"Half-Bogoliubons" as the intermediate states for the phase coherence in underdoped cuprates

Hai-Hu Wen; Han Li; Huan Yang; Jiaseng Xu; Shengtai Fan; Zhaohui Wang

arxiv: 2503.01519 · v1 · submitted 2025-03-03 · ❄️ cond-mat.supr-con

"Half-Bogoliubons" as the intermediate states for the phase coherence in underdoped cuprates

Han Li , Zhaohui Wang , Shengtai Fan , Jiaseng Xu , Huan Yang , Hai-Hu Wen This is my paper

Pith reviewed 2026-05-23 01:45 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con

keywords half-Bogoliubonsphase coherenceunderdoped cupratestunneling spectralocal pairingone-sided coherence peaksthree-hole statesBi2Sr2-xLaxCuO6

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The pith

In underdoped cuprates, half-Bogoliubons act as intermediate states that establish phase coherence between local two-hole pairs via three-hole and one-hole excitations.

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

The paper reports two kinds of tunneling spectra in underdoped Bi2Sr2-xLaxCuO6 crystals that display only one side of the coherence peak yet sit at symmetric energies of roughly 11 meV. These spectra are interpreted as half-Bogoliubons that correspond to three-hole and one-hole states excited from preformed two-hole pairs inside 4a0 by 4a0 plaquettes. Merging the two half-spectra reproduces the full particle-hole symmetric Bogoliubov dispersion. If the interpretation holds, phase coherence arises when the two half-Bogoliubons entangle and permit dynamic charge exchange between regions that already contain local pairs. A reader would care because the account separates the formation of local pairs from the onset of long-range coherence, a distinction often invoked for high-Tc materials.

Core claim

We observe tunneling spectra showing only one side of the coherence peak but with symmetric energies about ±11 meV. Merging these two kinds of spectra mimics the complete Bogoliubov dispersion, so the associated electronic states are named half-Bogoliubons. These states correspond to the three-hole and one-hole excitations out of the local pairing state of two holes within 4a0 x 4a0 plaquettes of CuO bonds. An entanglement of the two half-Bogoliubons produces the dynamic hopping of charge freedom that yields phase coherence between the local paired states. The results point to a process in which phase coherence is established by exchanging charge between regions that already contain local 4a

What carries the argument

Half-Bogoliubons, the three-hole and one-hole excited states from local two-hole pairs whose entanglement enables dynamic charge hopping that produces phase coherence.

If this is right

Phase coherence in the underdoped regime with fractional superconductivity is achieved by dynamic charge exchange between regions containing local pairs.
Merging the two one-sided spectra reproduces the full particle-hole symmetric Bogoliubov dispersion of conventional quasiparticles.
Local pairing of two holes inside each 4a0 x 4a0 plaquette supplies the starting state whose excitations become the half-Bogoliubons.
The mechanism supplies a route to phase coherence that operates through charge exchange rather than direct quasiparticle propagation.

Where Pith is reading between the lines

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

The picture implies that the energy scale of local pairing and the energy scale of coherence can be tuned separately by controlling plaquette formation.
Analogous half-states may appear in other doped Mott insulators where local pairing precedes global order.
Mapping the spatial distribution of the one-sided spectra could reveal the real-space network of local-pair regions that must exchange charge.

Load-bearing premise

The observed one-sided spectra arise specifically from three-hole and one-hole excitations out of a pre-existing two-hole local pair state inside 4a0 x 4a0 plaquettes.

What would settle it

Detection of identical one-sided spectra at energies unrelated to local-pair binding or in overdoped samples lacking 4a0 x 4a0 plaquette pairs would falsify the assignment.

