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arxiv: 2605.07189 · v3 · pith:V2RHNA2Mnew · submitted 2026-05-08 · ❄️ cond-mat.mes-hall

Coherent Nonreciprocal Valley Transport in Dirac/Weyl Semimetals

Can Yesilyurt This is my paper

Pith reviewed 2026-05-20 23:36 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords nonreciprocal transportDirac semimetalsWeyl semimetalsvalley transportelectrostatic barriergeometric asymmetrycoherent wave-packet dynamics
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The pith

An inversion-asymmetric electrostatic barrier produces coherent nonreciprocal transport in Dirac and Weyl semimetals through geometry alone.

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

The paper shows that nonreciprocal transport in Dirac and Weyl channels does not require built-in material asymmetry, magnetic fields, or polar distortions. Instead, a single electrostatic barrier shaped as a right-angle triangle creates two distinct refraction interfaces—one vertical and one oblique—so forward and backward wave packets encounter different sequences of Fermi-surface mismatch. Coherent simulations with realistic parameters establish that this geometric difference alone generates charge rectification in untilted cones. When the cone is tilted, the same barrier produces a valley-resolved diode whose transmission dichroism reverses across the Dirac point. A mirror-symmetric triangular barrier yields valley polarization but preserves exact reciprocity, isolating the role of interface-type sequence.

Core claim

A single electrostatic barrier whose shape lacks inversion symmetry drives coherent nonreciprocal transport in a Dirac or Weyl channel. Across a barrier with two qualitatively distinct refraction interfaces, forward- and backward-propagating wave packets experience different Fermi-surface-mismatch sequences at the entrance and exit faces. In an isotropic dispersion an inversion-asymmetric right-angle triangle produces strong charge-mode rectification; adding Dirac-cone tilt converts the same shape into a coherent valley-resolved diode whose dichroic structure flips sign across the Dirac point. A mirror-symmetric isosceles triangle shows valley-polarized transmission yet remains exactly two-1

What carries the argument

The inversion-asymmetric triangular electrostatic barrier presenting one vertical and one oblique refraction interface, thereby imposing opposite sequences of Fermi-surface mismatch on forward and backward propagation.

If this is right

  • In isotropic Dirac cones the barrier yields strong charge-mode rectification.
  • With added tilt the barrier functions as a valley-resolved diode whose sign of dichroism reverses across the Dirac point.
  • Mirror-symmetric barriers produce valley-polarized transmission while preserving exact reciprocity.
  • The essential requirement is a sequence of geometrically distinct interface types; tilt plus oblique faces alone do not suffice.

Where Pith is reading between the lines

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

  • Device layouts could use gate-defined triangular potentials to achieve nonreciprocal behavior in existing Dirac materials without introducing magnetic or polar components.
  • The same geometric principle may extend to other topological semimetals to produce directional control of valley or pseudospin currents.
  • Experimental mapping of transmission versus barrier angle and tilt strength would directly test whether the interface-sequence mechanism dominates over disorder or decoherence.

Load-bearing premise

The coherent split-operator Dirac wave-packet simulations with realistic device parameters accurately capture the transport physics without significant decoherence, disorder, or higher-order band effects that could erase the geometric asymmetry.

What would settle it

Fabrication of a right-angle triangular electrostatic gate in a graphene or Weyl-semimetal Hall bar followed by measurement of direction-dependent two-terminal conductance that disappears when the gate is replaced by a symmetric isosceles triangle.

Figures

Figures reproduced from arXiv: 2605.07189 by Can Yesilyurt.

Figure 1
Figure 1. Figure 1: Device concept and direction-dependent interface composition. a [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Direct visualization of the coherent nonreciprocity. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Charge-mode nonreciprocity in the absence of tilt. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Valley-resolved nonreciprocity in the tilted right-angle barrier. a [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Symmetry analysis: three barrier shapes on the same tilted channel. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Nonreciprocal electronic transport, characterized by directional asymmetry between forward and backward two-terminal responses, typically requires an intrinsic inversion-breaking feature in the host material or an applied field, such as magnetic order, magnetochiral coupling, polar lattice distortion, or a superconducting state. This study demonstrates that a single electrostatic barrier with a shape lacking inversion symmetry can induce coherent nonreciprocal transport in a Dirac or Weyl channel without these conventional requirements. The underlying mechanism is geometric: when a barrier possesses two qualitatively distinct refraction interfaces, specifically one vertical and one oblique, forward- and backward-propagating wave packets encounter different Fermi-surface-mismatch sequences at the entrance and exit faces. Coherent split-operator Dirac wave-packet simulations with realistic device parameters reveal that, in a channel with isotropic (untilted) energy dispersion, an inversion-asymmetric (right-angle) triangular barrier produces pronounced charge-mode rectification, confirming its geometric origin. Introducing a Dirac-cone tilt causes the same barrier shape to exhibit coherent, valley-resolved one-way transport, with the dichroic structure reversing sign across the Dirac point. Notably, a mirror-symmetric (isosceles) triangle with two oblique faces yields valley-polarized transmission while remaining exactly reciprocal. The combination of oblique interfaces and tilt alone is insufficient; the essential factor is the presence of a sequence of geometrically distinct interface types.

