Microwave-regime demonstration of plasmonic non-reciprocity in a flowing two-dimensional electron gas

Amir Yacoby; Donhee Ham; Han Sae Jung; Jingyee Chee; Kenneth West; Loren Pfeiffer; Shannon Harvey

REVIEW 3 major objections 4 minor 14 references

Microwave-regime demonstration of plasmonic non-reciprocity in a flowing two-dimensional electron gas

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read In a gated GaAs two-dimensional electron gas carrying a DC current, microwave network analysis directly resolves forward and backward plasmon speeds differing by the electron drift speed, confirming $v_{p,\pm} = v_{p,0} \pm v_0$ at 10–50…

desk verdict A clean, modest microwave-regime confirmation of a known 2DEG plasmon effect; the main weakness is a missing zero-current phase baseline, but the central extraction is independent and worth refereeing. read the letter →

arxiv 2502.05904 v1 pith:DJEDH3IO submitted 2025-02-09 cond-mat.mes-hall

Jingyee Chee , Han Sae Jung , Shannon Harvey , Kenneth West , Loren Pfeiffer , Amir Yacoby , Donhee Ham This is my paper · ORCID

classification cond-mat.mes-hall

keywords plasmonicnon-reciprocitytwo-dimensionalelectrongasmicrowavenetworkanalysisscatteringparameterskineticinductanceGaAs/AlAsheterostructurephasedelaydriftspeed

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

This paper reports a direct, quantitative demonstration of plasmonic non-reciprocity in the microwave regime. In a gated two-dimensional electron gas with a DC current, the authors measure the phase difference between the forward and backward scattering parameters $s_{12}$ and $s_{21}$ and show it grows linearly with frequency, with a slope that matches $4\pi L v_0 f / v_{p,0}^2$. The drift speed $v_0$ extracted from this microwave measurement agrees with the DC-transport value $I_0/(W e n_0)$ to within 10% for currents of 0.1–0.2 mA, directly confirming that $v_{p,+} = v_{p,0} + v_0$ and $v_{p,-} = v_{p,0} - v_0$. The result matters because it brings a phenomenon previously studied at THz and optical frequencies into a phase-coherent microwave measurement, where non-reciprocal device concepts could be developed and tested.

What carries the argument

The central object is the gated 2DEG strip treated as a plasmonic transmission line, with per-unit-length kinetic inductance $L_k = m^*/(n_0 e^2 W)$ and per-unit-length geometric capacitance $C$ giving the zero-current plasmon speed $v_{p,0} = (L_k C)^{-1/2}$, which the authors measure to be about $c/235$ at the operating bias. The measurement identity is $|\phi_+ - \phi_-| \approx 4\pi L v_0 f / v_{p,0}^2$, obtained from $v_{p,\pm} = v_{p,0} \pm v_0$ under $v_{p,0} \gg v_0$. A two-port network analyzer records the phases of $s_{12}$ and $s_{21}$; their difference plotted against frequency is a straight line whose slope yields $v_0$ once $L$ and $v_{p,0}$ are known, and this phase-slope method is what isolates the tiny drift-induced speed asymmetry from the much larger plasmon speed.

What would settle it

Fabricate an identical device but etch away the 2DEG from under the gate (or deplete it), then measure $s_{12}$ and $s_{21}$ phases: if a frequency-dependent phase difference of comparable magnitude to Eq. (5) remains, the signal is not purely plasmonic and the extracted drift speeds are not valid.

Watch

Extended reading notes

Core claim

The central discovery is a direct, quantitative confirmation that a drifting electron gas makes plasmon propagation direction-dependent at microwave frequencies. The phase difference between $s_{12}$ and $s_{21}$ increases linearly with frequency for a fixed DC current, and the slope of that line, equated to $4\pi L v_0 / v_{p,0}^2$, yields a drift speed that tracks the DC-transport prediction $v_0 = I_0/(W e n_0)$ to better than 10% for the larger currents. An example reported resolution is forward and backward wave speeds of $4.26 \times 10^{-3} c \pm 8.97 \times 10^{-6} c$, where $c$ is the speed of light. The experiment thereby establishes the relation $v_{p,\pm} = v_{p,0} \pm v_0$ at 10–50 GHz, not merely a qualitative asymmetry.

Load-bearing premise

The extraction treats the measured s-parameter phase as coming almost entirely from plasmon propagation through the gated 2DEG, with the phase delay from the coplanar waveguides assumed negligible; if that CPW phase is non-negligible or asymmetric, both the extracted zero-current speed $v_{p,0}$ and the drift speed $v_0$ are biased.

