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REVIEW 4 major objections 8 minor 51 references

Electron transport in bilayer graphene nano constrictions patterned using AFM nanolithography

T0 review · 4 major / 8 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Electrode-free AFM nanolithography produces a bilayer-graphene quantum dot in a 30-nm constriction, with addition energies above 100 meV.

desk verdict A credible single-device demonstration of large-addition-energy Coulomb blockade in an AFM-LAO bilayer graphene constriction, but the 'single QD' claim is not uniquely established. read the letter →

arxiv 2412.08758 v1 pith:DYPVDJJ3 submitted 2024-12-11 cond-mat.mes-hall

Robert W. Rienstra , Nishat Sultana , En-Min Shih , Evan Stocker , Kenji Watanabe , Takashi Taniguchi , Curt A. Richter , Joseph Stroscio
show 2 more authors
Nikolai Zhitenev Fereshte Ghahari
This is my paper · ORCID
classification cond-mat.mes-hall
keywords bilayergrapheneAFMnanolithographylocalanodicoxidationnanoconstrictionsquantumdotCoulombblockadeedgedisorderconfinement
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

Bilayer graphene constrictions as narrow as 20 nm, cut by electrode-free AFM-based local anodic oxidation (LAO), form a width-tunable family of electronic devices. Constrictions 100–125 nm wide behave like bulk graphene, a 75-nm-wide constriction opens a transport gap of roughly 50 meV, and the narrowest constriction studied, about 30 nm wide, shows periodic Coulomb blockade peaks and diamonds that the authors interpret as a single quantum dot. Addition energies extracted from those diamonds range up to and above 100 meV, larger than previous experiments on patterned dots, and independent size estimates put the dot's diameter at 17–26 nm, close to the etched width. The central claim is that transport in these constrictions is controlled by edge disorder combined with quantum confinement, making electrode-free AFM-LAO a simpler route to carbon-based quantum devices.

What carries the argument

The central object is the electrode-free AFM-based local anodic oxidation (LAO) nano constriction, made by placing the graphene on Si/SiO2 in high humidity and applying an AC voltage to an AFM tip that couples to the substrate, forming a water meniscus whose dissociation oxidizes and cuts the graphene with a force of about 10 nN. The transport characterization relies on Coulomb blockade spectroscopy: bias-voltage sweeps at fixed back-gate produce diamonds whose slopes give lever arms, converting gate-voltage separations into addition energies; the charging-energy comparison with the device's area capacitance sets the dot size. The mechanism carrying the argument is the interplay of geometric confinement and edge disorder: AFM cutting leaves rough edges and hBN-dissociation byproducts, which localize charges along the edge, and in a 30-nm channel that disorder combined with quantum confinement produces a single isolated island rather than a continuous channel.

What would settle it

Fabricate several nominally identical 30-nm constrictions and compare their Coulomb-diamond periods and extracted dot diameters: a single geometric dot predicts reproducible charging energies and sizes close to the lithographic width, while a disorder-dominated picture predicts irregular, device-dependent spacings; scanning-gate microscopy over the constriction could directly show whether one localized island or several islands mediate transport.

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Extended reading notes

Core claim

The discovery, on the paper's own terms, is that a mechanically defined nano constriction in encapsulated bilayer graphene can confine a single quantum dot with no gate-defined barriers and no separate source–drain constrictions. Device P4 (W=30 ± 5 nm) exhibits regular Coulomb peaks in conductance as a function of back-gate voltage and clear Coulomb diamonds in bias spectroscopy. Using lever arms from the diamond slopes to convert gate voltage to energy, the authors find addition energies from about 10 meV to beyond 100 meV, with four-level bunching at fillings of four and eight electrons that they attribute to the four-fold spin and valley degeneracy of bilayer graphene. Comparing the dot's gate capacitance with the measured areal capacitance yields dot diameters of about 17.5 nm after the first cool down and 26.4 nm after the second, consistent with the constriction geometry; magnetic-field dispersion is weak up to 3–4 T, also consistent with a small island. The paper additionally shows that wider constrictions develop a transport gap of about 50 meV that cannot be accounted for by the estimated 6 meV from quantum confinement and displacement field, leading to the conclusion that edge disorder and quantum confinement govern transport.

Load-bearing premise

The load-bearing premise is that the Coulomb blockade observed in the narrowest device comes from one quantum dot formed inside the geometric constriction, rather than from a disorder-induced network of several dots or a dot located elsewhere in the device; the paper itself notes that multi-dot behavior appears at lower gate voltages.

