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Switchable Non-Hermitian Skin Effect in Bogoliubov Modes

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A nonlinear driven-dissipative circuit shows an abruptly switchable non-Hermitian skin effect in Bogoliubov sideband modes above a drive-voltage threshold.

desk verdict A clean circuit demonstration of switchable NHSE in Bogoliubov sidebands with a predicted threshold that matches, though missing probe-linearity and kp-reversal controls that should be added in review. read the letter →

arxiv 2411.13841 v3 pith:HYIY7GZJ submitted 2024-11-21 cond-mat.mes-hall

Hsuan Lo , You Wang , Rimi Banerjee , Baile Zhang , Y. D. Chong This is my paper · ORCID
classification cond-mat.mes-hall
keywords non-HermitianskineffectBogoliubovquasiparticlesnonlineartransmissionlinepseudo-Hermiticitypoint-gaptopologydrivingthresholdsidebandmodestopologicalmetamaterial
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims to show, in a nonlinear transmission-line circuit of 30 unit cells, that Bogoliubov sideband modes undergo a non-Hmitian skin effect that switches on abruptly when the fundamental driving voltage rises past about 240 mV. Below the threshold the sideband modes are extended; above it they localize to one edge of the lattice. The authors interpret the switch as spontaneous breaking of a pseudo-Hermitian symmetry in the Bogoliubov–de Gennes (BdG) Hamiltonian, which opens a point gap in the complex spectrum and produces winding-protected skin modes. They identify this as the first experimental switchable NHSE in Bogoliubov modes that requires only a local Kerr-type nonlinearity, without asymmetric hoppings or p-wave pairing interactions. If correct, the result makes the NHSE actively controllable by an external drive rather than a fixed property of a lattice.

What carries the argument

The central object is the Bogoliubov–de Gennes (BdG) Hamiltonian that governs fluctuations on a coherently driven fundamental mode. For an envelope ansatz consisting of a pump plus small sideband components, the equations of motion close into a non-Hermitian eigenproblem of the form $H(u,v)^T = \omega_f (u,v)^T$, with $H$ written in terms of a driven-lattice Hamiltonian $H_u$ and a pairing block $H_v$ that is diagonal in the present circuit. $H$ obeys pseudo-Hermiticity ($\Gamma_3 H \Gamma_3 = H^\dagger$) and, under open boundary conditions, non-Hermitian particle–hole symmetry; these symmetries force a quadruplet structure of eigenvalues and give a 'non-Hermitian particle/hole pinning' property ($\|u\|^2 = \|v\|^2$) for pseudo-Hermiticity-broken eigenstates. The load-bearing mechanism is the spontaneous breaking of pseudo-Hermiticity as the drive amplitude $V_\mathrm{pp}$ crosses the threshold: below it all eigenvalues are real and there is no point gap; above it, complex eigenvalue quadruplets appear in a finite window of quasimomentum, the periodic-boundary spectrum forms point-gapped loops with winding $\pm 1$, and the open-boundary modes become one-sided skin modes. The drive wavenumber $k_p = 2\pi/3$ is what makes the effective hoppings nonreciprocal in the BdG description.

What would settle it

Measure the complex Bogoliubov band structure under periodic boundary conditions and check that the open-boundary localized modes are encircled by point-gap loops with winding ±1; absence of this winding would falsify the skin-effect interpretation.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that a one-dimensional chain of driven nonlinear RLC resonators, with back-to-back varactors providing a local Kerr nonlinearity, hosts Bogoliubov quasiparticles described by a non-Hermitian BdG Hamiltonian, and that these quasiparticles exhibit the non-Hermitian skin effect (NHSE). The NHSE is switchable: for drive amplitudes below roughly 240 mV the BdG eigenfrequencies are almost all real and the sideband modes are delocalized; above that threshold pseudo-Hermiticity spontaneously breaks, the complex spectrum develops point-gap winding under periodic boundary conditions, and the open-boundary eigenmodes become exponentially localized to one side. Experimentally, the authors observe a sideband at the auxiliary probe frequency and its mirror peak, measure the spatial sideband profile, and show that the inverse participation ratio and the left-to-right sideband amplitude ratio jump sharply at the same threshold predicted by the model. They further show that the localized modes occur only in the frequency window where the BdG eigenvalues are complex, consistent with the theoretical spectrum. The mechanism does not rely on asymmetric inter-site hopping or p-wave pairing; the fundamental drive itself imparts the left–right asymmetry to the BdG Hamiltonian.

