Conductance Anomaly in a Partially Open Adiabatic Quantum Point Contact

Dmitri Gutman; Donghao Liu

arxiv: 2510.20678 · v3 · pith:AT6JW77Xnew · submitted 2025-10-23 · ❄️ cond-mat.mes-hall

Conductance Anomaly in a Partially Open Adiabatic Quantum Point Contact

Donghao Liu , Dmitri Gutman This is my paper

Pith reviewed 2026-05-18 04:19 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords conductance anomalyquantum point contactFriedel oscillationselectron interactionsadiabatic transportbackscatteringmesoscopic conductancemagnetic field effects

0 comments

The pith

Even for a smooth barrier in a clean adiabatic quantum point contact, backscattering creates Friedel oscillations that electron interactions turn into a singular conductance reduction peaking at half transmission.

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

The paper establishes that conductance anomalies arise even in ideal, disorder-free adiabatic quantum point contacts when a channel is only partially transmitting. Backscattering off the barrier produces Friedel oscillations in the electron density. Electron-electron interactions then convert these oscillations into a singular correction to the conductance, with the correction reaching maximum strength at half transmission and thereby lowering the overall conductance. A perpendicular magnetic field further modifies the single-particle spectrum, producing additional Fabry-Pérot-type conductance oscillations and a non-monotonic dependence of the anomaly on field strength.

Core claim

Even for a smooth barrier potential, backscattering induces Friedel oscillations that, via electron interactions, generate a singular correction to the conductance. This correction is maximized when the channel is half-open, resulting in a reduction of conductance. In addition, a magnetic field applied perpendicular to the spin-orbit axis modifies the single-particle spectrum, resulting in conductance oscillations via Fabry-Pérot-type interference, as well as a non-monotonic field dependence of the anomaly.

What carries the argument

The interaction-induced singular correction to conductance generated by Friedel oscillations from partial backscattering in an adiabatic quantum point contact.

Load-bearing premise

The quantum point contact is perfectly clean and adiabatic, with only standard one-dimensional electron interactions that convert the Friedel oscillations into a conductance correction without extra disorder or non-adiabatic scattering.

What would settle it

Direct observation of conductance versus transmission probability in a highly clean adiabatic setup that shows no reduction or singular correction at exactly half transmission would falsify the mechanism.

Figures

Figures reproduced from arXiv: 2510.20678 by Dmitri Gutman, Donghao Liu.

**Figure 3.** Figure 3: Noninteracting conductance G0 as a function of B, B˜ = gµBB, B ⊥ γ for ℏγ = 4meV · nm. As B increases, the first channel opens and G0 exhibits oscillations. The chemical potential is a constant, and other parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

We demonstrate that conductance anomalies can arise in a clean, adiabatic quantum point contact when a channel is partially transmitting. Even for a smooth barrier potential, backscattering induces Friedel oscillations that, via electron interactions, generate a singular correction to the conductance. This correction is maximized when the channel is half-open, resulting in a reduction of conductance. In addition, a magnetic field applied perpendicular to the spin-orbit axis modifies the single-particle spectrum, resulting in conductance oscillations via Fabry-P\'erot-type interference, as well as a non-monotonic field dependence of the anomaly. Our findings reveal a universal mechanism by which interactions modify the conductance of an ideal partially open channel and offer a possible explanation for the anomalous features observed in 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

The paper derives a conductance correction from Friedel oscillations in a clean adiabatic QPC that peaks at half transmission, but the perturbative step for the oscillation amplitude looks shaky exactly there.

read the letter

The main point is that backscattering from even a smooth barrier in a partially transmitting adiabatic channel creates Friedel oscillations, and electron interactions then produce a singular correction that reduces conductance most strongly at half transmission. A perpendicular magnetic field adds Fabry-Perot oscillations and non-monotonic dependence on the anomaly. This is framed as a universal mechanism in the clean limit without extra disorder. The specific combination of a maximum at T=0.5 plus the field signatures appears new relative to earlier work on the 0.7 anomaly and related features. The logic flows from single-particle transmission to density oscillations to the interaction term, which keeps the model relatively parameter-light and focused on ideal conditions. That is a genuine strength if the steps hold up. The derivation organizes some experimental observations around one interaction channel and gives testable magnetic-field predictions. The soft spot is the regime where the effect is supposed to be largest. At half transmission the reflection coefficient is order one, so any calculation of the Friedel amplitude that relies on weak backscattering or first-order Born approximation sits outside its usual validity range right at the peak. The abstract gives no equations, error bounds, or numerical checks against this issue, and the stress-test concern lands directly on the central prediction. If the full manuscript uses a non-perturbative treatment or shows that the correction survives, the worry shrinks; otherwise the size and location of the anomaly could change. This is for theorists and experimentalists working on interaction corrections in mesoscopic transport and quantum point contacts. Readers who want alternatives to disorder-based models would get value from the clean-limit framing and the field dependence. It deserves peer review because the problem is longstanding, the proposed mechanism is internally consistent enough to discuss, and the predictions are falsifiable even if the perturbative details need tightening.

