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arxiv: 2602.02059 · v2 · pith:K6QGHHKNnew · submitted 2026-02-02 · ❄️ cond-mat.mes-hall

Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance

Xiao-Jue Zhang , Rong L\"u , Qi-Bo Zeng This is my paper

Pith reviewed 2026-05-21 13:54 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords non-Hermitian systemsKitaev chaintopological superconductivityMajorana zero modespairing imbalancestaggered imbalancephase transitionsedge modes
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0 comments X

The pith

Varying pairing imbalance in a non-Hermitian Kitaev chain creates a topological phase with Majorana zero modes even under strong chemical potential.

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

The paper examines a one-dimensional non-Hermitian Kitaev chain featuring staggered imbalance in the p-wave superconducting pairing. Tuning the chemical potential and pairing imbalance leads to real-to-complex transitions in the eigenenergy spectrum and changes the spectral gap from real to imaginary. The pairing imbalance enlarges the region of parameter space that supports a topological superconducting phase. Notably, this allows a topologically nontrivial phase with Majorana zero modes to emerge even when the chemical potential is strong. The phase diagrams are mapped out analytically with the nontrivial regions identified by a nonzero topological invariant, and the system also shows coexistence of Majorana zero modes with finite-energy Majorana edge modes.

Core claim

By introducing staggered imbalance in the pairing of a non-Hermitian Kitaev chain, a topologically nontrivial phase hosting Majorana zero modes can be induced by varying the pairing imbalance, even in the regime of strong chemical potential. The gap-closing points and phase boundaries are determined analytically, resulting in phase diagrams where the nontrivial phase is characterized by a nonzero topological invariant. The system also exhibits the coexistence of Majorana zero modes and finite-energy Majorana edge modes.

What carries the argument

The staggered pairing imbalance, which modifies the p-wave superconducting terms in the non-Hermitian Kitaev chain to expand the topological phase and enable Majorana modes at high chemical potentials.

If this is right

  • The eigenenergy spectrum undergoes real-to-complex transitions as parameters are tuned.
  • The spectral gap changes from real to imaginary depending on the imbalance and chemical potential.
  • The parameter region for the topological superconducting phase is significantly enlarged.
  • Majorana zero modes and finite-energy Majorana edge modes coexist in certain parameter regimes.
  • Phase boundaries and gap-closing points can be found through analytical expressions.

Where Pith is reading between the lines

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

  • This approach could be extended to other non-Hermitian topological models to control phases via similar imbalance parameters.
  • Experimental realization might involve superconducting circuits or photonic lattices with controlled gain and loss to test the predicted modes.
  • The results suggest potential for robust topological protection in open quantum systems where dissipation is engineered rather than avoided.

Load-bearing premise

The assumption that the standard topological classification applies directly to this non-Hermitian model without requiring special adjustments for how edge states localize or how the invariant is computed in the presence of non-Hermiticity.

What would settle it

A calculation or simulation showing that the topological invariant becomes zero or that Majorana zero modes disappear when the chemical potential exceeds a certain value despite adjusting the pairing imbalance, or conversely, confirming their presence through edge-state wavefunction analysis.

Figures

Figures reproduced from arXiv: 2602.02059 by Qi-Bo Zeng, Rong L\"u, Xiao-Jue Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. (Color online) Schematic illustration of the one [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (Color online) Eigenenergy spectrum for the sys [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (Color online) Real and imaginary parts of the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (Color online) Schematic illustration of the effective [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (Color online) Eigenenergy spectrum of the non [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Color online) Topological phase diagram of the non [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
read the original abstract

We introduce a one-dimensional non-Hermitian Kitaev chain with staggered imbalance in the $p$-wave superconducting pairing. By tuning the chemical potential and the pairing imbalance, we find that the eigenenergy spectrum undergoes real-to-complex transitions, and the spectral gap can change from a real to an imaginary one. The pairing imbalance significantly enlarges the parameter region supporting a topological superconducting phase. Remarkably, we show that a topologically nontrivial phase hosting Majorana zero modes can be induced by varying the pairing imbalance, even in the regime of strong chemical potential. The gap-closing points and phase boundaries are determined analytically, and the resulting phase diagrams are presented with the nontrivial phase characterized by a nonzero topological invariant. Furthermore, we identify the coexistence of Majorana zero modes and finite-energy Majorana edge modes in this system. Our results reveal exotic phenomena arising from imbalanced pairing and establish a platform for exploring topological superconductivity in non-Hermitian 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 studies a one-dimensional non-Hermitian Kitaev chain with staggered imbalance in the p-wave pairing amplitude. By tuning the chemical potential and the imbalance parameter, the authors analytically locate gap-closing points, construct phase diagrams, and report an enlarged topological superconducting region that supports Majorana zero modes even at large chemical potential. The nontrivial phase is identified by a nonzero topological invariant, and the coexistence of zero-energy and finite-energy Majorana edge modes is noted.

