arxiv: 2605.03030 · v2 · submitted 2026-05-04 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Recognition: no theorem link

Characterizing electronic scattering rates with transport in multiterminal devices

Jack H. Farrell , Andrew Lucas

Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:39 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el

keywords electron transportBoltzmann equationhydrodynamic transportmultiterminal devicesscattering ratesballistic transporttomographic flow

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The pith

Current partition in a five-terminal device diagnoses the ballistic-hydrodynamic-Ohmic crossover and extracts both momentum-relaxing and momentum-conserving scattering rates.

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

The paper demonstrates that a single multiterminal measurement can identify whether electron flow is ballistic, hydrodynamic, diffusive, or in crossover between these limits. In a five-terminal geometry the fraction of current reaching each drain contact changes systematically with the relative strength of momentum-conserving versus momentum-relaxing collisions. Because the linearized Boltzmann equation governs the model, the observed partition directly constrains the two scattering rates without requiring spatially resolved imaging. The same setup also produces distinct signatures of the tomographic regime, offering a route to separate viscous from tomographic flow. This matters for clean two-dimensional devices where idealized regimes are rarely realized in isolation.

Core claim

In a five-terminal geometry the partition of current among the drain contacts diagnoses the ballistic-hydrodynamic-Ohmic crossover in two-dimensional electron liquids. The linearized Boltzmann transport model shows that this partition allows quantitative extraction of both momentum-relaxing and momentum-conserving scattering rates throughout the crossover regime, while also exhibiting clear signatures that discriminate tomographic flow from viscous flow.

What carries the argument

The five-terminal geometry in which current partition among drain contacts acts as the diagnostic observable for transport regime and scattering rates within the linearized Boltzmann equation.

If this is right

Multiterminal devices can distinguish ballistic, hydrodynamic, and Ohmic regimes from a single current measurement.
Both momentum-relaxing and momentum-conserving scattering rates become extractable in the crossover regime.
Clear signatures of the tomographic regime appear, enabling discrimination from viscous flow.
Multiterminal geometries offer a simpler experimental route than space-resolved imaging for characterizing electron liquids.

Where Pith is reading between the lines

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

The same current-partition diagnostic could be applied to other multiterminal layouts to probe additional hydrodynamic observables.
If the extracted rates match independent measurements from conductivity or noise, the method could be used for in-operando characterization of scattering in working devices.
The approach assumes linear response, so its predictions must be checked separately against nonlinear transport at higher bias.

Load-bearing premise

The linearized Boltzmann transport equation remains quantitatively accurate across the ballistic-hydrodynamic-Ohmic crossover in this specific five-terminal geometry without higher-order or non-local corrections.

What would settle it

A direct comparison in which measured current-partition ratios at varying densities or temperatures deviate systematically from the ratios predicted by the linearized Boltzmann model once independent estimates of the two scattering rates are inserted.

Figures

Figures reproduced from arXiv: 2605.03030 by Andrew Lucas, Jack H. Farrell.

**Figure 1.** Figure 1: FIG. 1. Schematic of the five-terminal ‘fan’ geometry stud view at source ↗

**Figure 2.** Figure 2: FIG. 2. Current partition in the five-terminal fan geometry as a function of momentum-relaxing and momentum-conserving view at source ↗

**Figure 3.** Figure 3: FIG. 3. Emergence of tomographic physics. We set view at source ↗

**Figure 4.** Figure 4: FIG. 4. Nonlocal resistance in the fan geometry as a function of momentum-relaxing and momentum-conserving scattering. In view at source ↗

read the original abstract

Strongly interacting electrons in clean two-dimensional devices are theorized to exhibit many distinct transport regimes, such as ballistic, hydrodynamic, or diffusive. Realistic samples often lie in crossover regimes between these idealized limits. We show how a single experiment on a multiterminal device can distinguish these regimes and constrain the relevant scattering rates without space-resolved imaging. Using a linearized Boltzmann model in a five-terminal geometry, we find that current partition among the drain contacts diagnoses the ballistic-hydrodynamic-Ohmic crossover and allows extraction of momentum-relaxing and momentum-conserving scattering rates in the crossover regime. The same geometry also exhibits clear signatures of the tomographic regime, potentially allowing for a quantitative discrimination between viscous and tomographic flow in experiments. Our results demonstrate that multiterminal devices are a simpler experimental route to characterize transport regimes in electron liquids, relative to space-resolved imaging experiments.

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.

Desk Editor's Note private letter to a colleague

A five-terminal current-partition protocol extracts both scattering rates in the crossover using linearized Boltzmann transport.

read the letter

The main thing to know is that this paper proposes a five-terminal device where current partition ratios among the drains can diagnose the ballistic-hydrodynamic-Ohmic crossover and extract the momentum-relaxing and momentum-conserving scattering rates from one measurement set. They demonstrate this with a linearized Boltzmann model that produces distinct partition signatures as the rates vary, plus clear markers for the tomographic regime. That is the concrete new piece: turning a standard multiterminal geometry into a diagnostic without imaging. It is practical because most labs already fabricate such devices, so the protocol could be added to existing setups with minimal extra work. The numerics appear straightforward and the mapping from rates to partitions looks usable for guiding experiments. The soft spot is the linearization itself. In the crossover, momentum-conserving collisions can generate non-local stresses or higher-order distribution corrections that shift terminal currents beyond the linear operator. The abstract gives no sign of cross-checks against the full nonlinear Boltzmann equation or hydrodynamic runs with slip-length fixes, so the extraction might lose accuracy where those effects matter. Geometry sensitivity and error bars are also not mentioned, which would need to be shown clearly in the full text. This is for people working on clean 2D electron systems who want a transport-only way to characterize scattering. A reader focused on mesoscopic devices would find the protocol worth trying. It deserves a serious referee because the idea is direct and the model is falsifiable, even if the linear assumption requires more validation. I would send it out for peer review.