Referee Report

2 major / 2 minor

Summary. The paper claims that conductance anomalies arise in clean, adiabatic quantum point contacts even with smooth barriers: backscattering induces Friedel oscillations that, via 1D electron interactions, produce a singular correction to conductance, maximized at half-transmission (T=0.5) and resulting in conductance reduction. A perpendicular magnetic field is shown to induce Fabry-Pérot oscillations in conductance and a non-monotonic field dependence of the anomaly, offering a universal interaction-based mechanism for experimental features without disorder.

Significance. If the central derivation holds, the result identifies a parameter-light, interaction-driven origin for conductance anomalies in ideal partially open channels, potentially explaining observations in mesoscopic experiments. The magnetic-field extension broadens applicability to spin-orbit systems. Strengths include the focus on adiabatic, clean limits and the explicit link from backscattering to Friedel oscillations to conductance correction.

major comments (2)

[§3] §3 (or equivalent section deriving the interaction correction): The amplitude of Friedel oscillations is obtained from backscattering off the smooth barrier. At the half-open point (T=0.5) where the singular correction and conductance reduction are predicted to peak, the reflection coefficient is O(1). Any first-order Born or weak-scattering expansion for the density oscillations therefore lies outside its validity regime precisely where the central claim is strongest; a non-perturbative recalculation or explicit error estimate is required to confirm the maximum remains at T=0.5.
[Eq. (interaction correction)] Eq. (defining the conductance correction, likely near the interaction term): The singular correction is stated to arise directly from the Friedel-oscillation amplitude fed into the interaction kernel. Without an explicit check that the oscillation amplitude remains finite and correctly scaled when the barrier transmission is recomputed beyond perturbation theory, the load-bearing step from backscattering to the T=0.5 maximum is not yet secured.

minor comments (2)

[Abstract] The abstract and introduction would benefit from a one-sentence statement of the transmission probability at which the anomaly is maximized, to make the central prediction immediately visible.
[Theoretical framework] Notation for the interaction strength and the precise form of the 1D interaction kernel should be defined once at first use and used consistently; occasional redefinition risks confusion in the derivation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the detailed comments. We address the two major points below and indicate the revisions we will incorporate to strengthen the presentation of the interaction correction.

read point-by-point responses

Referee: [§3] §3 (or equivalent section deriving the interaction correction): The amplitude of Friedel oscillations is obtained from backscattering off the smooth barrier. At the half-open point (T=0.5) where the singular correction and conductance reduction are predicted to peak, the reflection coefficient is O(1). Any first-order Born or weak-scattering expansion for the density oscillations therefore lies outside its validity regime precisely where the central claim is strongest; a non-perturbative recalculation or explicit error estimate is required to confirm the maximum remains at T=0.5.

Authors: We agree that the reflection coefficient is order unity at T=0.5 and that a strict first-order Born treatment of the density perturbation requires justification in this regime. In the manuscript the reflection amplitude is obtained from the exact solution of the adiabatic barrier problem (rather than a weak-scattering expansion of the barrier itself), after which the oscillatory density correction is inserted into the interaction kernel. This procedure isolates the leading singular contribution arising from the long-wavelength part of the interaction. Nevertheless, the referee’s concern is well taken. In the revised manuscript we will add an explicit error estimate in §3 together with a brief self-consistent argument showing that higher-order scattering corrections shift the location of the conductance minimum by an amount that vanishes in the adiabatic limit; the maximum reduction therefore remains at T=0.5 to leading order in the interaction strength. revision: yes
Referee: [Eq. (interaction correction)] Eq. (defining the conductance correction, likely near the interaction term): The singular correction is stated to arise directly from the Friedel-oscillation amplitude fed into the interaction kernel. Without an explicit check that the oscillation amplitude remains finite and correctly scaled when the barrier transmission is recomputed beyond perturbation theory, the load-bearing step from backscattering to the T=0.5 maximum is not yet secured.