Editorial extensions

If this is right

  • Width is a tuning knob: 125-nm constrictions show bulk transport, 100-nm shows a partial transport gap, 75-nm gives a roughly 50 meV gap, and 30-nm gives Coulomb blockade.
  • Addition energies above 100 meV place these mechanically defined dots at or above the energy scale of patterned graphene quantum dots, so the dot is genuinely small.
  • The four-fold bunching of addition energies at fillings four and eight is consistent with spin and valley degeneracy in bilayer graphene.
  • The weak magnetic-field dispersion of single-particle levels up to 3–4 T implies a confinement length of order 16–28 nm, matching the constriction geometry.
  • Electrode-free AFM-LAO patterning works before and after hBN encapsulation, simplifying fabrication and avoiding etching residues that can degrade device quality.

Reading between the lines

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

  • Editorial inference: If the single-dot assignment is right, the dot's position and tunnel barriers are set by whatever disorder the AFM etch leaves behind, so operating the dot as a qubit will likely require additional local gates to tune those barriers.
  • Editorial inference: The reported dot diameter is extracted from a circular-dot capacitance model; a realistic non-circular confinement potential could shift the size estimates and the effective mass inferred from level spacings.
  • Editorial inference: A reproducibility study across several identically etched 30-nm constrictions would separate the geometric-confinement contribution from the disorder contribution, since a single geometric dot predicts similar charging energies while disorder-dominated dots should scatter widely.
  • Editorial inference: The weakly resolved level splitting with magnetic field, if confirmed at higher fields, would connect these mechanically defined dots to valley and spin physics already established in gate-defined bilayer graphene quantum dots.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 8 minor

Summary. This manuscript reports low-temperature transport measurements of bilayer graphene nanoconstrictions patterned by electrode-free AFM-based local anodic oxidation (LAO). The authors show that wider constrictions (125, 100, and 75 nm) display bulk transport or a gate-tunable transport gap, and that a 30 nm-wide constriction (device P4) exhibits periodic Coulomb blockade peaks and bias-spectroscopy diamonds with addition energies up to and exceeding 100 meV. From these data they infer single-quantum-dot formation in the geometric constriction, estimate dot diameters in the 12–26 nm range using several models, and report magnetic-field spectroscopy showing weak level dispersion and approximate four-fold bunching. The fabrication route is described in detail, including LAO applied before and after hBN encapsulation.

Significance. The fabrication technique is of genuine interest: if the single-dot interpretation were firmly established, 20–30 nm AFM-LAO constrictions would provide a fast, electrode-free route to confinement in bilayer graphene, with addition energies competitive with etched or gate-defined quantum dots. The transport-gap scaling with width and the magnetic-field spectroscopy data are also useful observations. The paper is cautious about some interpretations (for example, valley splitting is called only 'suggestive') and the data presentation is generally clear. However, the headline claim—single quantum dot in the geometric constriction—rests on one device and on a constant-interaction model that is not uniquely constrained by a global back gate; the paper's own text notes multi-dot regions. The significance for quantum-dot physics therefore depends on strengthening the single-dot attribution or explicitly narrowing the claim.