Editorial extensions

If this is right

The linear $|\phi_+ - \phi_-|$ versus frequency traces confirm the predicted $v_{p,\pm} = v_{p,0} \pm v_0$ form at 10–50 GHz with no free parameter beyond $L$, $v_{p,0}$, and the DC current.
The microwave-extracted drift speed matches $I_0/(W e n_0)$ to within 10% at $I_0 = 0.1$–$0.2$ mA and to within 5% in slope, providing an independent, AC-based measurement of electron drift.
The same setup measures $v_{p,0}$ and $n_0$ at zero current via Eq. (4), so a single device yields both the reciprocal and non-reciprocal plasmon parameters.
With $v_{p,0} \approx c/235$ and $v_0 \approx 2.69 \times 10^3$ m/s at $I_0 = 0.2$ mA, the reflection gain $G = (v_{p,0}+v_0)/(v_{p,0}-v_0)$ is about 1.004, too small for practical use; the paper argues that approaching the quantum-capacitance-dominated limit $v_{p,0,\min} = v_F/\sqrt{2}$ would be needed to enhance it.
These results bring plasmonic non-reciprocity into the microwave range, where network analyzers and standard electronic measurement techniques can be applied directly to the phenomenon.

Reading between the lines

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

Beyond the paper, if the phase-slope technique is as clean as this single device suggests, it could be applied to other two-dimensional conductors such as graphene to map drift velocity versus position locally, something DC transport cannot resolve spatially.
Beyond the paper, the reported wave-speed uncertainty of about $9 \times 10^{-6} c$ is far below the roughly 0.4% forward-backward split at 0.2 mA, so the method may resolve even smaller drift speeds; constructing a full systematic uncertainty budget (including CPW phase and ungated regions) would sharpen this claim.
Beyond the paper, a straightforward control experiment—measuring a device with the gated 2DEG etched away or depleted—would isolate whether any residual frequency-dependent $s_{12}$–$s_{21}$ phase split remains, directly testing the CPW-phase-loading assumption.
Beyond the paper, fabricating devices with different gate-to-2DEG separations $d$ and checking that the extracted $v_0$ slope is independent of $d$ would provide a quantitative check of the fringing-field analysis and the robustness of the drift-speed extraction.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The one thing you should know: this is a straightforward, well-executed experimental demonstration of plasmonic non-reciprocity in a gated GaAs 2DEG at 10–50 GHz, and the central claim holds up. The physics is not new—Eq. (1) is textbook, and non-reciprocity was already seen in THz and Raman work—but the direct, quantitative extraction of vp,+ and vp,− from s-parameter phase delays is new for this regime. That is a real, if modest, contribution: it gives device-oriented people a clean way to measure drift-induced speed splitting without going to THz. The paper is clearly written, the data are internally consistent, and the comparison of the extracted v0 against the DC-transport line v0 = I0/(Wen0) is an independent check with no fitted parameter forcing agreement. That independence is the load-bearing virtue of the paper, and the agreement to within 10% (except at the smallest current) is decent. Credit is also due for the explicit discussion of the gated versus ungated phase delay and the fringing correction, which shows the authors thought about the geometry. The soft spot is precisely where the stress-test points: the analysis before Eq. (4) assumes the CPW phase delay is negligible, and while that is likely true given vp,0 is c/235, there is no zero-current baseline trace of the S12–S21 phase difference, no quantitative CPW phase budget, and no error bars on v0. The 21% deviation at I0 = 0.05 mA has the signature of a constant slope offset, which is exactly what a parasitic reciprocal phase path would produce. That said, this is an addressable control issue, not a contradiction of the central result. The zero-current data clearly show s12 = s21 intra-device (Fig. 2), so a symmetric parasitic path would cancel; the residual worry is a CPW asymmetry, which is a second-order effect. I would not call the central claim into doubt, and I disagree with any referee who would sink the paper on this alone. For whom is this? Experimental condensed-matter and microwave-engineer readers who want a compact non-reciprocal component or a fast way to characterize drift in 2D conductors. The discussion of degeneracy pressure and vp,0,min is speculative but clearly labeled as a forward-looking application section. The citation pattern is appropriate: the classical theory is credited to Landau–Lifshitz and Dyakonov–Shur, and the prior THz/optical work is cited. No self-citation inflation. Serious referee: yes, send it out. It deserves a careful experimental referee who can ask for the baseline and error bars in revision, rather than a desk reject. My own verdict would be conditional accept after those controls are added.

