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REVIEW 3 major objections 4 minor 64 references

Lattice tuning of charge and spin transport in $\beta_{12}$-borophene nanoribbons

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper argues that lattice vibrations can tune both charge and spin transport in β12-borophene nanoribbons: phonon-assisted processes strengthen the weak spin polarization of zigzag edges and enhance current in nonmagnetic edge…

desk verdict The phonon-assisted transport derivation in Appendix D drops the ±ω₀ energy shifts, and the paper's own DOS makes that error load-bearing; the manuscript deserves a demanding referee, not a desk reject. read the letter →

arxiv 2507.22571 v2 pith:MUFQ6C6P submitted 2025-07-30 cond-mat.mes-hall physics.comp-phquant-ph

Masoumeh Davoudiniya , Jonas Fransson , Biplab Sanyal This is my paper · ORCID
classification cond-mat.mes-hallphysics.comp-phquant-ph PACS 73.63.-b72.10.Di71.38.-k
keywords β12-borophenenanoribbonselectron-phononcouplingHolsteinmodelspinpolarizationphonon-assistedtransportLandauer-Büttikerformalismzigzagedgestatesnonmagneticconfigurations
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

The paper claims that electron-phonon coupling (EPC) can be used as a tuning knob for transport in β12-borophene nanoribbons. In zigzag-edged ribbons, where intrinsic spin polarization is weak, lattice vibrations strengthen the spin polarization and make it appear at lower bias, while in nonmagnetic edge configurations they boost the charge current. The effect shows up as marked changes in current–voltage characteristics, including conductance peaks at biases near 1.1 V and 1.7 V, so it is open to direct experimental probing. The authors build a tight-binding model of the boron pz orbitals, add local Holstein phonons with coupling constants computed from first principles, and solve the resulting device currents with the Landauer–Büttiker Green's function formalism.

What carries the argument

The central object is the Holstein-model phonon self-energy $\Sigma_{\mathrm{ph}}$ added to the retarded Green's function of the central scattering region. It produces a total current $I = I_0 + I_{\mathrm{ph}}$, where $I_0$ is the coherent Landauer–Büttiker current and $I_{\mathrm{ph}}$ is the phonon-assisted inelastic current carried by electrons that emit or absorb a phonon. The coupling constants $g_{q\lambda}$ that feed this self-energy are Brillouin-zone-averaged first-principles electron-phonon matrix elements, and spin enters through a rigid exchange splitting applied to the tight-binding Hamiltonian. This machinery converts lattice motion into bias-dependent extra conduction channels and predicts the voltages at which those channels switch on.

What would settle it

Measure the current–voltage curve of a zigzag β12-borophene nanoribbon at low temperature and again at 300 K: if spin polarization appears at the same bias and the conductance peaks near 1.1 V and 1.7 V do not grow with temperature, the phonon-assisted mechanism is not what controls the transport. A complementary calculation would recompute the spin splitting self-consistently for each ribbon width and show whether it stays at 0.20 eV.

Watch

Extended reading notes

Core claim

The central discovery is that phonon-assisted inelastic processes open additional conduction channels in β12-borophene nanoribbons, and these channels can favor one spin direction. In zigzag-edged ribbons, where edge magnetism is weak and modeled as a rigid splitting Δ = 0.20 eV, adding EPC raises the current in both spin channels but selectively strengthens the spin-up channel in wider ribbons, enough to reverse the spin-conductance order found without phonons and to make spin polarization appear at lower bias. The extra current is dominated by the inelastic component $I_{\mathrm{ph}}$, while the coherent part barely changes. In nonmagnetic line-line, AC-AC, and AC-line edges, EPC smooths quantized conductance steps into a more ohmic-like response and raises the current; for line-line ribbons it reverses the length trend, so the longest ribbon carries the most current. The microscopic source is traced to two phonon modes—a long-wavelength acoustic mode and a bond-stretching optical mode—that together contribute more than 90 percent of the total coupling strength of about 0.55 eV.

Load-bearing premise

The calculations assume the magnetism of every zigzag ribbon can be captured by one fixed rigid energy splitting between the two spin directions, 0.20 eV, no matter how wide, long, biased, or hot the ribbon is.

