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arxiv: 2606.01785 · v1 · pith:I6PROVXCnew · submitted 2026-06-01 · ❄️ cond-mat.supr-con · cond-mat.mtrl-sci· cond-mat.str-el

Excitonic-Superconducting Coexistence and Emergent Nematic Superconductivity Driven by Spontaneous Symmetry Breaking

Fei Yang , Ruigang Li , Junwei Liu , Binghai Yan This is my paper

Pith reviewed 2026-06-28 12:28 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el
keywords excitonic insulatorsuperconductivitynematic superconductivityFermi surface mismatchspontaneous symmetry breakingelectron-hole pairingorder coexistence
0
0 comments X

The pith

An intrinsic mismatch between electron and hole Fermi surfaces enables coexistence of excitonic insulating and superconducting orders and drives spontaneous nematic superconductivity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how excitonic insulating and superconducting orders, usually seen as mutually exclusive, can actually coexist in systems with mismatched electron and hole Fermi surfaces. A self-consistent theory shows that this mismatch stabilizes a special type of electron-hole pairing and causes the excitonic state to break symmetry spontaneously. As a result, different parts of the Fermi surface support one order or the other, allowing both to exist together. The superconductivity that emerges then breaks rotational symmetry on its own, creating nematic superconductivity without needing external fields like magnetic fields or spin-orbit coupling. This mechanism could explain observations in materials such as monolayer 1T'-MoTe2 and NaAlSi.

Core claim

An intrinsic mismatch between electron and hole Fermi surfaces fundamentally reshapes the competition between excitonic insulating and superconducting orders by stabilizing FFLO-like electron-hole pairing and driving spontaneous symmetry breaking of the EI state. The resulting symmetry breaking reconstructs the pairing phase space such that different regions of the Fermi surface complementarily support either EI or SC correlations, leading to their natural coexistence. The emergent SC state breaks rotational symmetry and develops intrinsic nematic superconductivity even without explicit symmetry-breaking fields.

What carries the argument

The intrinsic mismatch between electron and hole Fermi surfaces, which stabilizes FFLO-like electron-hole pairing and drives spontaneous symmetry breaking of the EI state to reconstruct pairing phase space.

If this is right

  • EI and SC orders coexist naturally because different Fermi surface regions complementarily support each order.
  • The emergent superconducting state spontaneously breaks rotational symmetry to become nematic.
  • This occurs even without magnetic fields, spin-orbit coupling, or bare band-structure anisotropy.
  • Monolayer 1T'-MoTe2 and the square-net semimetal NaAlSi are candidate platforms where the coexistence and nematicity should appear.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Competing orders may generate spontaneous electronic nematicity across a broader range of correlated quantum materials.
  • The same Fermi-surface mismatch mechanism could be searched for in other semimetals that host electron and hole pockets.
  • Device concepts that rely on anisotropic transport or pairing might exploit this intrinsic route to nematicity.

Load-bearing premise

The self-consistent microscopic theory accurately captures the effects of the intrinsic Fermi surface mismatch on the competition between EI and SC orders without additional explicit symmetry-breaking terms.

What would settle it

Observation of rotational symmetry breaking in the superconducting state of monolayer 1T'-MoTe2 or NaAlSi in the complete absence of applied magnetic fields, spin-orbit coupling, or band anisotropy.

Figures

Figures reproduced from arXiv: 2606.01785 by Binghai Yan, Fei Yang, Junwei Liu, Ruigang Li.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Bare band structure showing the conduction and valence [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Carrier-density dependence of the EI gap, SC gap, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Superfluid-density tensor components [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Excitonic insulating (EI) and superconducting (SC) orders are generally regarded as mutually exclusive electronic instabilities. Within a self-consistent microscopic theory, we study electronic systems hosting an EI phase in the presence of SC pairing and show that an intrinsic mismatch between electron and hole Fermi surfaces fundamentally reshapes this competition. This mismatch stabilizes FFLO-like electron-hole pairing and drives spontaneous symmetry breaking of the EI state. The resulting symmetry breaking reconstructs the pairing phase space for SC and EI state, such that different regions of the Fermi surface complementarily support either EI or SC correlations, leading to a natural coexistence of the two orders. Notably, the emergent SC state consequently breaks rotational symmetry and develops intrinsic nematic superconductivity, even in the absence of explicit symmetry-breaking fields (such as magnetic fields, spin-orbit coupling, or bare band-structure anisotropy). Our results suggest that candidate materials such as monolayer 1T$'$-MoTe$_2$ and the square-net semimetal NaAlSi may provide promising platforms for observing this phenomenon. More broadly, these findings reveal a unique mechanism by which competing many-body orders generate electronic nematicity, suggesting a broader route toward spontaneous anisotropic electronic states in correlated quantum materials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript develops a self-consistent microscopic theory for systems hosting both excitonic insulating (EI) and superconducting (SC) orders. It claims that an intrinsic mismatch between electron and hole Fermi surfaces stabilizes FFLO-like electron-hole pairing, drives spontaneous symmetry breaking of the EI state, reconstructs the pairing phase space to allow natural coexistence of EI and SC on complementary Fermi-surface regions, and produces emergent nematic superconductivity without explicit symmetry-breaking fields. Candidate materials (monolayer 1T'-MoTe2, NaAlSi) are identified.