Referee Report

3 major / 4 minor

Summary. The manuscript reports a microwave network analysis of a gated GaAs two-dimensional electron gas at 4 K. At zero current, the authors extract the slow plasmon speed vp,0 from the frequency slope of the S12/S21 phase over 10–50 GHz and derive n0 from vp,0 through Eq. (3). With a DC current I0, they measure the frequency slope of |arg S12 − arg S21| and, using Eq. (5), extract a drift speed v0. They compare this with the DC-transport value v0 = I0/(Wen0) and report agreement to within 10% for I0 = 0.1–0.2 mA and 21% at I0 = 0.05 mA, with the slopes of the two lines within 5%. They conclude that this confirms vp,± = vp,0 ± v0 in the microwave regime and discuss how the quantum capacitance could be used to enhance non-reciprocity.

Significance. If the controls are adequate, this would be a valuable first microwave-regime demonstration of plasmonic non-reciprocity, obtained by a direct phase-delay measurement rather than by an indirect transport or emission signature. The central extraction in Eq. (5) is simple and parameter-free apart from vp,0, and the comparison with DC transport is not obtained by fitting. The paper is also candid about the likely influence of n0/vp,0 uncertainty and about gate fringing effects. The main risk is that the phase budget and the absence of a zero-current baseline leave the quantitative claim insufficiently controlled; this is a fixable issue rather than a fundamental flaw.

major comments (3)

[Text before Eq. (4) and Fig. 3] The statement that the CPW propagation phase is 'much smaller' than the plasmonic phase is not quantified, and this assumption is load-bearing for both vp,0 in Fig. 2(a) and v0 in Eq. (5). A reciprocal CPW delay biases the absolute phase slope used to obtain vp,0, while any asymmetry between the two CPW paths, impedance-mismatch phase at the contacts, or residual calibration error adds a slope to |arg S12 − arg S21| that is indistinguishable from the drift-induced term of Eq. (5). The authors should provide a numerical phase budget (L_CPW/v_CPW versus L/vp,0), a zero-current (I0 = 0) phase-difference trace showing zero slope, or both. Without such a control, the 21% discrepancy at I0 = 0.05 mA remains consistent with a small constant phase-slope offset and does not by itself confirm the extracted v0 at the lowest current.
[Fig. 3(b) and extraction via Eq. (5)] The v0 data points in Fig. 3(b) are plotted without error bars, and the stated 21%, <10%, and <5% comparisons are not accompanied by confidence intervals. Because the quantitative claim of the paper is the agreement between the microwave-extracted v0 and the DC-transport line, the authors should report the uncertainties on the fitted slopes in Fig. 3(a) and propagate them, together with the uncertainty in vp,0 and L, into the v0 values. This is necessary to decide whether the smallest-current point is actually discrepant or merely within a large uncertainty.
[Eq. (3), Eq. (5), and Fig. 3(b)] The comparison between the microwave result and the DC-transport line is only partially independent: the same zero-current vp,0 enters Eq. (5) directly, and via Eq. (3) it also determines n0 used in v0 = I0/(Wen0). The paper acknowledges this in the paragraph after Fig. 3(b), but it should quantify the sensitivity: for example, how much would a realistic 5% systematic error in vp,0 shift the microwave points and the DC line, and would the stated agreement survive? Without this propagation, the 'sufficient consistency' statement is not fully testable.

minor comments (4)

[Fig. 2(a) caption and text] The caption says 'Phase of s12 or s21'; since at I0 = 0 the expectation is s12 = s21, please state that both were measured and that they were equal within the measurement repeatability, or note any small difference.
[Eq. (3)] The value C□ ≈ 0.13 µF/cm2 should be derived explicitly from the 80-nm gate-to-2DEG distance and the AlGaAs/GaAs permittivity, or the source of this value should be cited, as it is used to convert vp,0 to n0.
[Abstract and conclusions] The phrase 'directly measuring out forward and backward wave speeds' is stronger than the analysis actually does: the experiment measures vp,0 and the phase-difference slope, then uses Eq. (1) to report vp,0 ± v0. The wording should be adjusted to say that the forward and backward speeds are extracted from the phase delays under Eq. (1), rather than measured independently.
[Fringing discussion] The estimate Leff ≈ 136 µm and the 'not realistic' conclusion about Leff ≈ 145 µm are plausible, but no formula or capacitance estimate is provided; a brief calculation of Leff from the gate capacitance would make the robustness argument quantitative.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central non-reciprocity check compares independently extracted microwave drift speeds against an unfitted DC-transport line, with explicit discrepancies reported.

