Excitonic condensates, bound states of electrons and holes, hold promise for applications in quantum computing and other technologies due to their unique transport properties and potential for hosting exotic particles. Early theoretical work focused on bulk semi-metallic crystals, but these were hampered by thermodynamic instability. Spatial separation of electrons and holes in quantum wells was proposed as a solution, but weak electron-hole interaction and surface roughness limited success. Two-dimensional (2D) materials offered renewed hope due to reduced screening, but challenges remained, including Peierls instability in single-layer systems and the need for voltage doping in bilayer systems, leading to non-equilibrium conditions. This work addresses these limitations by investigating 2D van der Waals heterostructures as a platform for realizing a stable, equilibrium excitonic condensate.

Previous research on excitonic condensation explored various approaches, including bulk semi-metallic crystals, where the overlap of valence and conduction bands under pressure could lead to spontaneous exciton formation. However, challenges included thermodynamic instability. Quantum wells provided spatial separation of electrons and holes but suffered from weak electron-hole interaction and surface roughness. 2D materials offered advantages like reduced screening, with bilayer graphene being extensively studied, although experimental results remained inconclusive. Other 2D hetero-bilayers showed potential but required applied voltages for doping, creating non-equilibrium systems and hindering observation of zero-bias Josephson effects. The layered semimetal 1T-TiSe₂ was suggested as a candidate, but its phonon instability raised concerns. This paper builds upon these previous efforts, aiming to overcome the limitations of previous approaches by identifying suitable 2D van der Waals heterostructures.

The authors employed a multi-step methodology. First, a model Hamiltonian analysis was performed to estimate optimal effective mass and carrier density for excitonic condensation in 2D bilayer heterostructures. The binding energies of interlayer excitons were calculated as a function of reduced mass and carrier density using the random phase approximation (RPA) for the screened potential. A phase diagram was constructed to identify optimal conditions for realizing excitonic condensation (BKT/BCS phases), considering factors such as carrier mass, density and critical temperature. Next, a comprehensive search of a 2D material database was conducted to identify candidate materials pairs with a lattice mismatch less than 2% and individual layer band gaps greater than 0.3 eV. Band gap calculations were performed for 23 heterostructures with broken and staggered band alignments. Three promising hetero-bilayers (Sb₂Te₂Se/BiTeCl, Hf₂N₂I₂/Zr₂N₂Cl₂, and LiAlTe₂/BiTeI) were selected based on calculated band overlaps. First-principles density functional theory (DFT) calculations were then used to determine the band structures, phonon spectra, and electron-phonon coupling coefficients for these selected heterostructures. The calculations aimed to investigate the stability of the structures and to verify the absence of phonon-driven instabilities like the Peierls instability observed in 1T-TiSe₂. Finally, effective masses and carrier densities were extracted from the DFT band structures to estimate critical temperatures for excitonic condensation, using the model Hamiltonian results and BCS mean field gap equation calculations.

The model Hamiltonian analysis revealed that favorable conditions for strong interactions and a strongly coupled regime exist at carrier masses around 0.5 *mₑ* and densities around 10¹¹ cm⁻². The calculated phase diagram indicated that optimal carrier densities for excitonic condensation are in the range of 10¹⁰–5 × 10¹² cm⁻². The search of the 2D material database and subsequent DFT calculations identified three promising hetero-bilayers: Sb₂Te₂Se/BiTeCl, Hf₂N₂I₂/Zr₂N₂Cl₂, and LiAlTe₂/BiTeI. These heterostructures exhibit broken type-III band alignments and have calculated band overlaps that fall within the optimal range for excitonic condensation. The DFT calculations confirmed the absence of detrimental Peierls instability in Hf₂N₂I₂/Zr₂N₂Cl₂, unlike the case of 1T-TiSe₂. The estimated critical temperatures for excitonic condensation in these heterostructures are on the order of tens of Kelvin. While the exact value of critical temperature depends on method-dependent spread of *n* values from different functionals, the feasibility of excitonic condensation is unaffected. External factors like strain and electric fields can be used to fine-tune carrier density and critical temperature. Hf₂N₂I₂/Zr₂N₂Cl₂ shows the highest estimated critical temperature of approximately 31 K.

The findings of this study demonstrate that 2D van der Waals heterostructures, specifically the identified hetero-bilayers, can serve as a platform for realizing a stable, equilibrium excitonic condensate. The absence of voltage doping, the lattice-matching, and the lack of detrimental electronic instabilities are key advantages compared to previous approaches. The ability to access different regions of the electron-hole phase diagram, including the BEC-BCS crossover, through external tuning offers exciting opportunities for investigating fundamental physics and exploring potential applications. The predicted superfluid transport properties, such as enhanced Josephson-like tunneling and dissipation-less charge counterflow, could have significant implications for future electronic devices. The potential for spintronics applications is also highlighted due to the excitons' spin degree of freedom and the possibility of excitonic ferromagnetism.

This research presents a compelling case for utilizing 2D van der Waals heterostructures as a platform for realizing equilibrium excitonic superfluidity. The identified materials offer significant advantages over previously explored systems, overcoming limitations associated with instability and the need for external voltage doping. The predicted superfluid transport properties and potential for spintronics applications highlight the significant promise of this approach for advancing quantum technologies. Further research could focus on experimental synthesis and characterization of these heterostructures, exploring the detailed properties of the excitonic condensate and investigating the potential for device applications.

The study relies on theoretical calculations and simulations, and experimental verification is necessary to confirm the predicted behavior. The estimation of critical temperatures involves approximations within the model Hamiltonian and BCS mean-field approaches; more sophisticated techniques could provide higher accuracy. While the study considers the absence of Peierls instability in the chosen heterostructures, other potential instabilities could exist. The impact of defects and disorder on the stability and properties of the excitonic condensate is not explicitly addressed.