Editorial extensions

If this is right

  • A zigzag β12-borophene nanoribbon device operated at finite temperature should show spin polarization at lower bias than its ballistic prediction, with the spin-down channel carrying more current at low bias and the spin-up channel catching up in wider ribbons.
  • Phonon-assisted transport lifts the exponential length suppression of coherent tunneling, so in nonmagnetic line-line ribbons longer channels can carry more current than shorter ones.
  • Differential-conductance measurements should reveal phonon-specific resonances near 1.1 V and 1.7 V in zigzag ribbons, effectively turning transport measurements into phonon spectroscopy.
  • Edge configuration becomes a design variable: line-line edges maximize phonon-enhanced charge current, while zigzag edges give phonon-enhanced spin polarization, so a single material can be patterned for either function.
  • Because the inelastic component dominates at 300 K, moderate heating acts as a controllable conductance boost rather than merely a scattering loss.

Reading between the lines

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

  • If the rigid-exchange-splitting model is replaced by a self-consistent magnetic treatment, the qualitative phonon-induced enhancement is likely to survive, but the bias at which spin polarization appears and the size of the I–V features could shift; this is a natural next calculation.
  • A direct experimental test would be to measure the temperature dependence of the differential conductance: the predicted resonances near 1.1 V and 1.7 V should grow as the phonon population increases, and should weaken toward the ballistic low-temperature limit.
  • The same Holstein-plus-NEGF machinery could be applied to other zigzag-edged 2D ribbons with weak edge magnetism, where phonon-assisted channels might similarly alter the dominant spin channel.
  • Because the two dominant phonon modes are identified, isotope substitution or selective strain could shift their frequencies and thereby move the conductance resonances, effectively phonon-engineering the spin filter.
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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

3 major / 4 minor

Summary. The manuscript presents a multiscale study of electron-phonon coupling (EPC) in β12-borophene nanoribbons (BNRs). The authors combine DFT-derived tight-binding parameters and EPC matrix elements with a Holstein-model self-energy and a nonequilibrium Green's function/Landauer-Büttiker transport calculation. Their central claim is that phonon-assisted inelastic processes substantially modify both charge and spin transport: in zigzag-edged BNRs, EPC enhances the weak intrinsic spin polarization at lower bias than in the ballistic case, while in nonmagnetic edge configurations, EPC increases the total charge current. The conclusions are based on spin-resolved current-voltage characteristics, differential conductance, and density-of-states comparisons for several ribbon widths and lengths.

Significance. If the central claim were established, the paper would identify lattice vibrations as a tunable knob for spin filtering in borophene-based nanoribbons, which is a potentially interesting result for 2D spintronics. The work also has genuine strengths: the EPC constants are obtained from DFT rather than fitted to the transport target, and the paper attempts a transparent multiscale workflow. However, the main quantitative conclusion rests on a phonon self-energy derivation in Appendix D that is not correct as written, and the spin-polarization mechanism is built on a rigid exchange-splitting assumption that is not validated at the device level. The significance of the paper therefore cannot be assessed until these load-bearing points are resolved.

