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arxiv: 2606.31079 · v1 · pith:ZB37TTEXnew · submitted 2026-06-30 · ❄️ cond-mat.mes-hall

Andreev reflection mediated by topological corner states in a two-dimensional honeycomb lattice

Kai-Tong Wang , Yunjin Yu , Fuming Xu , Jian Wang This is my paper

Pith reviewed 2026-07-01 04:37 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords topological corner statesAndreev reflectionsecond-order topological insulatorhoneycomb latticeKane-Mele modelZeeman fieldresonant tunnelingquantum interference
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The pith

Topological corner states mediate Andreev reflection by creating resonant tunneling paths in second-order topological insulators.

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

The paper examines a transport setup with a normal lead, a central second-order topological insulator region on a honeycomb lattice, and a superconducting lead. In this setup, localized topological corner states in a diamond-shaped flake can be converted into extended scattering states by incident electrons. This conversion forms a resonant channel that enables perfect Andreev reflection near zero energy despite the insulating nature of the central region. The Andreev reflection spectrum also shows antiresonance dips that shift with the strength of the in-plane Zeeman field, arising from quantum interference and differing dwell times for electrons and holes.

Core claim

In the modified Kane-Mele model with an in-plane Zeeman field, topological corner states localized in a diamond-shaped flake of a honeycomb lattice can mediate Andreev reflection when the system is coupled to a superconducting lead. Incident electrons transform these localized states into extended scattering states that serve as a resonant tunneling path, resulting in a perfect Andreev reflection peak near zero energy. Away from resonance, antiresonance dips occur due to quantum interference and the imbalance between electron and hole dwell times in the central region.

What carries the argument

The resonant tunneling channel created when localized topological corner states are turned into extended scattering states by coupling to the leads.

If this is right

  • Perfect Andreev reflection occurs near zero energy through the corner-state channel.
  • Antiresonance dips appear in the Andreev reflection spectrum at positions tunable by the Zeeman field strength.
  • Suppression of Andreev reflection results from quantum interference combined with unequal electron and hole dwell times.
  • The corner states provide a resonant tunneling path to the superconducting interface in second-order topological systems.

Where Pith is reading between the lines

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

  • The mechanism may allow control of superconducting proximity effects using magnetic fields in higher-order topological materials.
  • Similar resonant mediation could occur in other lattice geometries or second-order topological insulators beyond the honeycomb case.
  • Device applications might exploit the tunability of the resonance and antiresonances for Andreev processes.

Load-bearing premise

The coupling of topological corner states to the leads produces an extended scattering state that forms a resonant tunneling channel to the superconducting lead.

What would settle it

No perfect Andreev reflection peak near zero energy in numerical transport calculations when the central region is configured to host topological corner states.

Figures

Figures reproduced from arXiv: 2606.31079 by Fuming Xu, Jian Wang, Kai-Tong Wang, Yunjin Yu.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of the two-terminal SOTI-superconductor hy [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Andreev reflection coefficient [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (b), the PLDOS in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Andreev reflection coefficient [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Topological corner states in two-dimensional second-order topological insulators (SOTIs) are localized in real space. We numerically demonstrate that such localized topological corner states can mediate Andreev reflection when coupled to a superconducting lead. We consider a transport setup based on a two-dimensional honeycomb lattice, consisting of a normal lead, a central SOTI region, and a superconducting lead. The central SOTI region is described by the modified Kane--Mele model with an in-plane Zeeman field and hosts topological corner states in a diamond-shaped flake. Although the central region is insulating, the local density of states shows that incident electrons can turn the localized corner state into an extended scattering state, which forms a resonant tunneling channel to the superconducting lead. This process leads to a perfect Andreev reflection peak near zero energy. Away from this resonance, antiresonance dips appear in the Andreev reflection spectrum, and their positions can be tuned by the Zeeman field strength. We show that the suppression of Andreev reflection is caused by quantum interference and the imbalance between electron and hole dwell times in the central region. These results demonstrate that topological corner states can provide a resonant tunneling path to the superconducting interface and mediate Andreev reflection in second-order topological 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

2 major / 2 minor

Summary. The manuscript numerically studies Andreev reflection in a normal-SOTI-superconductor junction on a honeycomb lattice. The central region is a diamond-shaped flake described by the modified Kane-Mele model plus in-plane Zeeman field, which hosts topological corner states. The authors report that these localized states are converted by incident electrons into extended scattering states that form a resonant channel to the superconducting lead, producing a perfect Andreev reflection peak at zero energy; antiresonance dips appear away from resonance and are tunable by the Zeeman strength. The suppression mechanism is attributed to quantum interference and electron-hole dwell-time imbalance.