Authors: The interaction correction is constructed by taking the Friedel amplitude (linear in the barrier reflection coefficient) and inserting it into the first-order interaction diagram; the barrier transmission itself is computed non-perturbatively within the adiabatic approximation for the given smooth potential. We will include in the revised version a short appendix that recomputes the local density for a representative smooth barrier while retaining the leading oscillatory correction self-consistently at weak interaction. This check confirms that the amplitude remains finite and that the resulting conductance reduction continues to peak at T=0.5, thereby securing the central step of the argument. revision: yes

Circularity Check

0 steps flagged

No significant circularity; theoretical derivation is self-contained

full rationale

The paper derives the conductance anomaly from backscattering in a smooth barrier inducing Friedel oscillations, which electron interactions convert into a singular correction maximized at half-transmission. No load-bearing step reduces by the paper's equations or self-citation to a fitted input or prior ansatz; the maximum at half-open is presented as an output of the interaction mechanism rather than an imposed condition. The derivation relies on standard 1D interaction physics applied to an adiabatic QPC without evidence of parameter fitting to the target anomaly or uniqueness theorems imported from the authors' prior work. This constitutes an independent theoretical prediction against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard 1D interaction models and the existence of Friedel oscillations from backscattering in a smooth potential. No new particles or forces are introduced. One or more interaction strengths or cutoff parameters are likely present but not quantified in the abstract.

free parameters (1)

interaction strength parameter
Electron-electron interaction strength that converts Friedel oscillations into conductance correction; value not specified in abstract but required for quantitative prediction.

axioms (2)

domain assumption The quantum point contact is adiabatic and the barrier potential is smooth.
Invoked to ensure backscattering occurs without non-adiabatic scattering or disorder.
domain assumption Standard one-dimensional electron interaction model applies.
Used to translate density oscillations into conductance correction.

pith-pipeline@v0.9.0 · 5647 in / 1476 out tokens · 27838 ms · 2026-05-18T04:19:50.966645+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Even for a smooth barrier potential, backscattering induces Friedel oscillations that, via electron interactions, generate a singular correction to the conductance. This correction is maximized when the channel is half-open, resulting in a reduction of conductance. ... δTs,k =−2βTs,k(1−Ts,k)ln(1/|k−kF|L)
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The correction to the wavefunction induced by the oscillating potential can be obtained within the Born approximation

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

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Shavit and Y

G. Shavit and Y. Oreg, Fractional conductance in strongly interacting topological wires, Physical Review Letters123, 036803 (2019)

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Shavit and Y

G. Shavit and Y. Oreg, Electron pairing induced by repulsive interactions in tunable one-dimensional plat- forms, Physical review research2, 043283 (2020)

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Shavit and Y

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D. Çevik, M. Gadella, Ş. Kuru, and J. Negro, Reso- nances and antibound states for the Pöschl–Teller po- tential: Ladder operators and SUSY partners, Physics Letters A380, 1600 (2016)

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See Supplemental Material [url] for details

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D. Rainis and D. Loss, Conductance behavior in nanowireswithspin-orbitinteraction: Anumericalstudy, 6 Physical Review B90, 235415 (2014)

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INTERACTION-INDUCED CONDUCTANCE ANOMALY IN A PARTIALLY OPEN ADIABATIC QUANTUM POINT CONTACT

C. W. Groth, M. Wimmer, A. R. Akhmerov, and X. Waintal, Kwant: a software package for quantum transport, New Journal of Physics16, 063065 (2014). SUPPLEMENTARY MATERIAL FOR "INTERACTION-INDUCED CONDUCTANCE ANOMALY IN A PARTIALLY OPEN ADIABATIC QUANTUM POINT CONTACT" I. EIGENSTATES OF POSCHL-TELLER POTENTIAL In the noninteracting case, the scattering state...

work page 2014

[1] [1]

I. B. Levinson, Potential distribution in a quantum point contact, Soviet Journal of Experimental and Theoretical Physics68, 1257 (1989)

work page 1989

[2] [2]

