Excitonic order in quantum materials: fingerprints, platforms and opportunities

The exciton insulator (EI) is a unique many-body ground state of condensed, spontaneously formed excitons in equilibrium, distinct from conventional band or Mott insulators. The gist Excitonic insulators are a unique many-body ground state of condensed, spontaneously formed excitons in equilibrium, distinct from conventional band or Mott insulators.

Theoretical Foundations

The exciton insulator is characterized by the spontaneous formation of electron-hole pairs (excitons) which drives an insulating state through many-body electron-hole correlations rather than single-particle band structures or on-site Coulomb repulsion The insulating behavior in EIs emerges purely from many-body electron-hole correlations, forming a macroscopically coherent superfluid condensate characterized by charge neutral excitons This ordered state is characterized by an order parameter with collective amplitude and phase excitations, placing EIs alongside superconductors and density-wave systems in the framework of macroscopic quantum-coherent phenomena The study of EIs intersects multiple fields, offering a unique platform for probing spontaneous symmetry breaking, phase-transition phenomena and strong electron-hole correlations in materials

Excitonic Order Framework

The excitonic order is viewed from two limits: BCS-like, where electron-hole pairing is a Fermi-surface instability in the semimetallic regime, and BEC-like, where pre-formed tightly bound excitons undergo condensation In the semimetallic BCS regime, Coulomb interactions are screened by finite charge density, yielding loosely bound excitons that emerge only at Tc so pairing and coherence occur simultaneously In the semiconducting BEC regime, weaker screening allows excitons to exist without long-range phase-coherence as well-defined bosonic quasiparticles within the energy gap below the particle-hole continuum at T∗ > T > Tc The transition between these limits is known as the BEC-BCS crossover, controlled by interaction strength or band gap Strong coupling regimes are described by models like the extended Falicov-Kimball model (EFKM) and the two-band Hubbard model (2BHM) The 2BHM allows for consideration of spinful excitonic condensates, with a distinction between spin singlet and triplet order parameters

Experimental Fingerprints

Establishing the EI phase experimentally relies on identifying measurable fingerprints such as band reconstruction, VB flattening, and in-gap flat bands In indirect-gap systems, exciton order breaks translational symmetry producing a structural reconstruction which multiplies the original unit cell For direct-gap EIs, the VB top can exhibit pronounced flattening and shift toward higher binding energies as the temperature decreases and the excitonic gap opens Collective modes are classified as gapped (Higgs) amplitude modes and gapless (Nambu-Goldstone or Anderson–Bogoliubov) modes associated with fluctuations of the order parameter These can be probed using Raman spectroscopy for amplitude modes and THz response for phase modes

Material Platforms

Several material platforms have been identified, including layered chalcogenides and rare-earth systems Bulk 1T-TiSe2 is a prototypical candidate for a cooperative EI where electronic and lattice instabilities are strongly coupled, exhibiting band reconstruction via backfolding of bands Ta2NiSe5 provides a complementary example as a direct-gap system, showing pronounced flattening of the topmost valence band Monolayer 1T-TiSe2 exhibits temperature-dependent backfolded electronic bands in the CDW state via high-resolution ARPES

Challenges and Opportunities

The main outstanding challenges lie in the active control and engineering of excitonic condensates, requiring ultrafast, quantum-coherent schemes to manipulate order and collective modes Future opportunities include devices exploiting macroscopic quantum coherence, such as excitonic Josephson-like devices Artificial bilayers and photoinduced condensates extend excitonic physics into regimes inaccessible in equilibrium, raising prospects for exciton-mediated superconductivity and tunable spin-coherent phases Continued progress in material synthesis, disorder control, and nanoscale engineering will be essential for realizing robust, electrically addressable excitonic architectures The field is positioned for transformative developments through dimensional engineering, moiré superlattices and topology-protected platforms

Key Experimental Signatures Summary

Table 1 summarizes experimental fingerprints such as Gap opening, Backfolding Bandfolded band replicas at high symmetry points of the BZ, VB flattening Flattening of the VB top and shift towards higher binding energies, In-gap flat bands Emergent flat sharp states inside the gap, Persistence of excitonic features above Tc Ultrafast electronic collapse Amplitude (Higgs) mode Fast loss of backfolded weight after pump (10–100 fs), Phase mode Collective excitation associated with phase fluctuations φ of the excitonic order parameter, CDW without PLD Electronic CDW order in indirect-gap materials with no associated structural PLD, Gap closes under chemical/electrostatic doping or gating, Melting the excitonic order by pressure-induced CDW collapse, Drude and Hall carrier collapse Phase-transition temperature is suppressed upon pressure application melting the excitonic order