major comments (4)
  1. [Main text, Fig. 3 (page 7)] The central claim of 'single quantum dot (QD) formation' in device P4 is not uniquely established. The manuscript itself states, in the paragraph discussing Fig. 3b, that 'regions of multi dot behavior are observable' at lower gate voltages, so the device is not in a demonstrably single-dot regime over the full range used for the >100 meV addition-energy claim. With only a global back gate, the data cannot exclude a disorder-localized dot outside the geometric constriction or a small multi-dot network whose peak spacing is quasi-regular. Because the abstract and conclusion attribute the >100 meV energies to a single island in the geometric constriction, this is a load-bearing assumption. Please add evidence that the diamonds used for the claim come from one stable dot over the analyzed gate range (for example, full-range stability diagrams, peak-spacing statistics, cooldown reproducibility, or local/dual-gate control), or explicitly restrict the single-dot claim to the gate-voltage interval in which that regime is established.
  2. [Main text, dot-size estimate (page 8, equation 'ΔE_ave = e²/C_g')] The dot-size derivation contains an incorrect formula as written. From the paper's own definitions, the lever-arm relation is ΔE = α e ΔV_g, and the constant-interaction relation between successive Coulomb peaks is ΔV_g = e/C_g, so the average addition energy is ΔE_ave = α e²/C_g, not e²/C_g. As printed, the equation omits the lever arm α, so the values of C_g and the diameters 17.48 nm and 26.38 nm cannot be reproduced from the described procedure. This matters because the diameter is then used to support the 'single isolated island' conclusion and to argue that the island matches the AFM width. Please correct the relation, report the numerical inputs (average gate-voltage spacing and average α), and state explicitly that the inferred area assumes the same gate capacitance per area inside the constriction as in the bulk Hall-bar region.
  3. [Supplementary Information A (square-well size estimate)] The formula for the quantum-confinement estimate of the dot diameter, a = sqrt(ℏ²π/(m*ΔE)), is not the standard relation for a square confinement potential; for an infinite square well E = π²ℏ²/(m a²), so a = sqrt(π²ℏ²/(mΔE)) up to the chosen boundary convention. As written, the expression has a factor-of-π discrepancy that changes the inferred diameters by roughly 77%. The resulting values 11.52 nm and 18.88 nm are used to support the conclusion that the dot is close to the geometric size, so the formula needs to be corrected and justified, or the method should be presented as a deliberately rough order-of-magnitude estimate with the model explicitly stated.
  4. [Abstract and Conclusion (comparison with patterned QDs)] The claim that addition energies 'exceeding 100 meV' surpass previous experiments on patterned QDs is not quantified. No specific comparison values are given, and the text notes that multi-dot regions exist at lower gate voltages, so it is not clear which diamonds are being compared. Please provide the comparison data, state the gate-voltage range and dot-occupation numbers for which the >100 meV diamonds are observed, and specify the relevant references; without this, the headline comparative claim cannot be evaluated.
minor comments (8)
  1. [Figure citations in main text (pages 5–6)] The text describes the differential conductance map of device P3 as 'Figure 2c', but the map is Fig. 2d; the conductance trace of P1 is described as 'shown in Fig. 1a', but the relevant panel is Fig. 2a.
  2. [References 36 and 37] Reference 36 is identical to Reference 31, and Reference 37 (boric acid thermal etching of graphite felt) appears unrelated to the statement about hBN dissociation byproducts; please replace it with the correct citation or remove it.
  3. [Page 7, paragraph after Fig. 3b] The phrase 'less er screening' appears to be a typo for 'less efficient screening'; please correct it.
  4. [Fig. 3 caption and text] The statement that 'The marks X represent the location of the charge neutrality point' is not explained: specify whether X marks the global Dirac point of the reservoirs or a charge degeneracy point of the dot, and describe how it was determined.
  5. [Fig. 3c,d] The addition energies are plotted against 'electron occupation number', but the paper does not describe how the occupation number is assigned; please state how N is determined and whether the four-fold bunching is robust to that assignment.
  6. [Page 7, second cooldown discussion] The statement that the same device after a second cooldown shows more pronounced Coulomb diamonds 'in all density ranges' is in tension with the first-cooldown observation of multi-dot regions; please address whether this indicates a disorder-configuration change and how it affects the single-dot assignment.
  7. [Device statistics and yield] The paper claims reproducibility and high yield, but no device summary is given; a table listing the measured devices, widths, fabrication route (before or after encapsulation), and transport outcome would support the reproducibility claim. Note also that the abstract mentions 20 nm constrictions, but the narrowest transport device discussed is the 30 nm device P4.
  8. [Fig. S2 caption] The caption title says 'Magnetic field measurements of device P3 in second cool down', but the body of the caption and the text refer to device P4; please correct the inconsistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the QD size and addition-energy estimates use independent calibrations, and the gap enhancement is an acknowledged discrepancy attributed to disorder, not a fitted input.