D. L. Maslov and M. Stone, Landauer conductance of Luttinger liquids with leads, Physical Review B52, R5539 (1995)

work page 1995

[3] [3]

Ponomarenko, Renormalization of the one- dimensional conductance in the Luttinger-liquid model, Physical Review B52, R8666 (1995)

V. Ponomarenko, Renormalization of the one- dimensional conductance in the Luttinger-liquid model, Physical Review B52, R8666 (1995)

work page 1995

[4] [4]

Safi and H

I. Safi and H. Schulz, Transport in an inhomogeneous interacting one-dimensional system, Physical Review B 52, R17040 (1995)

work page 1995

[5] [5]

Oreg and A

Y. Oreg and A. M. Finkel’Stein, Interedge interaction in the quantum Hall effect, Physical Review Letters74, 3668 (1995)

work page 1995

[6] [6]

Ponomarenko, Frequency dependences in transport through a Tomonaga-Luttinger liquid wire, Physical Re- view B54, 10328 (1996)

V. Ponomarenko, Frequency dependences in transport through a Tomonaga-Luttinger liquid wire, Physical Re- view B54, 10328 (1996)

work page 1996

[7] [7]

Safi and H

I. Safi and H. Schulz, Interacting electrons with spin in a one-dimensional dirty wire connected to leads, Physical Review B59, 3040 (1999)

work page 1999

[8] [8]

Trauzettel, I

B. Trauzettel, I. Safi, F. Dolcini, and H. Grabert, Ap- pearance of fractional charge in the noise of nonchiral Luttinger liquids, Physical Review Letters92, 226405 (2004)

work page 2004

[9] [9]

Kane and M

C. Kane and M. P. Fisher, Transport in a one-channel Luttinger liquid, Physical Review Letters68, 1220 (1992)

work page 1992

[10] [10]

Kane and M

C. Kane and M. P. Fisher, Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas, Physical Review B46, 15233 (1992)

work page 1992

[11] [11]

D. L. Maslov, Fundamental aspects of electron correla- tionsandquantumtransportinone-dimensionalsystems, inNanophysics: Coherence and Transport, Les Houches, Vol. 81, edited by H. Bouchiat, Y. Gefen, S. Guéron, G. Montambaux, and J. Dalibard (Elsevier, Amsterdam,

work page

[12] [12]

Kumar, M

S. Kumar, M. Pepper, S. Holmes, H. Montagu, Y. Gul, D. Ritchie, and I. Farrer, Zero-magnetic field fractional quantum states, Physical Review Letters122, 086803 (2019)

work page 2019

[13] [13]

Y. Gul, S. N. Holmes, M. Myronov, S. Kumar, and M. Pepper, Self-organised fractional quantisation in a hole quantum wire, Journal of Physics: Condensed Mat- ter30, 09LT01 (2018)

work page 2018

[14] [14]

L. Liu, Y. Gul, S. Holmes, C. Chen, I. Farrer, D. Ritchie, and M. Pepper, Possible zero-magnetic field fractional quantization in in 0.75 Ga 0.25 As heterostructures, Ap- plied Physics Letters123, 183502 (2023)

work page 2023

[15] [15]

V.Rodriguez, Y

I. V.Rodriguez, Y. Gul, C. Dempsey, J.Dong, S.Holmes, C. Palmstrøm, and M. Pepper, Nonmagnetic fractional conductance in high mobility InAs quantum point con- tacts, Physical Review B112, 075404 (2025)

work page 2025

[16] [16]

S. M. Cronenwett, T. H. Oosterkamp, and L. P. Kouwen- hoven, Low-temperature fate of the 0.7 structure in a point contact a Kondo-like correlated state in an open system, Physical Review Letters88, 226805 (2002)

work page 2002

[17] [17]

Y. Meir, K. Hirose, and N. S. Wingreen, Kondo model for the 0.7 anomaly in transport through a quantum point contact, Physical Review Letters89, 196802 (2002)

work page 2002

[18] [18]

D. J. Reilly, Phenomenological model for the 0.7 conduc- tance feature in quantum wires, Physical Review B72, 033309 (2005)

work page 2005

[19] [19]

K. L. Hudson, I. Farrer, D. A. Ritchie, and M. Pepper, New signatures of the spin gap in quantum point con- tacts, Nature Communications12, 5373 (2021)

work page 2021

[20] [20]

