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arxiv: 2606.04097 · v1 · pith:6G43XNPYnew · submitted 2026-06-02 · ❄️ cond-mat.supr-con

Probing pairing symmetries through quasiparticle interference in chiral Bloch bands

Sayan Banerjee , Subrata Mandal , Peter P. Orth , Mathias S. Scheurer This is my paper

Pith reviewed 2026-06-28 07:52 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords quasiparticle interferencechiral Bloch bandspairing symmetrysuperconductivityquantum geometryvan der Waals materialsBogoliubov quasiparticlesimpurity scattering
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The pith

Quasiparticle interference patterns around impurities distinguish pairing states in chiral Bloch band superconductors.

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

The paper develops a theory for quasiparticle interference in superconductors whose normal state consists of chiral Bloch bands. It demonstrates that the quantum geometry of these bands already produces a pronounced sublattice dependence in the interference pattern above the transition temperature. Below the transition the same geometry interacts with the phase winding of the superconducting order parameter, making the real-space local spectral function sensitive to the center-of-mass momentum of the pairs. Consequently, spatial maps of the local density of states around impurities become a diagnostic capable of separating zero-momentum from finite-momentum pairing candidates. The work supplies concrete guidance for interpreting scanning-tunneling spectra in van-der-Waals multilayer systems that realize such chiral normal states.

Core claim

The spatial dependence of the local spectral function around impurities can be used to distinguish between different candidate pairing states, both with zero and finite center-of-mass momentum, because the non-trivial quantum geometry of the Bloch states affects the interference pattern even in the normal state and then combines with the momentum-dependent phase of the order parameter in the superconducting state.

What carries the argument

Quasiparticle interference of Bogoliubov quasiparticles that inherit the quantum geometry of the underlying chiral Bloch bands.

If this is right

  • The local spectral function already carries sublattice-dependent signatures above the superconducting transition.
  • Finite center-of-mass momentum pairings generate interference patterns distinct from those of zero-momentum pairings.
  • QPI measurements therefore provide a real-space probe of pairing symmetry in chiral-band materials.
  • Experimental analysis of impurity-induced patterns must incorporate the interplay between band geometry and gap phase.

Where Pith is reading between the lines

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

  • The same QPI approach could be tested in other platforms where normal-state bands carry nontrivial quantum geometry.
  • Site-resolved spectroscopy on different sublattices would directly test the predicted normal-state asymmetry.
  • Signatures of finite-momentum pairing may help identify candidate Fulde-Ferrell-Larkin-Ovchinnikov states in multilayer van-der-Waals superconductors.

Load-bearing premise

The non-trivial quantum geometry of the Bloch states crucially affects the interference pattern even in the normal state, inducing significant sublattice dependence.

What would settle it

If measured normal-state QPI patterns show no detectable sublattice asymmetry, or if calculated superconducting patterns fail to separate zero-momentum from finite-momentum pairings, the proposed diagnostic would not hold.

Figures

Figures reproduced from arXiv: 2606.04097 by Mathias S. Scheurer, Peter P. Orth, Sayan Banerjee, Subrata Mandal.

Figure 1
Figure 1. Figure 1: (iii). In this case, the change in the spec￾tral function δANS tb/bt(r, ω) vanishes at the origin, i.e. δANS tb/bt(0, ω) = 0. This surprising result is a direct conse￾quence of the nontrivial quantum geometry of the Bloch states and can be readily derived from Eq. (7), by noting that for r = 0, the change in the Green’s function takes the form δGR tb(0, ω) ∝ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (v), the set of all such momentum transfers forms a dumbbell-shaped region in momentum space. Therefore, the constant-energy contour defines the geometric bound￾ary of the allowed momentum-transfer vectors that can contribute to the QPI signal, explaining why the QPI patterns across different channels share the same overall shape in their envelope. However, the intensity distribu￾tion within this allowed r… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: clearly shows that the impurity induces oscillations in real space, with corresponding features appearing in momentum space. The inclusion of trigonal-warping terms leads to QPI patterns that display C6 symmetry in the same-layer channels (top-top and bottom-bottom) and C3 symmetry in the mixed-layer channels (top-bottom and bottom-top). While the nature of the QPI signal depends on the layer combination b… view at source ↗
read the original abstract

Recent experiments in van der Waals multi-layer systems have demonstrated that superconductivity can emerge from symmetry-reduced, chiral normal states. We here provide a theory for quasiparticle interference (QPI) of superconductors with chiral Bloch bands. Our analysis reveals how the non-trivial quantum geometry of the Bloch states crucially affects the interference pattern even in the normal state, inducing significant sublattice dependence. In the superconducting state, the behavior becomes more complex due to the interplay of the quantum geometry of the Bogoliubov quasiparticles with the momentum-dependent phase of the order parameter. We reveal how the spatial dependence of the local spectral function around impurities can be used to distinguish between different candidate pairing states, both with zero and finite center-of-mass momentum. Our work thus provides guidance to interpreting QPI patterns in materials with chiral bands, which may be useful when probing the rich physics of pairing in such systems.

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

0 major / 2 minor

Summary. The manuscript develops a theoretical framework for quasiparticle interference (QPI) in superconductors emerging from chiral Bloch bands in van der Waals multilayers. It argues that the quantum geometry of the normal-state Bloch states produces sublattice-dependent interference even without superconductivity, while in the paired state the geometry of Bogoliubov quasiparticles combines with the momentum-dependent phase of the order parameter to generate distinct spatial patterns in the local spectral function around impurities. These patterns are proposed to distinguish candidate pairing states with both zero and finite center-of-mass momentum.

Significance. If the central derivations hold, the work supplies a concrete diagnostic for pairing symmetry in a class of materials where conventional probes are limited. The explicit inclusion of quantum-geometry effects in both normal and superconducting states, together with the treatment of finite-momentum pairing, addresses a timely experimental need and could guide interpretation of STM data on chiral-band superconductors.

minor comments (2)
  1. The abstract states qualitative conclusions; the main text should supply at least one explicit model Hamiltonian (with band parameters) and the corresponding expression for the impurity-induced local spectral function to make the claimed distinction between pairing states reproducible.
  2. Figure captions and axis labels should explicitly indicate whether the plotted quantities are for the normal or superconducting state and whether the impurity potential is on-site or sublattice-selective.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, including the recognition of its timely relevance to QPI diagnostics in chiral-band superconductors, and for recommending minor revision.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents a theoretical framework analyzing how quantum geometry of chiral Bloch states affects QPI patterns in the normal and superconducting states, with the central claim that spatial dependence of the local spectral function around impurities can distinguish pairing symmetries (zero or finite momentum). No load-bearing steps reduce by construction to inputs: there are no self-definitional relations, no fitted parameters presented as predictions, no uniqueness theorems imported from self-citations, and no ansatzes smuggled via prior work. The derivation chain is self-contained, relying on standard quantum-geometric and Bogoliubov-de Gennes formalism applied to the problem, consistent with the low circularity assessment in the provided reader context.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; full model details are unavailable.

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