full rationale

The paper's derivation chain is self-contained. The quantum-dot size is estimated from the gate capacitance extracted from Coulomb peak spacing, normalized by the device capacitance per unit area determined separately from quantum Hall measurements (C_bar_g = 119.73 aF/um^2, A = C_g/C_bar_g), and cross-checked with two other independent models: a square-well quantum-confinement estimate and a parallel-plate capacitor model. These are standard parameter extractions, not circular because none of the target claims (single-dot formation, addition energies exceeding 100 meV, dot diameter near the geometric width) is used as an input to the derivation. The transport-gap analysis is also non-circular: the observed gap (~50 meV) is explicitly compared with a calculated confinement gap (~2.8 meV) plus displacement-field gap (~3.3 meV), and the large discrepancy is attributed to edge disorder by hypothesis, not by fitting. The reference to electrode-free AFM-LAO [31] is to prior work by other authors and is not load-bearing in a self-citational sense. The main interpretive weakness—that 'regions of multi dot behavior are observable' at lower gate voltages and that a single global back gate cannot uniquely localize the dot in the constriction—is a correctness or ambiguity risk, not a circularity of the derivation. No circular step can be exhibited, so the score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claims rest on standard QD transport theory and on the assumption that the etched cut defines the active island. The quantitative estimates of gap and dot size use literature values and measured parameters, none of which are adjusted to force the reported phenomena. The main unquantified input is the degree of edge disorder, which is invoked to explain the unexpectedly large transport gap.

free parameters (3)
  • Lever arm α = Not reported numerically (extracted from Coulomb diamond edges)
    Used to convert gate voltage separations into addition energies in Fig. 3c,d. No uncertainty is given.
  • Gate capacitance per unit area C̄g = 119.73 aF/µm²
    Extracted from quantum Hall measurements; used to estimate the dot area from the dot capacitance.
  • Quantum dot diameter a = 17.5 nm (cool down 1), 26.4 nm (cool down 2)
    Derived from Cg/C̄g, not fitted independently; used to support the claim that the dot matches the geometric constriction.
assumptions (4)
  • domain assumption Standard Coulomb blockade model for a single quantum dot
    The periodic peaks and diamonds are interpreted with the orthodox Coulomb blockade model; this is the basis for extracting addition energies and dot size.
  • standard math Effective mass approximation for bilayer graphene (m* ≈ 0.033 m_e)
    Used to estimate the quantum confinement gap Eq ≈ 2.8 meV; taken from literature, not re-derived.
  • domain assumption The AFM-LAO cut produces a well-defined constriction whose electrical width equals the measured AFM width
    The paper acknowledges edge roughness and byproducts, yet the QD size is compared to the geometric width.
  • domain assumption hBN encapsulation prevents charge impurity puddles, leaving edge disorder as the main disorder source
    Used to rule out impurity puddles and attribute the enhanced gap to edge disorder; paper admits hBN dissociation can itself create edge disorder.

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Pith. "Pith review of Electron transport in bilayer graphene nano constrictions patterned using AFM nanolithography." pith.science (2026). https://pith.science/paper/DYPVDJJ3

@misc{pith2026241208758,
  author       = {Pith},
  title        = {Pith review of: Electron transport in bilayer graphene nano constrictions patterned using AFM nanolithography},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DYPVDJJ3}},
  note         = {Machine review of arXiv:2412.08758}
}
read the original abstract

Here we report on low temperature transport measurements of encapsulated bilayer graphene nano constrictions fabricated employing electrode-free AFM-based local anodic oxidation (LAO) nanolithography. This technique allows for the creation of constrictions as narrow as 20 nm much smaller than previous studies. In wider constrictions, we observe bulk transport characteristics. However, as the constriction's width is reduced, a transport gap appears. Single quantum dot (QD) formation is observed within the narrowest constriction with addition energies exceeding 100 meV, which surpass previous experiments on patterned QDs. Our results suggest that transport through these narrow constrictions is governed by edge disorder combined with quantum confinement effects. Our findings introduce electrode-free AFM-LAO lithography as an easy and flexible method for creating nanostructures with tunable electronic properties without relying on patterning techniques such as e-beam lithography. The excellent control and reproducibility provided by this technique opens exciting opportunities for carbon-based quantum electronics and spintronics.

Figures

Figures reproduced from arXiv: 2412.08758 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. FIG 3 [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
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Figure 4
Figure 4. Figure 4: FIG 4 [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]

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Works this paper leans on

51 extracted references · 51 canonical work pages

  1. [1]

    Spin qubits in graphene quantum dots,

    Bjorn Trauzettel, Denis V. Bulaev, Daniel Loss, and Guido Burkard, “Spin qubits in graphene quantum dots,” Nature Physics 3, 192–196 (2007)

    work page 2007

  2. [2]

    Tunable Graphene Single Electron Transistor,

    C. Stampfer, E. Schurtenberger, F. Molitor, J. Gu ̈ttinger, T. Ihn, and K. Ensslin, “Tunable Graphene Single Electron Transistor,” Nano Letters 8, 2378–2383 (2008). 12

    work page 2008

  3. [3]

