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arxiv: 2605.19907 · v1 · pith:QKYQES3Tnew · submitted 2026-05-19 · ❄️ cond-mat.mes-hall

Non-Hermitian thermoelectric transport in graphene: Tunable anomalous transmission through complex barriers

Daniel A. Bonilla , Juan A. Ca\~nas , J. C. P\'erez-Pedraza , A. Mart\'in-Ruiz This is my paper

Pith reviewed 2026-05-20 04:06 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords non-Hermitian transportgraphenethermoelectric figure of meritcomplex barrierLandauer scatteringDirac-Weyl equationgain and loss
0
0 comments X

The pith

A complex barrier with imaginary potential in graphene produces a gain-loss trade-off that lets loss yield the largest thermoelectric figure of merit at finite temperature.

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

The paper solves the Dirac-Weyl scattering problem for a finite complex barrier in monolayer graphene and shows that the imaginary part makes the scattering matrix non-unitary. This replaces ordinary flux conservation with a generalized balance set by net gain or loss inside the barrier, selectively amplifying or attenuating resonant channels and making lead-resolved conductances depend on bias partition. At finite temperature the exact linear-response coefficients then display a clear trade-off: gain raises both electrical and thermal conductances while loss reduces the thermal conductance more efficiently and produces the highest figure of merit in the explored parameter range. A reader would care because the result extends the accessible transport behaviors of graphene beyond ordinary n-p-n junctions and supplies an effective description of environmental source-sink channels when a full microscopic model is unavailable.

Core claim

Solving the Dirac-Weyl problem exactly, the imaginary part of the barrier renders the scattering matrix nonunitary and replaces the usual Hermitian flux conservation by a generalized flux-balance relation determined by the net gain or loss inside the barrier. In the Hermitian limit the standard graphene n-p-n behavior is recovered, including perfect transmission at normal incidence and Fabry-Perot resonances. For finite imaginary part the same resonant channels are selectively attenuated or amplified, modifying both the angular response and the conductance profile; the lead-resolved conductances become dependent on the bias partition. At finite temperature the exact linear-response transport

What carries the argument

The complex potential barrier inserted into the Dirac-Weyl Hamiltonian, which produces a non-unitary scattering matrix together with a generalized flux-balance relation controlled by net gain or loss.

If this is right

  • Gain inside the barrier enhances both electrical and thermal conductances.
  • Loss suppresses the thermal conductance more efficiently than gain increases it.
  • The largest thermoelectric figure of merit occurs in the loss-dominated regime.
  • Lead-resolved conductances depend on how the bias is partitioned between the two terminals.
  • Resonant transmission channels are selectively amplified or attenuated according to the sign of the imaginary potential.

Where Pith is reading between the lines

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

  • The same complex-barrier construction could be applied to other Dirac materials to explore analogous non-Hermitian thermoelectric effects.
  • Device designs might deliberately introduce auxiliary probes or sinks to emulate the effective imaginary potential for practical tuning.
  • The breakdown of gauge invariance in the two-terminal response offers a measurable signature that could be tested independently of the thermoelectric coefficients.

Load-bearing premise

The imaginary potential serves as an effective reduced description of unresolved source-sink channels or additional probes coupled to the device when a fully microscopic model of the environment is unavailable.

What would settle it

A measurement of the thermoelectric figure of merit in a graphene device containing an engineered complex barrier, performed at finite temperature for both positive and negative values of the imaginary part, would show whether loss indeed produces the largest value within the studied range.

Figures

Figures reproduced from arXiv: 2605.19907 by A. Mart\'in-Ruiz, Daniel A. Bonilla, J. C. P\'erez-Pedraza, Juan A. Ca\~nas.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic setup. A monolayer graphene sheet is [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Setup for a monolayer graphene sheet with a finite [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Polar plots of the angular dependence of the [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Chemical-potential dependence of the dimensionless [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Dimensionless flux-balance quantities as functions of [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Dimensionless flux-balance quantities as functions of [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Zero-temperature electrical conductances for the [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Angular integrands entering the zero-temperature conductances. Panels (a) and (b) show the integrand of [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Temperature dependence of the electrical conductance per unit width [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
read the original abstract

We investigate thermoelectric transport in monolayer graphene across a finite complex barrier within a Landauer scattering framework. Solving the Dirac-Weyl problem exactly, we show that the imaginary part of the barrier renders the scattering matrix nonunitary and replaces the usual Hermitian flux conservation by a generalized flux-balance relation determined by the net gain or loss inside the barrier. In the Hermitian limit, the standard graphene $n$-$p$-$n$ barrier behavior is recovered, including perfect transmission at normal incidence and Fabry-Perot-type resonances. For a finite imaginary part, however, the same resonant channels are selectively attenuated or amplified, which significantly modifies both the angular response and the conductance profile. We further show that the lead-resolved conductances become dependent on the bias partition, providing a direct signature of the breakdown of gauge invariance in the effective two-terminal response. At finite temperature, the exact linear-response coefficients reveal a clear trade-off controlled by the imaginary part of the barrier: gain enhances both the electrical and thermal conductances, whereas loss suppresses the thermal conductance more efficiently and yields the largest thermoelectric figure of merit within the parameter range considered. These results demonstrate that complex barriers extend the range of transport behaviors accessible in graphene beyond the usual Hermitian $n$-$p$-$n$ junction. They also suggest a practical interpretation of the imaginary potential as an effective reduced description of unresolved source-sink channels or additional probes coupled to the device, particularly when a fully microscopic model of the environment is not available.

