials that confine polaritons and enable controlled condensation, bypassing phenomena like the Klein paradox.

Dirac exciton-polaritons are hybrid quasiparticles displaying effective Dirac-like dispersion originating from the strong coupling of excitons and photons in structured photonic environments. These systems, realized in planar microcavities, patterned metasurfaces, and photonic lattices, show linear energy-momentum relations and topological features analogous to electrons in graphene, but in a bosonic, nonequilibrium, and oftentimes non-Hermitian context. The Dirac character manifests through band crossings at discrete points in the Brillouin zone (“Dirac cones”), accompanied by high group velocity, Berry-phase physics, and exotic quantum condensate phenomena, especially under nonresonant optical excitation.

1. Theoretical Foundations of Dirac Exciton-Polaritons

The essential theoretical structure underpinning Dirac exciton-polaritons is the emergence of effective Dirac Hamiltonians—typically 2×2 or 4×4 matrix operators acting in either sublattice or mode space—arising from band-inversion and symmetry properties of the underlying photonic lattice or metasurface. For a honeycomb or triangular lattice, the single-particle Hamiltonian for the fundamental s-band or for multi-orbital (p-band) sectors generically yields a dispersion

$$E_\pm(\mathbf{k}) = E_D \pm \hbar v_D |\mathbf{q}|,$$

where $\mathbf{q} = \mathbf{k} - \mathbf{K}$ is the momentum relative to the Dirac point $\mathbf{K}$, and $v_D$ is the Dirac group velocity (Kim et al., 2012, Jacqmin et al., 2013, Betzold et al., 18 Jan 2024).

In metasurfaces and photonic crystal gratings, periodic modulation or Bragg scattering folds waveguide dispersion into a reduced zone, generating near-linear (Dirac) crossings at the $\Gamma$ or $K/K'$ points. Incorporating exciton–photon coupling (Rabi splitting $\hbar\Omega_R$), the full system is modeled by coupled-oscillator or generalized Gross-Pitaevskii equations, where the linear Dirac kinetic term is supplemented by complex-valued effective potentials and interparticle interactions (Sigurðsson et al., 2023, Masharin et al., 10 Dec 2025).

Driven–dissipative (i.e., non-Hermitian) extensions become central: gain/loss, reservoir-induced blueshift, and self-consistent feedback modulate the Dirac spectrum and enable phenomena—such as bound-state quantization—that are forbidden in the purely Hermitian (conservative) case (Masharin et al., 10 Dec 2025).

2. Experimental Realizations and Observations

Dirac exciton-polaritons have been demonstrated in several distinct experimental platforms:

• Semiconductor Microcavity Lattices and Pillar Arrays: Lithographically defined honeycomb lattices of GaAs/AlGaAs micropillars, where strong overlap yields sub-meV tunneling (first-neighbor $t\sim0.25$ meV, second-neighbor $t'\ll t$) and photonic bands with Dirac cones and flatbands (Jacqmin et al., 2013).
• Triangular Lattice Surface Microcavities: GaAs/AlGaAs DBR-backed systems patterned with periodic local blueshifts, giving rise to massless Dirac bands with group velocities $v_D\sim(1-2)\times10^8$ cm/s (Kim et al., 2012).
• Organic-Lattice “Polaritonic Graphene”: Honeycomb microcavity arrays incorporating mCherry protein, combining $t_1=2.38$ meV nearest-neighbor hopping, $a=2.00\,\mu$m lattice constant, Rabi splitting $\Omega_R=318$ meV, and exceptionally high Q-factors. Dirac cones are observed at room temperature, alongside flatbands and polariton lasing (Betzold et al., 18 Jan 2024).
• Perovskite Metasurfaces: One-dimensional methylammonium lead bromide (MAPbBr₃) gratings on SiO₂ with a period $\Lambda=320$ nm and relief depth 20 nm. These structures couple TE waveguide modes into Dirac-like dispersions evidenced by angle-resolved photoluminescence, with a measured Rabi splitting $\hbar\Omega_R\simeq38$ meV and polariton linewidth $\Gamma_p\simeq0.35$ meV (Masharin et al., 10 Dec 2025).

These platforms support direct momentum- and energy-resolved mapping of polariton dispersion, real-space imaging of condensate modes, measurement of threshold behavior, and quantification of group velocities and lifetimes.

3. Driven-Dissipative Condensation and Non-Hermitian Effects

Polariton condensation is typically induced via nonresonant optical pumping, producing a reservoir of high-energy carriers and localized exciton population, $N(x)$. The interplay between repulsive blueshift ($U_r(x) = \alpha N(x)$) and bosonic gain ($\Gamma_g(x) = \beta N(x)$) generates an effective non-Hermitian potential,

$U(x) + i\Gamma(x) = (\alpha + i\beta) N(x),$

enabling spatial trapping and size quantization of Dirac polaritons within optically defined “wells” (Masharin et al., 10 Dec 2025).

The eigenvalue problem then takes the form

$[\hat H_D + U(x)\mathbb{1}] \Psi(x) = E\Psi(x),$

where $\hat H_D$ is the driven-dissipative Dirac Hamiltonian (including group velocity $\hbar v_g$, complex energy $\Omega_p = E_0 - i\Gamma_p$, and complex coupling $V = V_r + iV_i$ in a grating geometry) (Masharin et al., 10 Dec 2025). For broad enough pump spots (9–17 μm FWHM), up to four quantized bound modes can be simultaneously occupied above threshold ($P_{th}\simeq1.27$ mJ/cm$^2$).

A defining consequence of non-Hermiticity is the circumvention of the Klein paradox. In conservative Dirac systems, true confinement is impossible outside a real gap due to perfect Klein tunneling. Here, local gain and loss engineer complex momentum boundary conditions, allowing Im $q_o>0$ so that polariton wavefunctions become spatially bound—enabling both below- and above-crossing quantized states (Masharin et al., 10 Dec 2025).