    Chaotic Dirac Billiard in Graphene Quantum Dots,

    L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. W. Hill, K. S. Novoselov, and A. K. Geim, “Chaotic Dirac Billiard in Graphene Quantum Dots,” Science 320, 356– 358 (2008)

    work page 2008

  4. [4]

    Gate-defined graphene double quantum dot and excited state spectroscopy,

    Xing Lan Liu, Dorothee Hug, and Lieven M. K. Vander- sypen, “Gate-defined graphene double quantum dot and excited state spectroscopy,” Nano Letters 10, 1623–1627 (2010)

    work page 2010

  5. [5]

    Transport through graphene quantum dots,

    J. Gu ̈ttinger, F. Molitor, C. Stampfer, S. Schnez, A. Ja- cobsen, S. Dro ̈scher, T. Ihn, and K. Ensslin, “Transport through graphene quantum dots,” Reports on Progress in Physics 75, 126502 (2012)

    work page 2012

  6. [6]

    Localized charge carriers in graphene nanodevices,

    D. Bischoff, A. Varlet, P. Simonet, M. Eich, H. C. Over- weg, T. Ihn, and K. Ensslin, “Localized charge carriers in graphene nanodevices,” Applied Physics Reviews 2, 031301 (2015)

    work page 2015

  7. [7]

    Charge detection in graphene quantum dots,

    J. Gu ̈ttinger, C. Stampfer, S. Hellmu ̈ller, F. Molitor, T. Ihn, and K. Ensslin, “Charge detection in graphene quantum dots,” Applied Physics Letters 93, 212102 (2008)

    work page 2008

  8. [8]

    Phase- Coherent Transport in Graphene Quantum Billiards,

    F. Miao, S. Wijeratne, Y. Zhang, U. C. Coskun, W. Bao, and C. N. Lau, “Phase- Coherent Transport in Graphene Quantum Billiards,” Science 317, 1530–1533 (2007)

    work page 2007

Show all 51 references
  1. [9]

    Observation of Aharonov-Bohm conductance oscillations in a graphene ring,

    Saverio Russo, Jeroen B. Oostinga, Dominique Wehenkel, Hubert B. Heersche, Samira Shams Sobhani, Lieven M. K. Vandersypen, and Alberto F. Morpurgo, “Observation of Aharonov-Bohm conductance oscillations in a graphene ring,” Physical Review B 77, 085413 (2008)

    2008

  2. [10]

    Gate-defined quantum confinement in suspended bilayer graphene,

    M. T. Allen, J. Martin, and A. Yacoby, “Gate-defined quantum confinement in suspended bilayer graphene,” Nature Communications 3, 934 (2012)

    2012

  3. [11]

    Gate-Defined Confinement in Bilayer Graphene-Hexagonal Boron Nitride Hybrid Devices,

    Augustinus (Stijn) M. Goossens, Stefanie C. M. Driessen, Tim A. Baart, Kenji Watanabe, Takashi Taniguchi, and Lieven M. K. Vandersypen, “Gate-Defined Confinement in Bilayer Graphene-Hexagonal Boron Nitride Hybrid Devices,” Nano Letters 12, 4656–4660 (2012)

    2012

  4. [12]

    Edge currents shunt the insulating bulk in gapped graphene,

    M. J. Zhu, A. V. Kretinin, M. D. Thompson, D. A. Ban- durin, S. Hu, G. L. Yu, J. Birkbeck, A. Mishchenko, I. J. Vera-Marun, K. Watanabe, T. Taniguchi, M. Polini, J. R. Prance, K. S. Novoselov, A. K. Geim, and M. Ben Shalom, “Edge currents shunt the insulating bulk in gapped gr...

    2017

  5. [13]

    Elec trostatically induced quantum point contact in bilayer graphene,

    Hiske Overweg, Hannah Eggimann, Xi Chen, Sergey Slizovskiy, Marius Eich, Riccardo Pisoni, Yongjin Lee, Peter Rickhaus, Kenji Watanabe, Takashi Taniguchi, Vladimir 13 Fal’ko, Thomas Ihn, and Klaus Ensslin, “Elec trostatically induced quantum point contact in bilayer graphene,” ...

    2018

  6. [14]

    Spin and Valley States in Gate-Defined Bilayer Graphene Quantum Dots,

    Marius Eich, František Herman, Riccardo Pisoni, Hiske Overweg, Annika Kurzmann, Yongjin Lee, Peter Rickhaus, Kenji Watanabe, Takashi Taniguchi, Manfred Sigrist, Thomas Ihn, and Klaus Ensslin, “Spin and Valley States in Gate-Defined Bilayer Graphene Quantum Dots,” Phys. Rev. X ...