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 / 3 minor

Summary. The manuscript solves the Dirac-Weyl scattering problem exactly for monolayer graphene with a finite complex barrier in the Landauer framework. It shows that a nonzero imaginary barrier component renders the S-matrix non-unitary, replaces Hermitian flux conservation with a generalized flux-balance relation set by net gain or loss inside the barrier, modifies angular transmission and conductance profiles, breaks gauge invariance in lead-resolved conductances, and produces a finite-temperature trade-off in which loss suppresses thermal conductance K more efficiently than electrical conductance G, yielding the largest ZT within the explored parameter range.

Significance. If the reported trade-off and ZT enhancement survive a corrected energy-current definition, the work is significant: it supplies an exactly solvable non-Hermitian extension of the canonical graphene n-p-n junction, demonstrates tunable thermoelectric response via an effective imaginary potential, and offers a practical interpretation of complex barriers as reduced models for unresolved source-sink channels. The recovery of perfect normal-incidence transmission and Fabry-Perot resonances in the Hermitian limit, together with the explicit generalized flux-balance relation, are clear strengths.

major comments (2)
  1. [finite-temperature thermoelectric coefficients] In the finite-temperature linear-response section, the thermal conductance is evaluated with the conventional Landauer integral K ~ ∫ (E-μ)^2 T(E) (-∂f/∂E) dE using the modified transmission probabilities from the non-unitary S-matrix. However, the generalized flux-balance relation is derived only for particle current; the manuscript does not re-derive the energy-current operator from the continuity equation of the non-Hermitian Dirac Hamiltonian or include possible extra terms proportional to Im(V). This omission is load-bearing for the central claim that loss yields the largest ZT via stronger K suppression.
  2. [lead-resolved conductances] The lead-resolved conductances are stated to depend on the bias partition, presented as a direct signature of gauge-invariance breakdown. An explicit side-by-side comparison with the Hermitian limit (where partition independence must hold) would strengthen this claim and clarify the magnitude of the effect.
minor comments (3)
  1. [model definition] The complex barrier potential is introduced as V = V_r + i V_i; an explicit equation number or definition box would help readers track the sign convention for gain versus loss.
  2. [figures] Figure captions for the angular transmission plots should state the precise value of the imaginary part used and whether the curves are normalized to the Hermitian case.
  3. [scattering solution] A brief remark on the numerical stability of the exact Dirac-Weyl solution for large |Im(V)| would be useful, given that the S-matrix becomes strongly non-unitary.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. Below we respond point by point to the major comments and indicate the revisions we will implement.

read point-by-point responses

  1. Referee: In the finite-temperature linear-response section, the thermal conductance is evaluated with the conventional Landauer integral K ~ ∫ (E-μ)^2 T(E) (-∂f/∂E) dE using the modified transmission probabilities from the non-unitary S-matrix. However, the generalized flux-balance relation is derived only for particle current; the manuscript does not re-derive the energy-current operator from the continuity equation of the non-Hermitian Dirac Hamiltonian or include possible extra terms proportional to Im(V). This omission is load-bearing for the central claim that loss yields the largest ZT via stronger K suppression.

    Authors: We thank the referee for identifying this point. The generalized flux-balance relation was derived from the continuity equation applied to the particle current. Because the non-Hermitian term is localized inside the barrier while the leads remain Hermitian, the energy flux operators in the asymptotic regions retain their standard form; the scattering matrix already incorporates the net gain or loss into the transmission probabilities used in the Landauer integrals. To make this explicit, we will add a short derivation of the energy current from the continuity equation in a new appendix of the revised manuscript, confirming that no additional Im(V)-dependent source terms appear in the lead-resolved energy currents. This addition will substantiate that the reported suppression of thermal conductance under loss and the resulting ZT enhancement remain valid. revision: yes

  2. Referee: The lead-resolved conductances are stated to depend on the bias partition, presented as a direct signature of gauge-invariance breakdown. An explicit side-by-side comparison with the Hermitian limit (where partition independence must hold) would strengthen this claim and clarify the magnitude of the effect.

    Authors: We agree that an explicit comparison would improve clarity. In the revised manuscript we will insert a new panel (or supplementary figure) that plots the lead-resolved conductances versus bias partition for both the Hermitian case (imaginary barrier component set to zero) and the non-Hermitian case. The Hermitian curves will be independent of partition, while the non-Hermitian curves will exhibit clear dependence, thereby quantifying the gauge-invariance breakdown and directly addressing the referee’s request. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained from Dirac-Weyl scattering and Landauer framework

full rationale

The paper begins from the Dirac-Weyl Hamiltonian with complex barrier potential, solves the scattering problem exactly to obtain the non-unitary S-matrix and the associated generalized flux-balance relation for particle current, then inserts the resulting transmission probabilities into the standard Landauer-Büttiker integrals for linear-response conductances and thermoelectric coefficients at finite temperature. No parameters are fitted to a data subset and then relabeled as predictions, no self-citation chain supplies a uniqueness theorem or ansatz that forces the central trade-off result, and the reported gain/loss effects on G and K follow directly from the modified transmission without reducing to the input definitions by construction. The derivation is therefore independent and self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work rests on the standard low-energy Dirac-Weyl description of graphene and introduces the complex barrier strength as a tunable parameter whose physical origin is interpreted as an effective model for open-system effects.

free parameters (1)
  • imaginary part of barrier potential
    Varied to control gain or loss; its specific values determine the attenuation or amplification of resonances and the figure-of-merit optimum.
axioms (2)
  • standard math Dirac-Weyl equation governs low-energy electrons in monolayer graphene
    Invoked to set up the scattering problem across the complex barrier.
  • domain assumption Landauer scattering framework applies to non-Hermitian systems with generalized flux balance
    Used to relate transmission probabilities to conductances and thermoelectric coefficients.

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Reference graph

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