4. Band Structure Engineering: Flatbands, Negative Mass, and Topology

The precise band structure of Dirac exciton-polaritons is tunable over a wide parameter range:

• Dirac Points and Cones: Observed at the $K$ and $K'$ corners in honeycomb and triangular lattices and at the $\Gamma$-point in patterned metasurfaces. The Fermi (Dirac) velocity can be engineered via geometry, hopping amplitude, cavity–exciton detuning, and photon fraction (Kim et al., 2012, Jacqmin et al., 2013, Betzold et al., 18 Jan 2024).
• Flatbands: p-orbital bands in honeycomb lattices produce nearly nondispersive flatbands, visible in both energy-resolved PL and real-space localization measurements. These are characterized by strongly frustrated hopping and intensity patterns localized on lattice links or interstitials (Jacqmin et al., 2013, Betzold et al., 18 Jan 2024).
• Negative Mass and Trapping: Pump-induced optical potentials in grating or lattice contexts can localize polaritons with negative effective mass (upper branch), facilitating condensation in states with $\pi$-phase-shifted spatial profiles (Sigurðsson et al., 2023).
• Topological Band Physics: Synthetic gauge fields, symmetry breaking, or complex-valued hopping terms can introduce nontrivial Chern numbers and Berry curvature to the bands—predicted to yield unidirectional edge states and quantized Hall effects in bosonic polariton systems (Kim et al., 2012).

5. Condensate Dynamics, Superfluidity, and Collective Effects

The Gross–Pitaevskii framework generalized for Dirac dispersions incorporates both condensate wavefunction dynamics and reservoir feedback:

$$i\hbar \partial_t \psi = [\hat H_D(-i\hbar\partial_x) + g|\psi|^2 + g_R(n_R + \eta P/\Gamma_R) + i(R n_R/2)]\psi,$$

where $g$ and $g_R$ are interaction constants (exciton-exciton, polariton-reservoir), and $R$ is the stimulated scattering rate (Sigurðsson et al., 2023).

Characteristic dynamical phenomena include:

• Coherence and Superfluidity: Above threshold, linewidth collapse and extended $g^{(1)}(x,x')$ coherence lengths ($>10\,\mu$m) are observed, with pump-dependent blue-shift signaling phase-space filling. The critical velocity for superflow is governed by $v_c\approx v_D$ near the Dirac point (Garnier et al., 2012, Betzold et al., 18 Jan 2024).
• High-Orbital (p) Condensation: Macroscopic occupation of $p_{x}\pm ip_{y}$ states at Dirac points, with measured angular momentum $L_z=\pm\hbar$. The order parameter near each Dirac cone follows a two-component spinor encoding a $\pi$ Berry phase (Kim et al., 2012).
• Zitterbewegung-like Limit Cycles: Conditions near the trapped/ballistic boundary allow coherent superpositions of lower and upper branches, leading to oscillatory (zitterbewegung) center-of-mass motion stabilized by gain–loss balance (Sigurðsson et al., 2023).

6. Measurement Modalities: Near-Field vs Far-Field, Spectroscopy, and Imaging

The detection of Dirac polariton features relies on fine control and analysis of both real-space and momentum-space signals:

• Near-Field Probes: Quantum state tomography and near-field imaging resolve intensity distributions within the physical lattice, sensitive primarily to the bare polariton population (Jacqmin et al., 2013, Sigurðsson et al., 2023).
• Far-Field (Emitted) Patterns: Far-field measurements probe out-coupled radiation, intimately connected to phase relationships between guided modes. For certain symmetry-protected states (e.g., BICs), far-field emission at $k=0$ may vanish, while the near-field remains finite (Sigurðsson et al., 2023).
• Energy- and Momentum-Resolved Spectroscopy: Angle-resolved PL and Fourier-plane imaging map full $E(\mathbf{k})$ dispersions, extracting band structure, Dirac velocities, and quantization ladders (Kim et al., 2012, Jacqmin et al., 2013, Betzold et al., 18 Jan 2024, Masharin et al., 10 Dec 2025).

Table: Representative Experimental Parameters for Dirac Exciton-Polaritons

Platform	Lattice Const. (µm)	Rabi Splitting (meV)	Dirac Velocity (m/s)
GaAs honeycomb (Jacqmin et al., 2013)	2.4	15	$1.3\times10^{6}$
Triangular GaAs (Kim et al., 2012)	2.0	13.8	$(1-2)\times10^{8}$
Organic honeycomb (Betzold et al., 18 Jan 2024)	2.0	318	$3.9\times10^6$ (exp)
MAPbBr₃ metasurface (Masharin et al., 10 Dec 2025)	0.32	38	Determined by device

7. Outlook and Implications

Dirac exciton-polariton systems provide a versatile platform for studying relativistic band physics, bosonic condensation, and non-Hermitian quantum effects in solid state. The ability to engineer linear dispersions, flatbands with geometric frustration, and complex potentials opens research avenues in superfluidity, topological photonics, and polaritonic device integration.

The demonstration of non-Hermitian trapping and quantization in fundamentally gapless Dirac systems, including the explicit breakdown of the Klein paradox by local gain and repulsion (Masharin et al., 10 Dec 2025), highlights the impact of driven-dissipative physics and positions these systems as optimal testbeds for exploring many-body, topological, and nonequilibrium quantum phenomena. The extension to room-temperature operation using organic active layers (Betzold et al., 18 Jan 2024) further expands technological relevance and experimental flexibility.

Future research will likely focus on the synthesis of chiral edge modes, measurement of Berry curvature and topological invariants, and the realization of strongly correlated states through flatband condensation and enhanced interactions.