read the original abstract

Superconductivity is achieved by the pairing of electrons and phase coherence between the Cooper pairs. According to the Bardeen-Cooper-Schrieffer theory, the quasiparticles with Bogoliubov dispersion exists and reveal particle-hole symmetric coherence peaks on the single particle tunneling spectrum. Here we report the observation of two kinds of tunneling spectra showing only one side of the "coherence peak" but with symmetric energies (about +-11 meV) in underdoped cuprate superconductor Bi2Sr2-xLaxCuO6 single crystals (p=0.114) with fractional superconductivity. Merging these two kinds of spectra can mimic the complete Bogoliubov dispersion, thus we name the electronic states associated with these half-peaked spectrum as "half Bogoliubons". In previous studies, it was shown that two doped holes may bind into a local pair within the 4a0 x 4a0 plaquette of CuO bonds (a0: distance between nearest Cu atoms). We attribute the "half-Bogoliubons" to the intermediate states for the phase coherence, and they correspond to the three-hole and one-hole states as the excited ones from the local pairing state of two holes. An entanglement of these two "half-Bogoliubons" would mean the dynamic hopping of charge freedom resulting in the phase coherence between the local paired states. Our results unravel a unique process for establishing the phase coherence through exchanging a charge between the regions with local pairs.

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.

Desk Editor's Note private letter to a colleague

The paper observes one-sided ±11 meV tunneling peaks in underdoped Bi2201 and interprets them as half-Bogoliubons from 3-hole/1-hole states out of local 2-hole pairs, but supplies no spectral calculations or spatial checks to back the assignment.

read the letter

The central observation is two families of spectra, each missing one coherence peak but sitting at symmetric energies. Merging them produces something that looks like a full Bogoliubov branch. The authors tie this to their earlier local-pair work inside 4a0 plaquettes and argue the missing sides correspond to three-hole and one-hole excitations that act as intermediates for phase coherence via charge exchange. That framing is the main novelty; the raw spectral asymmetry has been noted before, but the explicit half-Bogoliubon label and the proposed entanglement step are new here. The data appear to come from real measurements on fractional-superconductivity samples at p=0.114, which is a useful regime to examine. If the peaks are reproducible and the two families are cleanly separated, that part of the record is worth having. The interpretation, however, stays at the level of assignment. No spectral-function calculation, no estimate of matrix elements, and no Fourier or real-space map tying the half-peak locations to the cited 4a0 periodicity are described. Conventional alternatives such as gap inhomogeneity or surface asymmetry are mentioned only in passing. The final claim that entanglement of these states produces phase coherence is conceptual and not linked to any measured quantity such as a coherence length or critical current. The manuscript therefore rests on an observational pattern plus a plausible but untested story about hole-number states. Readers already working on local-pair scenarios in doped Mott insulators will find the suggestion worth discussing. Others will want to see the full data tables, fitting procedures, and any attempt to exclude disorder effects before treating the mechanism as established. The work is coherent on its own terms and engages the literature it cites, so it clears the bar for a serious referee even though the central link remains speculative. I would send it out with explicit instructions to the referees to focus on whether the spatial and microscopic support can be strengthened.

Referee Report

3 major / 1 minor

Summary. The paper reports observation of two kinds of one-sided tunneling spectra at symmetric energies ±11 meV in underdoped Bi2Sr2-xLaxCuO6 (p=0.114) crystals exhibiting fractional superconductivity. Merging the spectra is said to recover a full Bogoliubov dispersion, leading to the introduction of 'half-Bogoliubons' interpreted as three-hole and one-hole intermediate states excited from local two-hole pairs within 4a0×4a0 plaquettes; entanglement of these states is proposed to enable phase coherence via dynamic charge hopping.

Significance. If the attribution and interpretation hold, the work would identify a distinct route to phase coherence in underdoped cuprates that relies on local pairing and half-states rather than conventional particle-hole symmetric quasiparticles. The reported one-sided spectra constitute concrete observational data that could stimulate further STM studies of spectral asymmetry in the pseudogap regime.

major comments (3)

[Abstract] Abstract: the central claim that the observed one-sided ±11 meV peaks arise specifically from three-hole and one-hole excitations out of pre-formed two-hole local pairs inside 4a0×4a0 plaquettes is not supported by any spectral-function calculation, matrix-element estimate, or direct spatial correlation (Fourier analysis or real-space registry) with the cited plaquette periodicity.
[Abstract] Abstract and discussion: the assertion that merging the two one-sided spectra recovers the complete Bogoliubov dispersion is presented without raw data, error bars, or quantitative fitting, so the quantitative fidelity of the 'half' reconstruction cannot be assessed.
[Abstract] Abstract: the subsequent step that entanglement of the two half-Bogoliubons produces measurable phase coherence is stated conceptually but is not linked to any concrete observable or prediction (e.g., temperature dependence, doping evolution, or spatial modulation) extractable from the presented spectra.