Load-bearing premise

The load-bearing premise is that the measured sideband signals are governed by the linearized Bogoliubov–de Gennes eigenproblem with the slowly-varying envelope ansatz, so that the abrupt localization above 240 mV is the predicted topological skin effect rather than a generic higher-harmonic or nonlinear response.

Editorial extensions

If this is right

  • Raising the fundamental drive amplitude across the threshold switches the Bogoliubov sideband response from delocalized to edge-localized, giving an all-electrical on/off control of the skin effect.
  • The localization is frequency-selective: only sideband frequencies in the range $\mathrm{Re}(\Omega_f)$ where the BdG eigenvalues are non-real (about $\Omega < 0.03$ in the experiment) show strong edge localization; other frequencies remain extended.
  • The same circuit can be used to probe pseudo-Hermiticity breaking directly through the sideband spectrum and the left–right sideband amplitude ratio, which acts as an experimental signature of the symmetry breaking.
  • Because the mechanism uses only a local Kerr nonlinearity and the phase pattern of the drive, similar switchable NHSEs should be realizable in other nonlinear lattices and metamaterials with local nonlinearities.
  • The lossier set of skin modes predicted by the double-sided skin effect is not observed in this experiment; since the model says these modes exist but are too lossy, they could be accessed in future setups with lower loss or gain.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the BdG linearization remains valid, the switchable skin effect could be exploited as a voltage-controlled topological switch, for routing or sensing in microwave circuits, with the threshold tunable by component parameters.
  • The requirement of only a local Kerr nonlinearity suggests that the same mechanism could be transferred to photonic or optomechanical platforms with Kerr nonlinearity and a phase-structured pump, potentially enabling dynamically reconfigurable non-Hermitian topological states.
  • A quantitative test that would distinguish the BdG mechanism from generic nonlinear response is to check the linear-response scaling of the localized sideband amplitude with the auxiliary probe amplitude; a true BdG eigenmode should show a region of linear scaling, while higher-harmonic generation would deviate.
  • The paper's claim implies that the complex point-gap winding, not the static lattice geometry, controls the localization direction; one could verify this by reversing the sign of $k_p$ (drive phase gradient) and observing the skin modes move to the opposite edge, which the paper does not report explicitly.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper reports an experimental realization of a non-Hermitian skin effect (NHSE) in Bogoliubov quasiparticles of a nonlinear driven-dissipative circuit. The circuit is an RLC transmission line with varactor nonlinearity, driven by a fundamental tone with a phase gradient kp=2π/3 and probed by a weak auxiliary drive at a sideband frequency. The authors show theoretically that the Bogoliubov-de Gennes (BdG) Hamiltonian has a point-gap winding under periodic boundary conditions when pseudo-Hermiticity spontaneously breaks above a drive amplitude near Vpp≈240 mV, and that open-boundary modes localize to one edge. Experimentally, they observe a sideband whose spatial profile is right-localized in a frequency window consistent with the non-real part of the BdG spectrum, and an abrupt increase of the inverse participation ratio as Vpp crosses the predicted threshold. The central claim is that this is a switchable NHSE of Bogoliubov modes, distinct from both linear-circuit NHSE realizations and from the bosonic Kitaev chain experiments that require nonlocal pairing interactions.

Significance. If the claims hold, this is a valuable experimental demonstration of a nonlinearity-induced, actively switchable NHSE in a simple classical circuit. The threshold voltage is not fitted to the localization data but is computed from independently characterized circuit parameters, which is a genuine strength. The system also differs from earlier optomechanical and superconducting-circuit realizations of the bosonic Kitaev chain in using only a local Kerr-type nonlinearity, making the result potentially accessible to a broad range of synthetic metamaterial platforms. The paper ships a clear toy model and a plausible mapping from circuit equations to a BdG Hamiltonian, though the latter is partly deferred to the supplement. The main weaknesses are the absence of a direct linearity check of the auxiliary-drive probe and the absence of a kp-reversal control; these leave plausible alternative explanations for the observed localization.

