Their work reveals that an intrinsic mismatch between electron and hole Fermi surfaces stabilizes FFLO-like electron-hole pairing, driving spontaneous symmetry breaking within the exciton insulator. This symmetry breaking reconstructs how these states interact, allowing different regions of the Fermi surface to support either exciton insulating or superconducting correlations. The resulting superconducting state exhibits intrinsic nematicity, even without external influences like magnetic fields, and suggests that materials like monolayer 1T′-MoTe2 and NaAlSi could exhibit this phenomenon.

Electron-Hole Fermi Surface Mismatch Drives Symmetry Breaking

This finding challenges established theories assuming these electronic instabilities are mutually exclusive, offering a new pathway toward materials exhibiting both properties simultaneously. The stabilization of FFLO-like pairing actively reconstructs the pairing phase space for both exciton insulator and superconducting states. Different regions of the Fermi surface now complementarily support either exciton insulator or superconducting correlations, creating a natural coexistence rather than competition between the two orders.

The system doesn’t simply exhibit both states, but rather distributes them strategically across the electronic landscape. The work reveals that, without a perfect match between electron and hole bands, the conventional zero-momentum excitonic condensate becomes unstable, favoring this symmetry-breaking pairing mechanism.

The authors detail how, at charge neutrality, the system is dominated by the exciton insulator phase, characterized by a robust excitonic gap, while the superconducting gap and ordering wave vector vanish. However, as carrier density changes, the exciton insulator correlations are suppressed, allowing superconducting correlations to become isotropic. The ordering vector, a measure of the spatial modulation of the excitonic state, rapidly approaches the wavevector mismatch between the electron and hole Fermi surfaces.

This observation aligns with experimental findings in materials like monolayer 1T′-MoTe2 and NaAlSi, where spatially modulated electronic states and finite-momentum exciton condensation have been observed, indicating spontaneous breaking of translational symmetry. The researchers used a self-consistent microscopic many-body framework to model these interactions, focusing on low-energy regimes around the conduction and valence band extrema.

The valley separation vector was absorbed by folding the two band extrema onto a common momentum origin, as it does not affect the group velocity or the resulting gap equations. The interband Coulomb interaction drives excitonic electron-hole pairing, a process central to the observed phenomena. The study’s modeling shows that, without Fermi-surface mismatch, electrons and holes participate efficiently in excitonic pairing across the entire Fermi surface.

However, with the mismatch, the system favors the FFLO-like pairing, leading to the observed symmetry breaking and the complementary distribution of exciton insulator and superconducting correlations. This is visually represented in the paper’s schematic illustration, where purple dashed lines denote interband electron-hole exciton insulator pairings and blue dashed curves represent conventional zero-momentum superconducting pairing. The research suggests that candidate materials such as monolayer 1T′-MoTe2 and the square-net semimetal NaAlSi may provide promising platforms for observing this phenomenon, offering a pathway to explore and potentially harness this unique interplay between exciton insulation and superconductivity.

FFLO-Like Pairing Stabilizes Excitonic-Superconducting Coexistence

The conventional expectation of mutually exclusive excitonic insulating and superconducting states has been challenged by a theoretical framework revealing a pathway to their coexistence. This pairing, in turn, drives a spontaneous symmetry breaking within the exciton insulating state, fundamentally altering the interaction between these typically competing electronic orders. This reshaping of the electronic landscape isn’t simply an overlap of two distinct states, but a deliberate reorganization of pairing correlations across momentum space.

The study demonstrates that the identified Fermi surface mismatch allows for a complementary distribution of these correlations. exciton insulating pairings concentrate on specific portions of the Fermi surface, while superconducting Cooper pairings develop in the remaining regions. This spatial separation minimizes competition between the two orders, enabling a stable coexistence and lowering the overall energy of the electronic system. The resulting ground state simultaneously exhibits both finite-momentum excitonic pairings and superconducting Cooper pairings, a configuration previously considered improbable.

The emergence of this coexistence is directly linked to the development of a continuous transfer of pairing phase space from the particle-hole channel to the particle-particle channel. As the excitonic gap decreases, the superconducting gap grows, indicating a dynamic redistribution of electronic correlations. This contrasts sharply with previous models that predicted a mutually exclusive relationship between exciton insulation and superconductivity, often resulting in an abrupt suppression of the exciton insulating order with increasing carrier density.

Those earlier models assumed isotropic exciton pairing at zero center-of-mass momentum, leading to competition for the same low-energy electronic states. The current work, however, demonstrates that finite-momentum exciton pairing, driven by the Fermi surface mismatch, circumvents this limitation. The spontaneous symmetry breaking induced by the exciton insulating state also leads to an intriguing consequence: intrinsic nematic superconductivity.

