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REVIEW 2 major objections 4 minor 45 references

Tomographic electrons in a Corbino disk create an extended electrode boundary layer that superballistically injects current and enhances magnetoresistance, with a curvature-tunable slip that may explain anomalous viscosity scaling.

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2026-07-11 06:05 UTC pith:TIR6XNQL

load-bearing objection Clean asymptotic theory for electrode-driven tomographic flow in Corbino disks that produces a curvature-tunable magnetoresistance enhancement and three clear B-field regimes. the 2 major comments →

arxiv 2607.05540 v1 pith:TIR6XNQL submitted 2026-07-06 cond-mat.mes-hall cond-mat.quant-gascond-mat.stat-mech

Magnetotransport of tomographic electrons in a Corbino disk

Nitay Ben-Shachar , Johannes Hofmann This is my paper
classification cond-mat.mes-hall cond-mat.quant-gascond-mat.stat-mech
keywords tomographic transportCorbino diskelectron hydrodynamicsmagnetoresistanceboundary layersodd-parity modessuperballistic conductanceFermi liquid
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

In clean two-dimensional electron gases, Pauli blocking makes odd-parity deformations of the Fermi surface live much longer than even-parity ones. The resulting “tomographic” transport cannot be captured by ordinary hydrodynamics. This paper solves the kinetic equation for such electrons flowing between concentric electrodes in a Corbino disk. Near each electrode an extended non-equilibrium boundary layer forms; inside it the electrode conductance reaches twice the Sharvin value (superballistic injection) and the azimuthal velocity acquires an anomalously large slip that grows with electrode curvature. The enhanced slip produces a parametric boost of the quadratic magnetoresistance coefficient. As magnetic field is raised the coefficient passes through three successive regimes—tomographic, hydrodynamic, then Ohmic—separated by the two mean free paths. The weak-field tomographic corrections carry temperature and density scalings opposite to Fermi-liquid viscosity, offering a possible account of the anomalous viscosity reported in recent Corbino experiments.

Core claim

Tomographic flow in a Corbino disk generates an extended boundary layer of thickness set by the geometric mean of the short even-mode and long odd-mode mean free paths. Inside that layer current is injected superballistically (electrode conductance saturating twice the Sharvin value) and the azimuthal velocity obeys a curvature-dependent slip condition. The resulting enhancement of the quadratic magnetoresistance coefficient is therefore geometry-tunable and is rapidly suppressed once the cyclotron radius falls below the odd-mode mean free path, producing three distinct magnetic-field regimes whose weak-field scaling can mimic anomalous viscosity.

What carries the argument

Matched asymptotic expansion of the linearized Fermi-liquid kinetic equation in the even-mode Knudsen number ke ≪ 1. The expansion yields bulk Stokes–Ohm equations corrected by long-lived odd modes, together with tomographic boundary-layer solutions that enforce both the superballistic electrode condition and the curvature-dependent slip law used to compute the magnetoresistance.

Load-bearing premise

The collision integral is replaced by a simple fixed-rate model that assigns one short lifetime to every even mode and one long lifetime (with power-law angular dependence) to every odd mode; this model is assumed to stay accurate inside the curved electrode layers where the distribution is far from local equilibrium.

What would settle it

Measure the quadratic magnetoresistance coefficient versus magnetic field in a Corbino disk of known radii: if the coefficient first drops when the cyclotron radius becomes comparable to the expected odd-mode mean free path and later rises when it reaches the even-mode mean free path, and if the size of the low-field enhancement scales with the inverse of the inner electrode radius, the central claim is confirmed; absence of either signature falsifies it.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The strength of the tomographic correction can be dialed by changing only the inner electrode radius, giving experimental control over the anomalous scaling.
  • Moderate magnetic fields that suppress the odd-mode layer recover ordinary hydrodynamic viscosity, allowing a cleaner extraction of the Fermi-liquid viscosity from the same device.
  • The non-monotonic field dependence of the magnetoresistance coefficient itself becomes a diagnostic of the two distinct mean free paths.
  • Weak-field temperature and density scalings opposite to Fermi-liquid theory appear naturally once electrode boundary layers are treated, offering a route to reconcile existing viscosity data.