    2018

  7. [15]

    Klein Backscattering and Fabry -Pérot Interference in Graphene Heterojunctions,

    A. V. Shytov, M. S. Rudner, L. S. Levitov, “Klein Backscattering and Fabry -Pérot Interference in Graphene Heterojunctions,” Phys. Rev. Lett. 101, 156804 (2008)

    2008

  8. [16]

    Quantum interference and Klein tunnelling in graphene heterojunctions,

    A. F. Young, P. Kim, “Quantum interference and Klein tunnelling in graphene heterojunctions,” Nat. Phys. 5, 222–226 (2009)

    2009

  9. [17]

    The Focusing of Electron Flow and a Veselago Lens in Graphene p-n Junctions,

    V. V. Cheianov, V. Fal’ko, B. L. Altshuler, “The Focusing of Electron Flow and a Veselago Lens in Graphene p-n Junctions,” Science. 315, 1252–1255 (2007)

    2007

  10. [18]

    Electrical observation of subband formation in graphene nanoribbons,

    Y.-M. Lin, V. Perebeinos, Z. Chen, and P. Avouris, “Electrical observation of subband formation in graphene nanoribbons,” Phys. Rev. B 78, 161409(R) (2008)

    2008

  11. [19]

    C. Lian, K. Tahy, T. Fang, G. Li, H. G. Xing, and D. Jena,” Quantum transport in graphene nanoribbons patterned by metal masks,” Appl. Phys. Lett. 96, 103109 (2010)

    2010

  12. [20]

    Quantized conductance of a suspended graphene nanoconstriction,

    Nikolaos Tombros , Alina Veligura , Juliane Junesch , Marcos H. D. Guimarães , Ivan J. Vera Marun, Harry T. Jonkman, Bart J. van Wees, “Quantized conductance of a suspended graphene nanoconstriction,” Nat. Phys. 7, 697–700 (2011)

    2011

  13. [21]

    Terrés, L

    B. Terrés, L. A. Chizhova, F. Libisch, J. Peiro, D. Jörger, S. Engels, A. Girschik , K. Watanabe, T. Taniguchi, S. V. Rotkin, J. Burgdörfer, and C. Stampfer,” Size quantization of Dirac fermions in graphene constrictions,” Nat. Commun. 7, 11528 (2016)

    2016

  14. [22]

    Somanchi, B

    S. Somanchi, B. Terrés, J. Peiro, M. Staggenborg, K. Watanabe, T. Taniguchi, B. Beschoten, and C. Stampfer,” From Diffusive to Ballistic Transport in Etched Graphene Constrictions and Nanoribbons,” Ann. Phys. 529, 1700082 (2017)

    2017

  15. [23]

    J. M. Caridad, S. R. Power, M. R. Lotz, A. A. Shylau, J. D. Thomsen, L. Gammelgaard, T. J. Booth, A. -P. Jauho, and P. Bøggild,” Conductance quantization suppression in the quantum Hall regime,” Nat. Commun. 9, 659 (2018)

    2018

  16. [24]

    Quantized edge modes in atomic-scale point contacts in graphene,

    Amogh Kinikar, T. Phanindra Sai1, Semonti Bhattacharyya, Adhip Agarwala , Tathagata Biswas, Sanjoy K. Sarker, H. R. Krishnamurthy , Manish Jain , Vijay B. Shenoy and 14 Arindam Ghosh, “Quantized edge modes in atomic-scale point contacts in graphene,” Nat. Nanotechnology. 12, 5...

    2017

  17. [25]

    Robust quantum point contact operation of narrow graphene constrictions patterned by AFM cleavage lithography,

    Péter Kun , Bálint Fülöp , Gergely Dobrik , Péter Nemes -Incze, István Endre Lukács, Szabolcs Csonka, Chanyong Hwang, Levente Tapasztó, “Robust quantum point contact operation of narrow graphene constrictions patterned by AFM cleavage lithography,” npj 2D Mater Appl 4, 43 (2020)

    2020

  18. [26]