The resulting electronic state exhibits an anisotropy in its properties, specifically a difference in the response along different crystallographic directions. This nematicity arises directly from the finite-momentum excitonic order, which self-organizes an anisotropic partitioning of momentum space to maximize electron-hole pairing. Unlike conventional charge-density wave-superconducting coexistence, where the ordering vector is dictated by nesting, this finite-momentum exciton order emerges spontaneously.

The emergent superconducting state remains a conventional zero-momentum pairing state. But its nematic character is intrinsically tied to the underlying finite-momentum excitonic density wave order and can be potentially tuned by external gating or doping. This offers a novel route toward spontaneous anisotropic electronic states in correlated quantum materials, moving beyond scenarios reliant on external symmetry-breaking fields.

These materials, with their specific band structures and potential for Fermi surface mismatch, could exhibit the predicted coexistence of exciton insulation and superconductivity, along with the associated nematicity. The work presented offers a unique mechanism by which competing many-body orders generate electronic nematicity, demonstrating a redistribution of pairing phase space that minimizes mutual competition and stabilizes a previously unexpected coexistence.

Excitonic Insulators and Superconductors: Competing Orders

This reshaping of the competition between these electronic instabilities relies on the emergence of finite-momentum electron-hole pairing, a phenomenon akin to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state observed in some superconductors. As the excitonic order develops finite center-of-mass momenta, the associated correlations become strongly anisotropic, concentrating along one axis of the Fermi surface while diminishing near the orthogonal direction. This selective concentration of excitonic correlations effectively creates “depaired” regions where electrons no longer participate in exciton formation, but instead become available for superconducting pairing.

This dynamic interplay is consistent with experimental observations in materials already known to exhibit both excitonic and superconducting characteristics. The emergence of finite-momentum excitonic pairing fundamentally alters the expected behavior of the system, enabling a continuous evolution of the exciton insulating and superconducting orders as the material is doped with additional charge carriers.

Specifically, as doping increases, the exciton insulating gap gradually diminishes and eventually disappears, leaving a purely superconducting state dominated by superconducting pairing. The regions of the Fermi surface not involved in excitonic pairing become prime locations for superconducting correlations to develop, resulting in a twofold anisotropy in superfluid transport, even when the underlying band structure is isotropic. Unlike conventional scenarios where electronic nematicity is induced by external factors like magnetic fields or inherent band anisotropy, this research suggests a spontaneous transition from an isotropic system to one with a preferred direction.

This direction is driven by the interplay between competing orders, indicating a potentially universal mechanism for intrinsic electronic nematicity in complex quantum materials. The theoretical framework presented offers a novel route toward understanding and potentially engineering materials with tailored anisotropic electronic properties.

Emergent Nematic Superconductivity from Spontaneous Anisotropy

The key to this coexistence lies in the way momentum space is partitioned. The model predicts that exciton insulating correlations and superconducting correlations occupy distinct momentum sectors, minimizing suppression between them. This arrangement isn’t merely about both phenomena occurring simultaneously, but about a specific spatial organization of their properties within the material’s electronic structure. The theoretical framework, detailed in a recent preprint, demonstrates that the conventional zero-momentum excitonic condensate is destabilized by the electron-hole band mismatch.

Instead, the system favors a spontaneous symmetry breaking, establishing finite-momentum electron-hole pairing. The authors write, describing the complementary distribution of these orders. The researchers further modeled the resulting nematic superconductivity by computing the superfluid density tensor, revealing a pronounced anisotropy in the coexistence regime.

Specifically, the calculations show that the superfluid density develops a C₂ symmetry, indicating a clear distinction between the x and y directions, despite an isotropic normal-state conduction-band structure. This anisotropy, they state, directly leads to a greater superfluid density along one axis than the other, confirming the emergence of intrinsic nematic superconductivity. The team’s analysis shows that this anisotropy is not a result of external forces, but arises spontaneously from the interplay between the exciton insulating and superconducting orders.

The team’s model considers a two-band system with conduction and valence bands, using a Hamiltonian that incorporates an effective attractive interaction in the s-wave channel for superconductivity originating exclusively from the conduction band. The researchers emphasize that the nematic superconducting response is directly linked to the underlying finite-excitonic density-wave order and can potentially be tuned through gating or doping.

This self-organization of momentum space is an important aspect of the observed nematicity, distinguishing it from other known mechanisms. The work suggests that this approach could be broadly applicable to engineering materials with tailored electronic properties and exploring new states of matter in correlated systems.

👉 More information
🗞 Excitonic-superconducting coexistence and emergent nematic superconductivity driven by spontaneous symmetry breaking
✍️ Fei Yang, Ruigang Li, Junwei Liu and Binghai Yan
🧠 DOI: http://link.aps.org/doi/10.1103/fnnn-n593

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