major comments (5)
  1. [Nonlinear circuit, Eqs. (7)-(9)] The derivation of the effective BdG Hamiltonian from the circuit equation of motion is entirely relegated to the Supplemental Materials [57]. The sentence "It can then be shown [57]" is the foundation for the central theoretical interpretation: the measured sideband is identified with a BdG eigenmode, the threshold at 240 mV is computed from this Hamiltonian, and the winding and skin-mode properties follow from it. The main text should reproduce the essential steps of this derivation, or the supplement must be clearly available for review, because the experimental claims inherit all of their meaning from this mapping.
  2. [Results, Figs. 3(b)-3(f)] No auxiliary-drive linearity check is reported. All sideband measurements use V'_pp = 50 mV, and the paper does not show that the normalized spatial profile and IPR are independent of V'_pp. If varactor nonlinearity generates intermodulation or harmonic products whose spatial distribution sharpens as Vpp increases, the same abrupt IPR increase could appear without any point-gap winding. The authors should test this by varying V'_pp across the drive range and showing either that the sideband amplitude scales linearly with V'_pp or that the normalized profile and IPR are unchanged; this is a direct test of the BdG linearization assumption that underlies the whole claim.
  3. [Results, Fig. 3(c) and Fig. 3(f)] The predicted dependence of the localization direction on the drive phase pattern is not tested. The model states that the winding number, and hence the skin-mode direction, is set by kp, but the experiment only demonstrates right-localized modes for kp = 2π/3. Reversing the drive phase gradient to kp = -2π/3 should flip the localization to the left if the mechanism is the predicted NHSE. Without this control, a fixed right-localized response could be an instrumental asymmetry, and the claim that the edge direction is tied to the drive phase is not directly supported.
  4. [Results, Fig. 3(f)] The experimental IPR and sideband ratio are measured at a single sideband frequency Ω = 0.018, while the theoretical curves in the lower panel are averaged over all BdG modes. The authors note that the averaged curves are smoothed because not all modes break pseudo-Hermiticity simultaneously, but this makes the comparison of the sharpness of the transition indirect. The manuscript should show the theoretical IPR for the specific probed mode (or a narrow frequency window around Ω = 0.018) so that the abruptness of the experimental transition is compared with the same quantity that is measured.
  5. [Results, paragraph after Fig. 2(c)] The statement that "the lossier set of skin modes is not observable in our present experiment [57]" is a selection rule that is essential for interpreting the observed one-sided localization, and it is not justified in the main text. Since the model predicts a double-sided skin effect, the paper should specify in the main text why only the less-lossy set is expected to appear in the measured sidebands, rather than only citing the supplement.
minor comments (5)
  1. [Abstract and Introduction] The abstract says the system "does not contain unconventional asymmetric hopping nonlinearities," while the introduction says it "does not rely on p-wave-like pairing interactions." These are different statements; the wording should be harmonized to avoid confusion about what is being contrasted with the bosonic Kitaev chain.
  2. [Fig. 3(f)] No error bars or repeated measurements are shown for the IPR and sideband-ratio data, making it difficult to assess whether the transition near 240 mV is statistically significant and abrupt.
  3. [Fig. 3 caption] The normalized sideband frequency Ω = (ω' - ωp)/ωp is introduced only in the caption of Fig. 3; it should be defined in the main text when the auxiliary drive is first described.
  4. [References] Reference [44] and reference [51] are the same paper (Y. Wang et al., Nature Communications 10, 1102 (2019)) and should be merged or cross-referenced once.
  5. [Eqs. (8)-(9)] The slowly-varying envelope approximation is invoked without stating the required separation of time scales or the condition that g|ψ|^2 in the toy model is small. A brief statement of these validity conditions would help the reader judge when the BdG description is expected to hold.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the pseudo-Hermiticity-breaking threshold and the associated skin-mode localization are computed from the circuit equations and independently characterized parameters, then compared to external measurements.

full rationale

The central claim is that a nonlinear transmission line hosts Bogoliubov modes whose point-gap topology switches when the driving amplitude crosses a threshold. The derivation chain starts from the measured circuit equation (7), applies the explicit ansatz (8) and (9), and leads to a BdG eigenproblem whose parameters (R, L, Ls, C0, C1, Lb) are quoted from the constructed circuit. The predicted threshold Vpp ≈ 240 mV and the associated IPR increase are computed from that Hamiltonian, not fitted to the measured IPR curves; the experimental data in Fig. 3(f) are compared to those calculations afterward. The sideband localization and particle/hole ratio are measured quantities external to the model. Although several citations are to prior work by the same group (e.g., Refs. 17, 18, 19, 26), those citations provide background or nomenclature (such as the double-sided skin effect) rather than an unverified premise that forces the present result; the switchable-NHSE model is re-derived from the circuit equations here. The only material omitted from the main text, the explicit reduction of Eqs. (7)-(9) to the BdG eigenproblem, is delegated to the Supplemental Material, which is an omitted derivation rather than a circular step. No equation is defined in terms of the quantity it purports to predict, and no fitted parameter is renamed as a prediction. The paper is therefore self-contained against its own theoretical prediction and the experimental observation is external to the model's assumptions.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central interpretation rests on the BdG linearization and the standard point-gap-to-skin-effect correspondence. The model uses independently characterized circuit parameters and a chosen drive phase kp, but the observability of only the less-lossy skin branch is an assumption made after the fact that the main text does not justify.