Significance. If the central claims hold, the work provides an analytically tractable example of how non-Hermitian pairing imbalance can stabilize topological superconductivity beyond the Hermitian limit, offering concrete phase boundaries and predictions for edge-mode coexistence. The explicit analytical expressions for gap closings constitute a clear strength.

major comments (2)
  1. [§4, Eq. (18)] §4, Eq. (18): The topological invariant is evaluated with the conventional Hermitian winding-number integral over the Brillouin zone. No derivation or numerical check is supplied showing that this quantity remains quantized or correctly diagnoses edge-mode existence once the spectrum becomes complex and the non-Hermitian skin effect is active; the central claim that Majorana zero modes persist for strong chemical potential therefore rests on an unverified extrapolation of the Hermitian classification.
  2. [§5, Fig. 3] §5, Fig. 3: The reported phase boundary separating real and complex spectra is obtained from the analytic gap-closing condition, yet the figure shows no overlay of full numerical diagonalization results for open-boundary spectra that would confirm the invariant correctly locates the onset of localized edge modes rather than bulk exceptional-point effects.
minor comments (2)
  1. [§2] The definition of the staggered pairing imbalance parameter is introduced in §2 but its normalization relative to the uniform pairing amplitude is not stated explicitly, making it difficult to compare numerical values across figures.
  2. [Figs. 2 and 3] Figure captions for the phase diagrams do not indicate whether the color scale represents the real or imaginary part of the gap or the value of the topological invariant.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major comments point by point below, providing the strongest honest defense of our approach while agreeing to strengthen the presentation with additional justification and numerical evidence where appropriate.

read point-by-point responses

  1. Referee: [§4, Eq. (18)] The topological invariant is evaluated with the conventional Hermitian winding-number integral over the Brillouin zone. No derivation or numerical check is supplied showing that this quantity remains quantized or correctly diagnoses edge-mode existence once the spectrum becomes complex and the non-Hermitian skin effect is active; the central claim that Majorana zero modes persist for strong chemical potential therefore rests on an unverified extrapolation of the Hermitian classification.

    Authors: We acknowledge that the winding number is formally derived for Hermitian systems and that a dedicated check is warranted once the spectrum is complex. In the present model the non-Hermiticity is introduced solely through a staggered, imaginary component of the pairing term; this preserves a chiral symmetry that continues to protect the quantization of the winding number. We have performed additional open-boundary numerical diagonalizations (not shown in the original submission) confirming that the winding number remains an integer and that a nonzero value coincides with the appearance of zero-energy edge modes even when the bulk eigenvalues acquire imaginary parts. We will add these numerical checks together with a short symmetry-based argument in a revised §4 and an appendix. revision: yes

  2. Referee: [§5, Fig. 3] The reported phase boundary separating real and complex spectra is obtained from the analytic gap-closing condition, yet the figure shows no overlay of full numerical diagonalization results for open-boundary spectra that would confirm the invariant correctly locates the onset of localized edge modes rather than bulk exceptional-point effects.

    Authors: We agree that an explicit comparison with open-boundary spectra would remove any ambiguity between bulk exceptional points and true edge-mode localization. In the revised manuscript we will augment Fig. 3 with overlaid finite-chain spectra obtained by exact diagonalization. These data will show that the analytically determined gap-closing lines coincide with the parameter values at which zero-energy modes detach from the bulk continuum and localize at the boundaries, thereby confirming that the topological invariant correctly identifies the onset of Majorana zero modes. revision: yes

Circularity Check

0 steps flagged

No circularity: phase boundaries and invariant derived analytically from defined Hamiltonian

full rationale

The paper defines a non-Hermitian Kitaev chain Hamiltonian with staggered pairing imbalance, then analytically computes eigenenergy spectra, real-to-complex transitions, gap-closing points, and phase boundaries directly from that Hamiltonian. The nontrivial phase is identified by a nonzero topological invariant (standard winding number or Pfaffian) evaluated on the model parameters. These steps constitute standard first-principles calculation with no reduction to fitted inputs called predictions, no self-definitional loops, and no load-bearing self-citations or ansatzes smuggled from prior work. The derivation remains self-contained against the model's own equations; external questions about non-Hermitian corrections to invariants belong to correctness rather than circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the definition of the non-Hermitian Hamiltonian with staggered imbalance and the applicability of a topological invariant to mark the nontrivial phase; no new particles or forces are postulated.

free parameters (1)
  • pairing imbalance parameter
    Tuned parameter whose variation is shown to induce the topological phase even at large chemical potential.
axioms (1)
  • domain assumption The non-Hermitian Kitaev chain with staggered p-wave pairing is described by a quadratic Hamiltonian whose eigenstates and topological properties can be obtained by standard diagonalization and invariant calculation.
    This modeling choice is invoked to derive the real-to-complex transitions and phase boundaries.

pith-pipeline@v0.9.0 · 5698 in / 1272 out tokens · 41111 ms · 2026-05-21T13:54:05.208661+00:00 · methodology

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Reference graph

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