minor comments (1)

The manuscript introduces the term 'half-Bogoliubons' without a formal definition or explicit comparison to the standard Bogoliubov-de Gennes quasiparticle spectrum used in the cuprate literature.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We address each major comment below in a point-by-point manner, indicating planned revisions where appropriate to clarify or strengthen the presentation without altering the core observational findings.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the observed one-sided ±11 meV peaks arise specifically from three-hole and one-hole excitations out of pre-formed two-hole local pairs inside 4a0×4a0 plaquettes is not supported by any spectral-function calculation, matrix-element estimate, or direct spatial correlation (Fourier analysis or real-space registry) with the cited plaquette periodicity.

Authors: The proposed attribution of the one-sided peaks to three-hole and one-hole excitations from local two-hole pairs in 4a0×4a0 plaquettes is grounded in our prior experimental and theoretical work establishing such local pairing. The current manuscript focuses on the new spectral observation and its consistency with that framework rather than repeating those calculations. We acknowledge the absence of new spectral-function computations, matrix-element estimates, or direct Fourier/real-space registry with plaquette periodicity in this study. In revision we will expand the discussion to explicitly reference the supporting prior literature and note the lack of direct spatial correlation as a limitation of the present data set. revision: partial
Referee: [Abstract] Abstract and discussion: the assertion that merging the two one-sided spectra recovers the complete Bogoliubov dispersion is presented without raw data, error bars, or quantitative fitting, so the quantitative fidelity of the 'half' reconstruction cannot be assessed.

Authors: The merging is presented conceptually to show how the two one-sided spectra together recover features resembling the full Bogoliubov dispersion. We agree that the abstract and discussion would benefit from explicit display of the underlying raw spectra together with error bars and a quantitative comparison. In the revised manuscript we will include these elements, either in the main text or as supplementary material, to permit direct evaluation of the reconstruction fidelity. revision: yes
Referee: [Abstract] Abstract: the subsequent step that entanglement of the two half-Bogoliubons produces measurable phase coherence is stated conceptually but is not linked to any concrete observable or prediction (e.g., temperature dependence, doping evolution, or spatial modulation) extractable from the presented spectra.

Authors: The link between entanglement of the half-Bogoliubons and phase coherence via dynamic charge hopping is proposed on the basis of the observed fractional superconductivity. While the connection remains conceptual in the present work, we will add a short paragraph outlining testable signatures, such as expected temperature or doping trends, that could be examined in future experiments to make the proposal more concrete. revision: partial

Circularity Check

0 steps flagged

No significant circularity; interpretive attribution to prior local-pair studies

full rationale

The paper reports STM spectra showing one-sided coherence peaks at symmetric energies and attributes them to 'half-Bogoliubons' as 3-hole/1-hole excitations from pre-existing 2-hole local pairs in 4a0 plaquettes. This attribution explicitly references 'previous studies' for the local-pair premise rather than deriving it via equations or fits within the present work. No self-definitional loops, fitted inputs renamed as predictions, load-bearing self-citations, or ansatzes smuggled via citation appear in the provided text. The central claim remains an observational interpretation without reduction to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities beyond the newly named half-Bogoliubons are quantified. The local-pair premise is taken from cited prior work.

axioms (1)

domain assumption Two doped holes bind into a local pair within the 4a0 x 4a0 plaquette of CuO bonds
Invoked in the abstract as established by previous studies to anchor the interpretation of half-Bogoliubons as three-hole and one-hole excitations.

invented entities (1)

half-Bogoliubons no independent evidence
purpose: Intermediate electronic states corresponding to one-sided coherence peaks that enable phase coherence via charge hopping between local pairs
Newly introduced term for the observed spectral features; no independent falsifiable prediction (e.g., specific mass or decay channel) is supplied in the abstract.

pith-pipeline@v0.9.0 · 5828 in / 1610 out tokens · 46836 ms · 2026-05-23T01:45:04.696791+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean (D=3 from circle linking) alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

two doped holes may bind into a local pair within the 4a0 x 4a0 plaquette

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