Significance. If the derivations are internally consistent and the Hamiltonian is shown to remain fully rotationally invariant, the work would identify a mechanism by which Fermi-surface mismatch alone generates spontaneous nematicity from competing orders, with direct relevance to semimetal platforms.

major comments (2)
  1. [Abstract; model construction] Abstract and model section: The central claim that nematic SC emerges 'even in the absence of explicit symmetry-breaking fields' requires explicit verification that the single-particle dispersions and interaction terms remain fully rotationally invariant while still producing unequal electron-hole Fermi surfaces. Any directional dependence in band parameters or cutoffs would constitute an implicit breaking term that seeds the observed anisotropy, undermining the spontaneous character of the symmetry breaking.
  2. [Abstract; results] Results on symmetry breaking and coexistence: The reconstruction of pairing phase space and the emergence of nematic SC are asserted to follow from the self-consistent solution, yet the abstract supplies no equations, order-parameter definitions, or numerical validation steps. Without these, it is impossible to confirm that the reported coexistence and nematic order are independent of fitted parameters or implicit anisotropies.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed reading and valuable feedback on our manuscript. We address each major comment below with clarifications on the model construction and results. We believe the central claims hold under a fully rotationally invariant setup, but we will incorporate explicit verifications where helpful.

read point-by-point responses

  1. Referee: [Abstract; model construction] Abstract and model section: The central claim that nematic SC emerges 'even in the absence of explicit symmetry-breaking fields' requires explicit verification that the single-particle dispersions and interaction terms remain fully rotationally invariant while still producing unequal electron-hole Fermi surfaces. Any directional dependence in band parameters or cutoffs would constitute an implicit breaking term that seeds the observed anisotropy, undermining the spontaneous character of the symmetry breaking.

    Authors: The model employs isotropic parabolic dispersions for electrons and holes with different effective masses (or chemical potentials) that produce a radial Fermi-surface mismatch while preserving full rotational invariance in both the kinetic term and the interaction Hamiltonian. No angular dependence is introduced in the band parameters, cutoffs, or coupling constants. The spontaneous symmetry breaking and nematic SC then arise purely from the self-consistent solution of the coupled EI-SC gap equations under this mismatch. We will add an explicit paragraph in the revised model section (and a footnote in the abstract) confirming the rotational invariance of all terms and noting that the mismatch is purely radial. revision: yes

  2. Referee: [Abstract; results] Results on symmetry breaking and coexistence: The reconstruction of pairing phase space and the emergence of nematic SC are asserted to follow from the self-consistent solution, yet the abstract supplies no equations, order-parameter definitions, or numerical validation steps. Without these, it is impossible to confirm that the reported coexistence and nematic order are independent of fitted parameters or implicit anisotropies.

    Authors: Abstracts are by design concise and omit technical details; the full manuscript (Sections II–IV) defines the order parameters (EI and SC gaps with FFLO modulation), presents the self-consistent equations, and shows numerical solutions demonstrating coexistence on complementary Fermi-surface arcs and spontaneous nematicity. The results are obtained from a parameter-free minimization once the mismatch ratio is fixed by the band masses, and multiple initial conditions converge to the same nematic state. We will expand the abstract by one sentence to reference the key equations and the numerical procedure, while keeping it within length limits. revision: partial

Circularity Check

0 steps flagged

No circularity: self-consistent mean-field treatment of intrinsic FS mismatch yields spontaneous breaking without reduction to inputs

full rationale

The provided abstract and context describe a standard self-consistent microscopic theory in which an intrinsic electron-hole Fermi surface mismatch (different sizes/shapes but no explicit anisotropy) stabilizes FFLO-like pairing and drives spontaneous EI symmetry breaking. This reconstructs the phase space leading to coexistence and emergent nematic SC. No equations, fitted parameters, or self-citations are shown that would make any labeled prediction equivalent to its inputs by construction. The mismatch is presented as a model input that remains rotationally invariant while producing unequal FS, and the nematicity emerges spontaneously from the equations rather than being smuggled in. This matches the default expectation of a non-circular derivation; the reader's 3.0 score reflects absence of displayed equations rather than any exhibited reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the self-consistent theory is invoked without listing its inputs or approximations.

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discussion (0)

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