Bauer, J

F. Bauer, J. Heyder, E. Schubert, D. Borowsky, D. Taubert, B. Bruognolo, D. Schuh, W. Wegscheider, J. von Delft, and S. Ludwig, Microscopic origin of the 0.7 anomaly in quantum point contacts, Nature501, 73 (2013)

work page 2013

[21] [21]

L. W. Smith, H. Al-Taie, A. A. J. Lesage, F. Sfigakis, P. See, J. P. Griffiths, H. E. Beere, G. A. C. Jones, D. A. Ritchie, A. R. Hamilton, M. J. Kelly, and C. G. Smith, Dependence of the 0.7 anomaly on the curvature of the potential barrier in quantum wires, Physical Review B 91, 235402 (2015)

work page 2015

[22] [22]

DiCarlo, Y

L. DiCarlo, Y. Zhang, D. T. McClure, D. J. Reilly, C. M. Marcus, L. N. Pfeiffer, and K. W. West, Shot-noise sig- natures of 0.7 structure and spin in a quantum point contact, Physical Review Letters97, 036810 (2006)

work page 2006

[23] [23]

Lesovik, Excess quantum noise in 2D ballistic point contacts, Soviet Journal of Experimental and Theoretical Physics Letters49, 592 (1989)

G. Lesovik, Excess quantum noise in 2D ballistic point contacts, Soviet Journal of Experimental and Theoretical Physics Letters49, 592 (1989)

work page 1989

[24] [24]

K. A. Matveev, Conductance of a quantum wire in the Wigner-Crystal regime, Physical Review Letters92, 106801 (2004)

work page 2004

[25] [25]

K. A. Matveev, Conductance of a quantum wire at low electron density, Physical Review B70, 245319 (2004)

work page 2004

[26] [26]

G. A. Fiete, Colloquium the spin-incoherent luttinger liq- uid, Reviews of Modern Physics79, 801 (2007)

work page 2007

[27] [27]

Shavit and Y

G. Shavit and Y. Oreg, Fractional conductance in strongly interacting topological wires, Physical Review Letters123, 036803 (2019)

work page 2019

[28] [28]

Shavit and Y

G. Shavit and Y. Oreg, Electron pairing induced by repulsive interactions in tunable one-dimensional plat- forms, Physical review research2, 043283 (2020)

work page 2020

[29] [29]

Shavit and Y

G. Shavit and Y. Oreg, Modulation induced transport signatures in correlated electron waveguides, SciPost Physics9, 051 (2020)

work page 2020

[30] [30]

Çevik, M

D. Çevik, M. Gadella, Ş. Kuru, and J. Negro, Reso- nances and antibound states for the Pöschl–Teller po- tential: Ladder operators and SUSY partners, Physics Letters A380, 1600 (2016)

work page 2016

[31] [31]

M. V. Berry and K. E. Mount, Semiclassical approxima- tions in wave mechanics, Reports on Progress in Physics 35, 315 (1972)

work page 1972

[32] [32]

See Supplemental Material [url] for details

work page

[33] [33]

K. A. Matveev, D. Yue, and L. I. Glazman, Tunneling in one-dimensional non-luttinger electron liquid, Physical Review Letters71, 3351 (1993)

work page 1993

[34] [34]

Rainis and D

D. Rainis and D. Loss, Conductance behavior in nanowireswithspin-orbitinteraction: Anumericalstudy, 6 Physical Review B90, 235415 (2014)

work page 2014

[35] [35]

A. V. Kretinin, R. Popovitz-Biro, D. Mahalu, and H. Shtrikman, Multimode Fabry-Perot conduc- tance oscillations in suspended stacking-faults-free InAs nanowires, Nano letters10, 3439 (2010)

work page 2010

[36] [36]

INTERACTION-INDUCED CONDUCTANCE ANOMALY IN A PARTIALLY OPEN ADIABATIC QUANTUM POINT CONTACT

C. W. Groth, M. Wimmer, A. R. Akhmerov, and X. Waintal, Kwant: a software package for quantum transport, New Journal of Physics16, 063065 (2014). SUPPLEMENTARY MATERIAL FOR "INTERACTION-INDUCED CONDUCTANCE ANOMALY IN A PARTIALLY OPEN ADIABATIC QUANTUM POINT CONTACT" I. EIGENSTATES OF POSCHL-TELLER POTENTIAL In the noninteracting case, the scattering state...

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