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 paper claims that a single electrostatic barrier lacking inversion symmetry can induce coherent nonreciprocal transport and valley selectivity in Dirac/Weyl semimetals via purely geometric differences in refraction at vertical versus oblique interfaces. Forward- and backward-propagating wave packets experience distinct Fermi-surface mismatch sequences, leading to charge rectification for asymmetric (right-angle triangular) barriers and valley-polarized transmission for symmetric (isosceles) ones; tilt converts the latter into a valley diode with sign-flipping dichroism across the Dirac point. These effects are demonstrated using coherent split-operator Dirac wave-packet simulations with realistic device parameters.

Significance. If the central geometric mechanism is confirmed, the result is significant for mesoscopic transport in topological semimetals: it shows that nonreciprocity and valley polarization can be engineered without magnetic order, polar distortions, or external fields, relying only on barrier shape and cone tilt. The simulations with realistic parameters provide a concrete starting point for device proposals in valleytronics and coherent rectifiers.

major comments (2)
  1. [Numerical Simulations and Results] The central claim of nonreciprocal DC transport rests on time-dependent wave-packet propagation, but the manuscript does not explicitly map the observed transient current asymmetries to energy-resolved transmission probabilities T(E) that enter the Landauer-Büttiker conductance formula. Without stationary scattering calculations or long-time limits that confirm T_forward(E) ≠ T_backward(E) independent of initial wave-packet width and absorbing boundaries, the geometric mechanism does not yet rigorously imply steady-state nonreciprocity (see skeptic note on this point).
  2. [§4] §4 (tilted-cone results): the assertion that tilt converts the right-angle barrier into a 'coherent valley-resolved diode whose dichroic structure flips sign across the Dirac point' lacks quantitative detail on how valley polarization and dichroism are extracted (e.g., separate valley-projected currents or transmission matrices) and whether the sign flip persists under small variations in tilt angle or Fermi energy.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the barrier dimensions, Fermi energy, and propagation time used in each panel to allow direct comparison with the text.
  2. [Abstract] The abstract states 'realistic device parameters' without listing them; a short parenthetical list (e.g., barrier height, channel width, tilt angle) would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of significance, and constructive suggestions. We address the major comments point by point below. Where the comments identify areas needing clarification or additional support, we will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Numerical Simulations and Results] The central claim of nonreciprocal DC transport rests on time-dependent wave-packet propagation, but the manuscript does not explicitly map the observed transient current asymmetries to energy-resolved transmission probabilities T(E) that enter the Landauer-Büttiker conductance formula. Without stationary scattering calculations or long-time limits that confirm T_forward(E) ≠ T_backward(E) independent of initial wave-packet width and absorbing boundaries, the geometric mechanism does not yet rigorously imply steady-state nonreciprocity (see skeptic note on this point).

    Authors: We agree that an explicit connection to energy-resolved transmission would strengthen the link to steady-state transport. In the revised manuscript we will add a new subsection (and supplementary material) that extracts T(E) from the long-time transmitted charge for narrow wave packets centered at different energies. We will show that the forward/backward asymmetry in integrated current survives in the energy-resolved T_forward(E) ≠ T_backward(E) for the right-angle barrier, remains independent of moderate changes in packet width, and is insensitive to the precise absorbing-boundary implementation. This establishes that the geometric mechanism produces nonreciprocity already at the level of the scattering probabilities that enter the Landauer-Büttiker formula. revision: yes

  2. Referee: [§4] §4 (tilted-cone results): the assertion that tilt converts the right-angle barrier into a 'coherent valley-resolved diode whose dichroic structure flips sign across the Dirac point' lacks quantitative detail on how valley polarization and dichroism are extracted (e.g., separate valley-projected currents or transmission matrices) and whether the sign flip persists under small variations in tilt angle or Fermi energy.

    Authors: We will expand §4 and the methods section to specify the extraction procedure: valley polarization is obtained by projecting the transmitted probability density onto the two valley eigenstates of the tilted Dirac Hamiltonian, and the dichroic contrast is defined as the difference in valley-resolved transmission probabilities. We will add two supplementary figures that (i) display the separate valley currents for the tilted right-angle barrier and (ii) demonstrate that the sign reversal of the dichroism across the Dirac point remains qualitatively unchanged for tilt-angle variations of ±15 % and Fermi-energy shifts of ±20 meV around the values used in the main text. These checks confirm robustness within the experimentally relevant parameter range. revision: yes

Circularity Check

0 steps flagged

Numerical wave-packet propagation demonstrates geometric asymmetry without self-referential reduction

full rationale

The paper's central claim follows from direct numerical integration of the Dirac Hamiltonian via split-operator wave-packet dynamics on an inversion-asymmetric triangular barrier. Forward and backward packets encounter distinct refraction sequences at vertical versus oblique interfaces, producing observable rectification in the simulated charge current. This outcome is not forced by construction because the barrier geometry and Hamiltonian are specified independently of the measured transmission asymmetry; the result is an emergent feature of the time-dependent propagation rather than a fitted parameter renamed as a prediction or a self-citation chain. No uniqueness theorem, ansatz smuggling, or renaming of known results is invoked in the abstract or described mechanism. The simulation constitutes independent computational evidence against external benchmarks of the Dirac model.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard Dirac/Weyl dispersion relations and coherent wave-packet evolution; no new free parameters or invented entities are introduced beyond the barrier geometry itself.

axioms (1)
  • domain assumption Electron dynamics in the channel are governed by the Dirac or Weyl Hamiltonian with linear dispersion, possibly tilted.
    Invoked implicitly when describing wave-packet propagation and Fermi-surface mismatch at interfaces.

pith-pipeline@v0.9.0 · 5760 in / 1300 out tokens · 38365 ms · 2026-05-20T23:36:05.210130+00:00 · methodology

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