Where Pith is reading between the lines

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

  • Because the slip condition depends explicitly on electrode curvature, a series of Corbino disks with systematically varied inner radii should map out the tomographic contribution independently of bulk scattering rates.
  • The same matched-expansion machinery should apply to other electrode-driven geometries (e.g., multi-terminal Hall bars), predicting analogous superballistic contact resistances whenever long-lived odd modes are present.
  • If the odd-mode mean free path can be extracted from the first crossover field, its measured density and temperature dependence would furnish a direct experimental test of the p = 4 Pauli-blocking prediction.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper develops a matched asymptotic expansion of the linearized Fermi-liquid kinetic equation for tomographic electron flow in a Corbino disk, treating even- and odd-parity modes with disparate mean free paths. It identifies an extended tomographic boundary layer of thickness √(ℓ_e ℓ_o) near the electrodes that produces superballistic electrode conductance saturating twice the Sharvin value and a curvature-dependent azimuthal slip velocity. These effects parametrically enhance the quadratic magnetoresistance coefficient α, which exhibits three magnetic-field regimes (tomographic at weak B when r_c ≳ k_o, hydrodynamic at intermediate fields, and Ohmic at large B). The weak-field tomographic corrections carry anomalous density and temperature scalings that may reconcile the non-Fermi-liquid viscosity extracted from recent Corbino experiments.

Significance. If correct, the work supplies a concrete, geometry-tunable mechanism that converts the long-lived odd modes of a 2D Fermi liquid into measurable magnetoresistance signatures, thereby offering a route to extract both even- and odd-mode mean free paths from a single device. Strengths include a systematic O(k_e) expansion that recovers known bulk Stokes–Ohm equations while deriving new electrode boundary conditions, analytic bulk solutions in terms of modified Bessel functions, numerical layer functions, and direct benchmarks against full kinetic-equation solutions (error ≤9 % at k_e=0.1). The superballistic conductance result saturates a model-independent upper bound, and the predicted non-monotonic α(B) is a sharp, falsifiable signature of tomography.

major comments (2)
  1. Paragraph after Eq. (3) and End Matter: the fixed-relaxation-time collision model (constant γ_e for even m≥2, γ_MC_m=(γ'm^p+γ_e)^{-1} for odd m≥3) is assumed to remain accurate inside the curved electrode layers where the distribution is far from local equilibrium. While the leading electrode conductance saturates the model-independent Raichev bound and the p=0 asymptotics match full numerics of Eq. (1) to ≤9 %, the more realistic p=4 case is shown only for the layer functions Y_E and T_E; a corresponding full-device magnetoresistance comparison for p=4 would strengthen that the three-regime structure and curvature-tuned slip survive a more faithful collision operator.
  2. Discussion of experimental link (final two paragraphs): the claim that tomographic corrections “may account for” the anomalous viscosity scaling reported in Ref. [21] remains qualitative. The paper correctly notes that the relative weight of the (τ'_η)^{-1}∼n^4/T^4 term can be tuned by electrode curvature, yet no explicit fit or estimate of the prefactors for the device parameters of [21] is provided; without this, the connection stays suggestive rather than diagnostic.
minor comments (4)
  1. Fig. 2 caption and main text: the hydrodynamic reference curve is shown only for 1/r_c=0.1; adding the corresponding hydrodynamic curve for 1/r_c=0.2 would make the shaded tomographic correction easier to compare across panels.
  2. Eq. (13) and surrounding text: the conventional slip length ℓ_slip=(32/15π)ℓ_e is quoted without a brief reminder of its origin (diffuse-wall kinetic theory); a short parenthetical citation would help non-specialist readers.
  3. End Matter, Eq. (21b): the finite-wavelength correction u^{(1)}_{FW|θ} is stated to lack a closed form; noting that it vanishes identically for G→∞ (as used in the main figures) would clarify why the clean-limit analytics remain simple.
  4. References: the recent channel-geometry companion papers [34,35] are cited, but a one-sentence contrast of the electrode-driven versus wall-driven boundary layers would orient the reader more quickly.

Circularity Check

1 steps flagged

Minor self-citation of bulk Stokes-Ohm expansion and slip form from authors' prior work [34]; electrode boundary layers, superballistic conductance, and Corbino magnetoresistance are re-derived here and validated against independent numerics of the kinetic equation.

specific steps
  1. self citation load bearing [paragraph after Eq. (6c) and text surrounding Eq. (13)]
    "This expansion is independent of the flow domain boundaries and thus identical to the bulk expansion in [34]. For brevity, we omit details of this derivation... A velocity slip condition arises at O(k_e), [Eq. (13)] which is identical to the condition derived in [34] at a diffuse boundary."