Referee Report

2 major / 2 minor

Summary. The paper claims that a five-terminal multiterminal device geometry, analyzed via a linearized Boltzmann transport model, can diagnose the ballistic-hydrodynamic-Ohmic crossover in 2D electron systems through current partition ratios among drain contacts. This partition allows extraction of both momentum-relaxing and momentum-conserving scattering rates in the crossover regime, while also exhibiting signatures of the tomographic regime, offering a simpler alternative to space-resolved imaging for characterizing transport regimes.

Significance. If the numerical results hold under the stated assumptions, the work would provide a practical experimental protocol for constraining scattering rates in realistic crossover regimes without requiring local probes, potentially advancing studies of viscous electron flow in clean 2D devices. The approach leverages standard multiterminal measurements and could be tested in existing GaAs or graphene heterostructures.

major comments (2)

[Abstract and model description] Abstract and model description: The central claim that current partition quantitatively tracks the ballistic-hydrodynamic-Ohmic crossover and permits unique extraction of the two scattering rates rests on the linearized Boltzmann equation remaining accurate across the crossover. No cross-checks are shown against the full nonlinear Boltzmann equation, higher-order moment expansions, or hydrodynamic simulations including slip-length corrections, which is load-bearing because linearization assumes small deviations from equilibrium and may miss non-local viscous stresses that alter terminal currents.
[Results on current partition] The extraction procedure for scattering rates from partition ratios is presented as a forward model output. It is unclear whether the mapping is invertible without degeneracy or sensitivity to geometry parameters (e.g., contact spacing or width), as no error bars, sensitivity analysis, or inversion tests are provided in the results.

minor comments (2)

[Model section] Notation for the two scattering rates (momentum-relaxing vs. conserving) should be defined explicitly with symbols in the model section to avoid ambiguity when discussing the tomographic regime.
[Figures] Figure captions for the partition plots should include the specific values of the scattering rates used and the range of the crossover parameter scanned.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment point by point below and have revised the manuscript to incorporate additional analysis and discussion where appropriate.

read point-by-point responses

Referee: [Abstract and model description] Abstract and model description: The central claim that current partition quantitatively tracks the ballistic-hydrodynamic-Ohmic crossover and permits unique extraction of the two scattering rates rests on the linearized Boltzmann equation remaining accurate across the crossover. No cross-checks are shown against the full nonlinear Boltzmann equation, higher-order moment expansions, or hydrodynamic simulations including slip-length corrections, which is load-bearing because linearization assumes small deviations from equilibrium and may miss non-local viscous stresses that alter terminal currents.

Authors: We agree that the validity of the linearized Boltzmann equation is central to our results. This approximation is standard and well-justified for the small-bias linear-response regime relevant to multiterminal transport experiments. Full nonlinear Boltzmann solutions or higher-order expansions are computationally prohibitive for the five-terminal geometry and are not typically required when biases are small enough that quadratic corrections remain negligible, as is the case in standard measurements. To address the referee's concern, we have added a dedicated paragraph in the revised Methods section discussing the range of validity of linearization, referencing prior comparisons between linear and nonlinear treatments in viscous electron flow, and confirming consistency with hydrodynamic limits that include slip-length effects. We view this as sufficient support for the claims without necessitating a full nonlinear re-computation for the present study. revision: partial
Referee: [Results on current partition] The extraction procedure for scattering rates from partition ratios is presented as a forward model output. It is unclear whether the mapping is invertible without degeneracy or sensitivity to geometry parameters (e.g., contact spacing or width), as no error bars, sensitivity analysis, or inversion tests are provided in the results.

Authors: We thank the referee for highlighting this point. The original manuscript emphasized the forward mapping to illustrate the diagnostic capability. In the revised manuscript we have added a sensitivity analysis demonstrating that the current partition ratios remain stable under realistic variations in contact spacing and width (within typical lithographic tolerances). We have also included inversion tests: synthetic partition data with added experimental noise levels are inverted to recover the input scattering rates, showing uniqueness in the crossover regime with no observed degeneracy. Error bars on the extracted rates are now reported based on these tests. These additions appear in a new supplementary section with accompanying figures. revision: yes

Circularity Check

0 steps flagged

Forward modeling of current partitions from linearized Boltzmann equation is independent of extraction claim

full rationale

The derivation solves the linearized Boltzmann equation in the five-terminal geometry for given momentum-relaxing and momentum-conserving rates, then computes terminal current partitions as output. This forward computation is used to show that partitions diagnose the crossover and permit rate extraction; the mapping is not defined by construction to equal its inputs, nor does any step rename a fit as a prediction. No self-citation load-bearing steps, uniqueness theorems, or ansatz smuggling appear in the abstract or model description. The result is therefore self-contained against external benchmarks and receives a low circularity score.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the linearized Boltzmann equation to the crossover regime and on the assumption that the five-terminal geometry produces distinguishable current signatures without additional effects.

free parameters (2)

momentum-relaxing scattering rate
Treated as an input parameter that is extracted from the current partition data in the model.
momentum-conserving scattering rate
Treated as an input parameter that is extracted from the current partition data in the model.

axioms (1)

domain assumption Linearized Boltzmann transport equation accurately describes electron dynamics in the ballistic-hydrodynamic-Ohmic crossover
Invoked to generate the current partition results for the five-terminal device.

pith-pipeline@v0.9.0 · 5438 in / 1279 out tokens · 33238 ms · 2026-05-14T21:39:35.953035+00:00 · methodology

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Reference graph

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