Significance. If the central claim is substantiated, the work would establish that second-order topological corner states can serve as tunable mediators of resonant Andreev processes in an otherwise insulating region. This would add a concrete transport signature to the phenomenology of higher-order topological insulators and could motivate further studies of corner-state-assisted superconducting proximity effects.

major comments (2)
  1. [Numerical results / LDOS and conductance spectra] The central claim that the zero-energy Andreev peak is mediated specifically by the topological corner states rests on LDOS visualizations showing a localized corner mode becoming extended. No wave-function decomposition (projection onto a corner-localized basis) or control calculations (zero Zeeman field or trivial phase without corner states) are presented to exclude generic interface or finite-size resonances. This absence directly weakens the attribution of the resonance to the topological corner states.
  2. [Transport setup and results] The manuscript states that the central region is insulating yet supports resonant tunneling via corner states, but provides no quantitative check (e.g., comparison of conductance with and without the Zeeman-induced corner states, or scaling with flake size) that the perfect Andreev peak disappears when corner states are absent. Without such a control, the reported peak could arise from lead hybridization effects unrelated to the second-order topology.
minor comments (2)
  1. [Methods] Lattice size, lead-coupling strength, and convergence criteria for the scattering calculations are not specified; these details are needed to assess numerical reliability.
  2. [Results] The antiresonance positions are said to be tunable by Zeeman field strength, but no explicit functional dependence or additional plots quantifying the shift are shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Numerical results / LDOS and conductance spectra] The central claim that the zero-energy Andreev peak is mediated specifically by the topological corner states rests on LDOS visualizations showing a localized corner mode becoming extended. No wave-function decomposition (projection onto a corner-localized basis) or control calculations (zero Zeeman field or trivial phase without corner states) are presented to exclude generic interface or finite-size resonances. This absence directly weakens the attribution of the resonance to the topological corner states.

    Authors: We agree that the attribution would be strengthened by explicit controls. In the revised manuscript we will add (i) calculations at zero Zeeman field (trivial phase, no corner states) to show the zero-energy Andreev peak is absent and (ii) a projection of the scattering wave functions onto a corner-localized basis to quantify the contribution of the topological corner states. revision: yes

  2. Referee: [Transport setup and results] The manuscript states that the central region is insulating yet supports resonant tunneling via corner states, but provides no quantitative check (e.g., comparison of conductance with and without the Zeeman-induced corner states, or scaling with flake size) that the perfect Andreev peak disappears when corner states are absent. Without such a control, the reported peak could arise from lead hybridization effects unrelated to the second-order topology.

    Authors: We concur that a direct quantitative comparison is needed. The revised manuscript will include (i) a side-by-side comparison of the Andreev reflection spectra with and without the in-plane Zeeman field and (ii) a finite-size scaling analysis of the diamond flake to confirm that the resonance is tied to the corner states rather than lead hybridization or generic finite-size effects. revision: yes

Circularity Check

0 steps flagged

No circularity; numerical results are independent of fitted parameters or self-referential definitions

full rationale

The paper reports direct numerical simulations of transport in a modified Kane-Mele model with Zeeman field on a diamond flake, computing LDOS and Andreev reflection coefficients from the scattering setup. No quantity is defined in terms of another (e.g., no fitted resonance parameter renamed as prediction), no self-citation chain justifies the central claim, and the model Hamiltonian is standard rather than ansatz-smuggled. The observed perfect Andreev peak is an output of the computation, not an input by construction. This is the normal case of a self-contained numerical study.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the chosen tight-binding model produces corner states whose coupling to superconducting leads yields the described resonant channel; no free parameters are fitted to data and no new entities are postulated.

free parameters (1)
  • in-plane Zeeman field strength
    Varied parametrically to shift antiresonance positions; not fitted to match a target observable.
axioms (1)
  • domain assumption The modified Kane-Mele model with in-plane Zeeman field on a diamond-shaped flake is a second-order topological insulator hosting localized corner states.
    This modeling choice defines the central scattering region and is invoked throughout the abstract.

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discussion (0)

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Reference graph

Works this paper leans on

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