    The bulk force-balance equations and the functional form of the tomographic slip are imported from the authors' own prior work rather than re-derived in full. While the electrode-layer problem and Corbino application are new, the load-bearing hydrodynamic skeleton of the calculation rests on that self-citation.

full rationale

The paper's central results (extended tomographic electrode layers, saturation of the Raichev superballistic bound G_e = 4/(\pi k_e), curvature-dependent slip that parametrically enhances the quadratic magnetoresistance coefficient \alpha, and the three magnetic-field regimes) are obtained by matched asymptotic expansion of the kinetic equation specialized to perfect electrodes, followed by explicit solution of the Corbino Stokes-Ohm problem and direct numerical checks of Eq. (1) (error \le9 % in Figs. 2-3). No parameter is fitted to data and re-labeled a prediction; the experimental link remains a qualitative suggestion. The only self-citations that appear are (i) the statement that the bulk expansion is identical to that already performed in the authors' arXiv:2503.14461 and (ii) the observation that the O(k_e) slip condition coincides with the diffuse-wall result of the same paper. These are used for brevity and cross-check, not as the sole justification of the electrode-driven phenomena that constitute the new claim. The collision-rate parametrization is taken from independent exact-diagonalization literature. Consequently the derivation chain does not reduce by construction to its inputs, and the circularity score remains low.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 1 invented entities

The central claim rests on a standard linearized Fermi-liquid kinetic equation plus a phenomenological but literature-supported relaxation-time model for even/odd modes, perfect-electrode injection boundary conditions, and a controlled asymptotic expansion in the even-mode Knudsen number. No new particles or forces are postulated; free parameters are physical mean-free-path ratios and geometry that can be varied experimentally.

free parameters (2)
  • odd-mode exponent p and ratio γ'/γ_e
    Chosen as p=0 (constant odd rate) or p=4 (from exact diagonalization) with γ'/γ_e =0 or 1; controls the precise shape of the tomographic layer functions but not the existence of the three regimes.
  • even- and odd-mode Knudsen numbers k_e, k_o and Gurzhi number G
    Dimensionless ratios of mean free paths to device size; treated as free inputs that set the regime boundaries and the magnitude of the enhancement.
axioms (4)
  • domain assumption Linearized stationary Fermi-liquid kinetic equation with magnetic field and diagonal angular collision operator
    Standard starting point for 2D electron hydrodynamics/tomography; invoked from Eq. (1) onward.
  • domain assumption Even modes relax at single rate γ_e; odd modes at long rate interpolating between γ'm^p and γ_e
    Taken from exact-diagonalization literature [26,38,39]; used to define k_e and k_o after Eq. (3).
  • domain assumption Perfect electrodes inject/drain quasiparticles with fixed chemical potential (Eq. 11)
    Idealized contact model that produces the superballistic conductance; alternative diffuse or partially specular contacts would alter the layer.
  • standard math Matched asymptotic expansion in small even-mode Knudsen number k_e ≪1 with k_o,G ~ O(1)
    Systematic expansion that yields bulk hydrodynamics plus tomographic boundary layers; validity checked numerically for k_e=0.1.
invented entities (1)
  • tomographic boundary layer of thickness √(ℓ_e ℓ_o) independent evidence
    purpose: Captures non-equilibrium odd-mode dynamics near electrodes that generate the enhanced slip and superballistic injection
    Derived rather than postulated; thickness follows from the two-scale scattering rates already present in the collision model. Independent evidence is the numerical match to the full kinetic equation and the predicted curvature dependence that can be tested by varying r_1.

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read the original abstract

In clean electron gases at low-to-moderate temperatures, odd-parity modes of the Fermi surface are anomalously long-lived due to Pauli blocking, giving rise to ``tomographic transport'' that is not captured by a hydrodynamic model. Here we show that tomographic flow in a Corbino disk induces an extended boundary layer near electrodes with superballistic transport and enhanced slip velocity, which leads to a parametric enhancement of the quadratic magnetoresistance coefficient. The enhancement depends explicitly on the electrode curvature, allowing its strength to be controlled by the device geometry. The magnetoresistance coefficient reveals three distinct regimes as a function of magnetic field: a tomographic regime at weak fields; a hydrodynamic regime at intermediate fields, reached when the cyclotron radius becomes comparable to a large odd-mode mean free path; and a conventional Ohmic regime at large fields, reached when the cyclotron radius becomes comparable to the short even-mode mean free path. The tomographic regime is characterized by an anomalous dependence of the magnetoresistance on temperature and density, which may account for recent experimentally observed anomalous scaling of the electron viscosity.

Figures

Figures reproduced from arXiv: 2607.05540 by Johannes Hofmann, Nitay Ben-Shachar.

Figure 1
Figure 1. Figure 1: FIG. 1. Left: Schematic of transport in a Corbino disk with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Resistance as a function of the magnetic field [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Tomographic layer functions (a) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

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Reference graph

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