full rationale

Walking the derivation chain: vp,0 is obtained from the zero-current s-parameter phase slope via Eq. (4); n0 is then derived from vp,0 via the standard transmission-line relation Eq. (3). The non-reciprocal measurement extracts v0 from the phase-difference slope via Eq. (5), using this same independently measured vp,0. The DC-transport line v0 = I0/(W e n0) is drawn from I0, W, and the measured n0; it is not fitted to the microwave data. The paper reports explicit disagreements (21% at I0 = 0.05 mA, less than 10% at higher currents), so the agreement is not forced. No parameter is fitted to a subset and then renamed as a prediction; the phase-difference slope is a direct observable. The only shared quantity entering both sides is vp,0/n0 from the reciprocal measurement, which acts as a calibration input rather than as the target conclusion; because the extracted v0 scales as vp,0^2 while the DC-transport v0 scales as n0^{-1} ~ vp,0^{-2}, the comparison is actually stringent rather than tautological. Self-citations (refs 3-7) supply background formulas for 2D plasmonic transmission lines and prior demonstrations; they do not provide a uniqueness theorem and are not load-bearing in the sense of making the result equivalent to an author's earlier assertion. The CPW phase-delay assumption and the ungated-region correction are acknowledged modeling/uncertainty issues, not circular steps. The paper is self-contained against its own data and external transport formula, so no circularity is identified.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The paper's central confirmation rests on a standard gated-2DEG transmission-line model, a classical Doppler shift ansatz, and several simplifying assumptions (negligible CPW phase, constant n0 under current bias, nominal gate capacitance). No new physical entities are introduced. The only hand-set numerical input of consequence is the per-unit-area capacitance C_square used to convert vp0 into n0 for the DC-transport comparison.

free parameters (1)

per-unit-area gate capacitance C_square = 0.13 uF/cm2
Approximate parallel-plate value used in Eq. (3) to convert the measured vp0 into electron density n0, which sets the DC-transport theory line. It is not independently measured in the paper, and an error in C_square directly shifts the comparison.

assumptions (4)

domain assumption Gated 2DEG plasmonic transmission-line model vp0 = (Lk*C)^(-1/2) with Lk = m*/(n0*e^2*W)
Invoked via refs 4-7 to interpret the measured phase slope as a plasmon speed and to derive n0. The model is standard for gated 2DEGs but is assumed rather than independently re-derived here.
domain assumption Doppler velocity addition vp,+ = vp0 + v0 and vp,- = vp0 - v0
Taken from Landau-Lifshitz fluid mechanics and Dyakonov-Shur; this is the central predicted relation the experiment aims to test.
ad hoc to paper Phase delay through the coplanar waveguides is negligible compared with the plasmonic phase delay
Stated before Eq. (4) without a quantitative phase budget. If the CPW delay is non-negligible or asymmetric, the extracted vp0 and v0 are biased.
domain assumption Electron density n0 remains approximately at its zero-current value when V1 and V2 are split to create I0
Assumed in the sentence 'keeping n0 approximately at the value determined at Vbias.' Used to justify applying the zero-current vp0 and n0 in the non-reciprocal analysis.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Microwave-regime demonstration of plasmonic non-reciprocity in a flowing two-dimensional electron gas." pith.science (2026). https://pith.science/paper/DJEDH3IO

@misc{pith2026250205904,
  author       = {Pith},
  title        = {Pith review of: Microwave-regime demonstration of plasmonic non-reciprocity in a flowing two-dimensional electron gas},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DJEDH3IO}},
  note         = {Machine review of arXiv:2502.05904}
}

abstract

The speed of a plasmonic wave in the presence of electron drift in a conductor depends on the wave's propagation direction, with the wave traveling along the drift (`forward wave') faster than the wave traveling against the drift (`backward wave'). Phenomena related to this plasmonic non-reciprocity -- which is relatively more pronounced in two-dimensional conductors than in bulk conductors and could lead to solid-state device applications -- have been studied in THz and optical spectral regimes. Here we demonstrate the plasmonic non-reciprocity at microwave frequencies (10 $\sim$ 50 GHz). Concretely, we conduct, at 4K, a microwave network analysis on a gated GaAs two-dimensional electron gas with electron drift (i.e., DC current), directly measuring out forward and backward wave speeds via their propagation phase delays. We resolve, for example, forward and backward wave speeds of $4.26 \times 10^{-3} \pm 8.97 \times 10^{-6}$ (normalized to the speed of light). Sufficient consistency between the electron drift speed obtained from the microwave measurement and that alternatively estimated by a DC transport theory further confirms the non-reciprocity. We conclude this paper with a discussion on how to enhance the non-reciprocity for real-world applications, where degeneracy pressure would play an important role.