Device Applications

Exciton-based transistors can be realized through interlayer exciton(IX)- based field effect transistors (FET) where charge separation increases the lifetime of the exciton The prediction of an excitonic Josephson effect involves the formation of a Josephson-like tunnelling current between two spatially separated electron/hole layers Quantum information platforms can utilize Josephson-like interlayer tunnelling to enable qubit implementations based on controlled phase differences or collective excitations of the condensate

Future Directions

Ultrafast spectroscopy is key to distinguish excitonic contributions from lattice ones, revealing coherent, micrometer-scale propagation of collective modes Ultrafast control and coherent dynamics are essential for manipulating the order parameter via tailored multi-pulse fields Novel material synthesis focuses on moiré superlattices to enhance exciton binding energies and stabilize condensates at higher temperatures The search for spin-triplet EIs in 2D ferromagnets like Ta3X8 points toward electrically tunable spin-coherent quantum devices

The paper concludes that combining evidence across different material families provides a unified framework for interpreting many-body electron–hole correlations in materials Continued progress in material synthesis, disorder control, and nanoscale engineering will be essential for realizing robust, electrically addressable excitonic architectures that harness macroscopic coherence as a resource for next-generation quantum and optoelectronic technologies.

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The paper is about the study of exciton insulators (EIs), which are unique many-body ground states where electron–hole pairing drives an insulating behavior distinct from conventional band or Mott insulators. The gist Excitonic insulators are a unique many-body ground state of condensed, spontaneously formed excitons in equilibrium, distinct from conventional band or Mott insulators.

1. A model capable of predicting phase diagrams in strongly correlated electron systems can be improved by incorporating the two-band Hubbard model with spinful electrons to characterize phases such as the band insulator (corresponding to a saturated spin-polarized state), excitonic insulator (the XY magnetic order), and staggered orbital order (Néel antiferromagnet along z axis) [Box 1].

2. An AI system can be enhanced to perform tr-ARPES analysis by utilizing the quantitative distinction it provides between phases, allowing it to differentiate "the order melting times of structural CDWs (slow atomic lattice timescale, ∼ 60–300 fs) and electronic phases (< 100 fs)" [Section 2.6].

3. An improved system can use time-resolved optical reflectivity measurements to analyze the dynamics of excitonic systems, specifically identifying coherent excitonic–phononic oscillations and predicting the behavior of a pump pulse based on its BEC or BCS nature [Section 2.2.2].

4. A machine learning model can be trained on transport data to identify signatures of charge-neutral pairing by correlating a collapsing Drude weight in optical conductivity coupled with a drop in Hall carrier density with the formation of an excitonic gap [Section 2.5.1].

5. An AI system can be developed to distinguish between competing phases by utilizing STM provides highly complementary local information, capable of measuring the spatial dependence of order parameters, specifically identifying the Kondo insulator by the magnetic field dependence of its band gap versus the excitonic quasiparticle gap [Section 2.6].

6. A predictive model can be built to forecast material stability under external stimuli by using pressure-induced melting of the ordered phase as a fingerprint, which occurs when pressure pushes the Fermi level deeper into both bands and increasing Coulomb screening [Section 2.4.2].

7. An AI system can simulate the effect of dimensional reduction on excitonic binding energies, predicting that reduced dimensionality leads to weaker screening and larger excitonic binding energies, increasing from tens of meV in three-dimensional materials, to hundreds of meV in two-dimensional layers [Section 1.4].

8. A system can be engineered for artificial platforms by using moiré superlattices in twisted vdW heterostructure to predict enhanced exciton binding and stabilization due to reduced dielectric screening and flat-band formation [Section 3.3.2].

9. An AI system can analyze experimental data from time-resolved ARPES to confirm the scenario where photoexcitation can induce an excitonic gap simultaneously both in the electron and hole bands - signature of a transient exciton condensate [Section 3.3.3].

The exciton insulator (EI) is a unique many-body ground state of condensed, spontaneously formed excitons (electron-hole pairs) in equilibrium, distinct from conventional band or Mott insulators. Originally proposed over half a century ago, the concept has recently gained renewed experimental traction thanks to advances in spectroscopic resolution, ultrafast probes, and materials synthesis. In this Review, we outline the essential theoretical ingredients underpinning excitonic order and discuss how dimensionality, disorder and screening affect stability. We then examine the diverse experimental fingerprints of the excitonic state, with central focus on strategies to disentangle excitonic order from competing phases such as charge density waves, Mott insulating states, and hybridization-driven insulators, particularly in systems where non-trivial band topology plays a role. We survey the rapidly expanding family of candidate materials, from layered chalcogenides and correlated rare-earth compounds to artificial excitonic platforms and optically driven non-equilibrium condensates. Finally, we discuss the key challenges and emerging opportunities in the field, identifying the theoretical and experimental frontiers that promise to shape the next decade of research.