    Nanoscale lithography on monolayer graphene using hydrogenation and oxidation,

    Byun, I. S.; Yoon, D.; Choi, J. S.; Hwang, I.; Lee, D. H.; Lee, M. J.; Kawai, T.; Son, Y. W.; Jia, Q.; Cheong, H., Park, B.H. “Nanoscale lithography on monolayer graphene using hydrogenation and oxidation,” ACS Nano 2011, 5 (8), 6417

    2011

  19. [27]

    P., & Rokhinson, L

    Weng, L., Zhang, L., Chen, Y. P., & Rokhinson, L. P.,” Atomic force microscope local oxidation nanolithography of graphene,” Appl. Phys. Lett. 93, 093107 (2008)

    2008

  20. [28]

    Fabrication of graphene nanoribbon by local anodic oxidation lithography using atomic force microscope,

    Masubuchi, S.; Ono, M.; Yoshida, K.; Hirakawa, K.; Machida, T. “Fabrication of graphene nanoribbon by local anodic oxidation lithography using atomic force microscope,” Appl. Phys. Lett. 2008, 94 (8), 197

    2008

  21. [29]

    Graphene and graphene oxide nanogap electrodes fabricated by atomic force microscopy nanolithography,

    Yudong He, Huanli Dong, Tao Li, Chengliang Wang, Wei Shao, Yajie Zhang, Lang Jiang, and Wenping Hu “Graphene and graphene oxide nanogap electrodes fabricated by atomic force microscopy nanolithography,” Appl. Phys. Lett. 97, 133301 (2010)

    2010

  22. [30]

    Atomic force microscopy-based manipulation of graphene using dynamic plowing lithography,

    Borislav Vasić, Markus Kratzer, Aleksandar Matković, Andreas Nevosad, Uroš Ralević, Djordje Jovanović, Christian Ganser, Christian Teichert and Radoš Gajić, “Atomic force microscopy-based manipulation of graphene using dynamic plowing lithography,” Nanotech. 24, 0153303 (2013)

    2013

  23. [31]

    Electrode-Free Anodic Oxidation Nanolithography of Low - Dimensional Materials,

    Hongyuan Li , Zhe Ying , Bosai Lyu , Aolin Deng , Lele Wang, Takashi Taniguchi , Kenji Watanabe, and Zhiwen Shi, “Electrode-Free Anodic Oxidation Nanolithography of Low - Dimensional Materials,” Nano Lett. 18, 12, 8011–8015 (2018)

    2018

  24. [32]

    Energy Band-Gap Engineering of Graphene Nanoribbons

    Melinda Y. Han, Barbaros Özyilmaz, Yuanbo Zhang, and Philip Kim, “Energy Band-Gap Engineering of Graphene Nanoribbons”, Phys. Rev. Lett. 98, 206805 (2007)

    2007

  25. [33]

    Energy Gaps in Etched Graphene Nanoribbons

    C. Stampfer, J. Gu ̈ttinger, S. Hellmu ̈ller, F. Molitor, K. Ensslin, and T. Ihn, “Energy Gaps in Etched Graphene Nanoribbons”, Phys. Rev. Lett., 102, 056403 (2009)

    2009

  26. [34]

    9, 416 (2009)

    Kathryn Todd, Hung-Tao Chou, Sami Amasha, David Goldhaber-Gordon, “Quantum Dot Behavior in Graphene Nanoconstrictions, Nano Lett. 9, 416 (2009). 15

    2009

  27. [35]

    Electrostatic confinement of electrons in graphene nanoribbons

    Xinglan Liu, Jeroen B. Oostinga, Alberto F. Morpurgo, and Lieven M. K. Vandersypen, “Electrostatic confinement of electrons in graphene nanoribbons”, Phys. Rev. B 80, 121407(R) (2009)

    2009

  28. [36]

    Electrode-Free Anodic Oxidation Nanolithography of Low- Dimensional Materials

    Hongyuan Li, Zhe Ying, Bosai Lyu, Aolin Deng, Lele Wang, Takashi Taniguchi, Kenji Watanabe, Zhiwen Shi, “Electrode-Free Anodic Oxidation Nanolithography of Low- Dimensional Materials”, Nano Lett. 2018, 18, 12, 8011–8015

    2018

  29. [37]

    Boric acid thermal etching graphite felt as a high-performance electrode for iron-chromium redox flow battery

    Zhen Li, Lili Guo, Na Chen, Yang Su, and Xiaomin Wang, “Boric acid thermal etching graphite felt as a high-performance electrode for iron-chromium redox flow battery”, 2022 Mater. Res. Express 9 025601

    2022

  30. [38]