Figures

Figures reproduced from arXiv: 2502.05904 by the authors.

**Figure 2.** FIG. 2. Measurement of reciprocal plasmonic waves ( [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. Measurement of non-reciprocal plasmonic waves for [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

[1]

L. D. Landau and E. M. Liftshitz, Fluid Mechanics , 2nd Edition, Pergamon Press (1987)

work page 1987
[2]

Dyakonov and M

M. Dyakonov and M. Shur, Phys. Rev. Lett. 71 , 2465 (1993)

work page 1993
[3]

Andress, H

W. Andress, H. Yoon, K. Yeung, L. Qin, K. West, L. Pfeiffer, and D. Ham, Nano Lett. , 12 , 2272 (2012)

work page 2012
[4]

H. Yoon, K. Yeung, P. Kim, and D. Ham, Phil. Trans. R. Soc. A 372 , 20130104 (2014)

work page 2014
[5]

H. Yoon, K. Yeung, V. Umansky, and D. Ham, Nature 488 , 65 (2012)

work page 2012
[6]

H. Yoon, C. Forsythe, L. Wang, N. Tombros, K. Watanabe, T. Taniguchi, J. Hone, P. Kim, and D. Ham, Nat. Nanotechnol. 9 , 594 (2014)

work page 2014
[7]

Yeung, H

K. Yeung, H. Yoon, W. Andress, K. West, L. Pfeiffer, and D. Ham, Appl. Phys. Lett. 102 , 021104 (2013)

work page 2013
[8]

L. C. \' O . S\' u illeabh\' a in, H. P. Hughes, A. C. Churchill, D. A. Ritchie, M. P. Grimshaw, and G. A. C. Jones, J. Appl. Phys. 76 , 1701 (1994)

work page 1994

Show all 14 references

[9]

Lusakowski, W

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, J. Appl. Phys. 97 , 064307 (2005)

2005
[10]

W. Knap, J. Lusakowski, T. Parenty, S. Bollaert, A. Cappy, V. V. Popov, and M. S. Shur, Appl. Phys. Lett. 84 , 2331 (2004)

2004
[11]

Dyakonova, A

N. Dyakonova, A. E. Fatimy, J. Lusakowski, W. Knap, M. Dyakonov, M. A. Poisson, E. Morvan, S. Bollaert, A. Shchepetov, Y. Roelens, C. Gaquiere, D. Theron, and A. Cappy, Appl. Phys. Lett. 88 , 141906 (2006)

2006
[12]

A. E. Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Th\' e ron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, J. Appl. Phys. 107 , 024504 (2010)

2010
[13]

Marks, IEEE Trans

R. Marks, IEEE Trans. Microw. Theory Techn. 39 , 1205 (1991)

1991
[14]

Luryi, Appl

S. Luryi, Appl. Phys. Lett. 52 , 501 (1988)

1988

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

L. D. Landau and E. M. Liftshitz, Fluid Mechanics , 2nd Edition, Pergamon Press (1987)

work page 1987

[2] [2]

Dyakonov and M

M. Dyakonov and M. Shur, Phys. Rev. Lett. 71 , 2465 (1993)

work page 1993

[3] [3]

Andress, H

W. Andress, H. Yoon, K. Yeung, L. Qin, K. West, L. Pfeiffer, and D. Ham, Nano Lett. , 12 , 2272 (2012)

work page 2012

[4] [4]

H. Yoon, K. Yeung, P. Kim, and D. Ham, Phil. Trans. R. Soc. A 372 , 20130104 (2014)

work page 2014

[5] [5]

H. Yoon, K. Yeung, V. Umansky, and D. Ham, Nature 488 , 65 (2012)

work page 2012

[6] [6]

H. Yoon, C. Forsythe, L. Wang, N. Tombros, K. Watanabe, T. Taniguchi, J. Hone, P. Kim, and D. Ham, Nat. Nanotechnol. 9 , 594 (2014)

work page 2014

[7] [7]

Yeung, H

K. Yeung, H. Yoon, W. Andress, K. West, L. Pfeiffer, and D. Ham, Appl. Phys. Lett. 102 , 021104 (2013)

work page 2013

[8] [8]

L. C. \' O . S\' u illeabh\' a in, H. P. Hughes, A. C. Churchill, D. A. Ritchie, M. P. Grimshaw, and G. A. C. Jones, J. Appl. Phys. 76 , 1701 (1994)

work page 1994