free parameters (3)
  • C1, varactor nonlinear capacitance coefficient = -1.649 pF/V^2
    Taken from varactor characterization; it sets the Kerr coefficient g and directly controls the pseudo-Hermiticity breaking threshold in the theory.
  • kp, drive phase gradient = 2π/3
    Chosen nonzero to produce asymmetric Hv couplings; the sign of kp determines which edge the skin mode selects.
  • Probe detuning Ω = (ω' - ωp)/ωp = 0.018 and 0.058
    Auxiliary drive frequency is a control whose value selects whether the probed Bogoliubov mode lies inside the point-gap region where localization occurs.
assumptions (5)
  • domain assumption The fluctuation dynamics are captured by a linearized BdG equation obtained from the slowly-varying envelope ansatz of Eqs. (8) and (9).
    The central spectrum and IPR calculations assume weak nonlinearity and a coherently driven background; the derivation is delegated to the supplement.
  • domain assumption Varactor capacitance obeys C(V) ≈ C0 + C1 V^2 for V ≲ 1 V.
    This empirical form defines the Kerr nonlinearity in Eq. (7) and sets the scale of the nonlinear term that drives the switching.
  • standard math Pseudo-Hermiticity and non-Hermitian particle-hole symmetry determine the spectral structure, and point-gap winding under periodic boundary conditions implies open-boundary skin modes in this 1D circuit.
    Standard non-Hermitian band topology results from Refs. 25, 30, and 58 are used to interpret the measured spatial localization as NHSE.
  • domain assumption The auxiliary probe tone at V'_pp = 50 mV is a weak perturbation that excites Bogoliubov modes without substantially altering them; adding phase differences does not affect results.
    Needed for the sideband voltage to represent BdG eigenmode amplitudes; details are given only in the supplement.
  • ad hoc to paper Only the less-lossy set of skin modes is observable; the paired lossier modes are not seen in the measured sidebands.
    Invoked in the main text to reconcile the double-sided skin effect of the theory with a single-sided experimental profile. The observability analysis is not presented in the main text, so this is a post hoc selection rule.

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Cite this review

Pith. "Pith review of Switchable Non-Hermitian Skin Effect in Bogoliubov Modes." pith.science (2026). https://pith.science/paper/HYIY7GZJ

@misc{pith2026241113841,
  author       = {Pith},
  title        = {Pith review of: Switchable Non-Hermitian Skin Effect in Bogoliubov Modes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HYIY7GZJ}},
  note         = {Machine review of arXiv:2411.13841}
}
read the original abstract

Interacting or nonlinear lattices can host emergent particle-like modes, such as Bogoliubov quasiparticles, whose band topology and other properties are potentially highly tunable. Despite originating in the study of superconducting materials, Bogoliubov quasiparticles can also occur in synthetic metamaterials. Here, we implement a nonlinear driven-dissipative circuit whose fluctuations are Bogoliubov modes possessing nontrivial non-Hermitian band topology. We show experimentally that the system exhibits a switchable non-Hermitian skin effect (NHSE), which abruptly appears when the on-site driving voltage amplitude exceeds a threshold. In contrast to earlier realizations of the NHSE and related phenomena in circuit models, the switchable NHSE in our system occurs in Bogoliubov modes, which are strongly affected by how the system is driven. Moreover, unlike other experimental platforms hosting non-Hermitian Bogoliubov modes, our system does not contain unconventional asymmetric hopping nonlinearities, only a local Kerr-type nonlinearity.

Figures

Figures reproduced from arXiv: 2411.13841 by the authors.

Figure 1
Figure 1. FIG. 1. Design of a driven nonlinear transmission line circuit [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Bogoliubov eigenfrequency spectrum calculated [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Circuit implementation of BdG modes with actively switchable NHSE. The sample consists three identical printed [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

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