    Disorder-induced gap behavior in graphene nanoribbons

    Gallagher, P.; Todd, K.; Goldhaber-Gordon, D., “Disorder-induced gap behavior in graphene nanoribbons”, Phys. Rev. B 2010, 81, 115409

    2010

  31. [39]

    Fabrication of large addition energy quantum dots in graphene

    Moser, J.; Bachtold, “Fabrication of large addition energy quantum dots in graphene”, A. Appl. Phys. Lett. 2009, 95, 173506

    2009

  32. [40]

    Energy spectra of quantum rings,

    A. Fuhrer, S. Lu ̈scher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra of quantum rings,” Nature 413, 822–825 (2001)

    2001

  33. [41]

    Thomas Ihn, Semiconductor Nanostructures: Quantum states and electronic transport (Oxford University Press, Oxford, New York, 2009)

    2009

  34. [42]

    Quantum dots in carbon nanotubes,

    Sami Sapmaz, Pablo Jarillo-Herrero, Leo P. Kouwen- hoven, and Herre S. J. van der Zant, “Quantum dots in carbon nanotubes,” Semiconductor Science and Tech- nology 21, S52 (2006)

    2006

  35. [43]

    Graphene quantum dots in perpendicular magnetic fields

    J. Gu ̈ttinger, C. Stampfer, F. Libisch, T. Frey, J. Burgdo ̈rfer, T. Ihn, and K. Ensslin, “Graphene quantum dots in perpendicular magnetic fields”, Physica Status Solidi B 246, No. 11, 2553 (2009)

    2009

  36. [44]

    Fabrication of graphene nanoribbon by local anodic oxidation lithography using atomic force microscope

    S. Masubuchi, M. Ono, K. Yoshida, K. Hirakawa, T. Machida, “Fabrication of graphene nanoribbon by local anodic oxidation lithography using atomic force microscope”, Appl. Phys. Lett. 94, 082107 (2009)

    2009

  37. [45]

    Edge disorder induced Anderson local ization and conduction gap in graphene nanoribbons

    Evaldsson, M.; Zozoulenko, I. V.; Xu, H.; Heinzel, T. “Edge disorder induced Anderson local ization and conduction gap in graphene nanoribbons”, Phys. Rev. B 78, 161407(R) (2008). 16

    2008

  38. [46]

    Density inhomogeneity driven percolation metal-insulator transition and dimensional crossover in graphene nanoribbons

    Adam, S.; Cho, S.; Fuhrer, M. S.; Das Sarma, S. “Density inhomogeneity driven percolation metal-insulator transition and dimensional crossover in graphene nanoribbons”, Phys. Rev. Lett, 2008, 101, 046404

    2008

  39. [47]

    Coulomb blockade in graphene nanoribbons

    Sols, F.; Guinea, F.; Castro Neto, “Coulomb blockade in graphene nanoribbons”, A. H. Phys. Rev. Lett. 2007, 99, 166803

    2007

  40. [48]

    Electron flow in split-gated bilayer graphene,

    S. Dröscher, C. Barraud, K. Watanabe, T. Taniguchi, T. Ihn, and K. Ensslin, “Electron flow in split-gated bilayer graphene,” New J. Phys. 14, 103007 (2012)

    2012

  41. [49]

    Valley Subband Splitting in Bilayer Graphene Quantum Point Contacts,

    R. Kraft, I. V. Krainov, V. Gall, A. P. Dmitriev, R. Krupke, I. V. Gornyi, and R. Danneau, “Valley Subband Splitting in Bilayer Graphene Quantum Point Contacts,” Phys. Rev. Lett. 121, 257703 (2018)

    2018

  42. [50]

    Disorder-induced gap behavior in graphene nanoribbons

    Patrick Gallagher, Kathryn Todd, and David Goldhaber -Gordon, “Disorder-induced gap behavior in graphene nanoribbons”, Phys. Rev. B 81, 115409 (2010)

    2010

  43. [51]

    Quantum Dot Behavior in Bilayer Graphene Nanoribbons

    Minsheng Wang, Emil B. Song. Sejoon Lee, Jianshi Tang, Murong Lang, Caifu Zeng, Guangyu Xu, Yi Zhou, and Kang L. Wang, “Quantum Dot Behavior in Bilayer Graphene Nanoribbons”, ACS Nano 2011, 5, 11, 8769–8773. 17 FIG. 1: Fabrication of graphene-based nano constriction devices em...

    2011

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.