major comments (3)
  1. [Appendix D, Eqs. (D1)–(D6)] Evaluating the convolution in Eq. (D1) with D< from Eq. (D2) and g< from Eq. (D3) gives, up to the common prefactor i/(2N)∑g², the expression n_B(ω0) f_C(ω−ω0) A_C(ω−ω0) + [1+n_B(ω0)] f_C(ω+ω0) A_C(ω+ω0). Equation (D5) instead states f_C(ω) A_C(ω)[2 n_B(ω0)+1], which is valid only if the spectral function and Fermi function are approximately constant on the scale of the phonon energy. The paper's own DOS features (Sec. III.A, Fig. 3) have widths of order 50–70 meV, comparable to the phonon energies relevant here, and the claimed mechanism relies on phonon-assisted access to sharp spin-split states. Since Eq. (14) builds Iph directly from Σ<,>ph, the central quantitative claim that EPC enhances spin polarization is not supported by the equations as written.
  2. [Sec. III.B and Supplemental Eq. (S1)] The spin polarization in the transport model is introduced as a fixed, rigid exchange splitting Δ = 0.20 eV taken from prior DFT work and applied uniformly to the nonmagnetic Hamiltonian for all ribbon widths, lengths, biases, and temperatures. The claimed phonon enhancement of spin polarization is therefore conditional on this rigid-band approximation being quantitatively valid for the finite devices studied. This is an assumption that can be tested: a comparison with spin-resolved DFT density of states for the relevant ribbon widths, or a self-consistent treatment of the exchange splitting under bias, would show whether the splitting remains rigid and of the assumed magnitude. I do not regard the use of Δ as circular, since the EPC parameters are computed independently, but the paper should provide such a test before claiming that EPC enhances intrinsic polarization.
  3. [Sec. II.C, Sec. II.D, and Appendix D] It is not clear which phonon self-energy is actually used in the numerical calculations. The main text presents the retarded self-energy in Eq. (10) with the expected ±ωqλ energy shifts, while Appendix D derives lesser and greater self-energies in Eqs. (D5)–(D6) that omit these shifts. If the latter are analytically continued and used in Eq. (11), the peak-shift error propagates into the renormalized DOS and the coherent current I0 as well as into Iph. If, instead, the exact Eq. (10) is used for the retarded self-energy, then the manuscript uses two inconsistent phonon self-energies, and the origin of the numerical results is not reproducible. The authors should specify the exact self-energies used and provide a corrected derivation.
minor comments (4)
  1. [Appendix B and main text] The tight-binding block notation is inconsistent: the main text and the first version of Appendix B use α, β, βw, βl, while the duplicated version of the appendix uses ε, ω, ωw, ωl for the same objects. This makes it unnecessarily difficult to reconstruct the device Hamiltonian.
  2. [General presentation] Several paragraphs and figure captions appear twice with different wording and corrupted symbols (e.g., the description of Fig. 3 near the start of Sec. III.A and the repeated Fig. 3/Fig. 4 captions). These artifacts must be removed and replaced by a single consistent text.
  3. [Sec. III.B, Fig. 4] The text refers to 'Fig. 3(e)' when discussing the decomposition of the differential conductance into coherent and phonon-assisted components, but the corresponding panel appears to be Fig. 4(e). Please correct cross-references between figures and text.
  4. [Appendix C, Eqs. (C2)–(C3)] The transfer-matrix expansion in Eq. (C2) uses quantities t0, ¯t0, t1, etc., but the recursion relations in Eq. (C3) are written for tn and ¯tn without explicitly defining the relationship between these sequences; adding a short definition would make the algorithm reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the transport predictions follow from independent DFT-derived tight-binding and electron-phonon inputs, with spin polarization entered as an external exchange splitting rather than fitted to the target.

full rationale

The paper's derivation chain is not circular. The spin-polarized transport is computed from a tight-binding Hamiltonian whose hopping parameters and on-site energies are taken from independent DFT calculations and prior literature, and the exchange splitting Δ = 0.20 eV is imported from refs [22,24] rather than fitted to any transport output. The electron-phonon coupling strengths come from DFT dynamical matrices and Hamiltonian derivatives (Sec. II.B), and there is no indication they were adjusted to reproduce the reported I–V curves. The central comparison is between the same Hamiltonian with and without phonon self-energies, so the claimed phonon-induced current enhancement and changes in spin polarization are genuine model outputs rather than restatements of the inputs. The self-citations [51,52] provide the tight-binding transport formalism of the same authors, but they are not the load-bearing justification for the new electron-phonon physics; the phonon self-energy and Landauer-Büttiker equations are standard and cited to non-overlapping references. The rigid exchange-splitting assumption is a modeling limitation and makes the predictions conditional, but it is not a circular step because the target quantity is not used to define the input. The Appendix D evaluation of Σ<ph (Eq. D5) appears to omit the ±ω0 energy shifts that are explicit in Eq. D1; this is a technical correctness concern about the inelastic current calculation, but it does not reduce the derivation to a definitional identity. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' own prior work, and no known empirical result is merely relabeled in new coordinates. Therefore the circularity score is 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The transport model rests on externally supplied tight-binding parameters (Table S1) and a rigid exchange splitting; the paper's own DFT provides phonons and EPC. No new physical entities are introduced. The main model assumptions are pz-only tight-binding, BZ-averaged EPC, local Holstein coupling, and ballistic leads.

free parameters (2)
  • Exchange splitting Δ = 0.20 eV
    Applied uniformly to the spin-degenerate Hamiltonian (Eq. S1 in SM); taken from refs [22,24], not recomputed for each ribbon; all spin transport results depend on it.
  • Effective phonon frequency ω0 (Appendix D) = not specified
    The inelastic self-energy in Eqs. (D5)-(D6) is evaluated at a single phonon frequency ω0; its value determines the Bose occupation factor and the energy shift, but the paper does not state which phonon mode or value is used in the transport calculations.
assumptions (5)
  • domain assumption pz-only tight-binding model
    Hamiltonian Eq. (1) keeps only pz orbitals; justified by orbital-projected band structure in Fig. 1(c), following ref [39].
  • ad hoc to paper Rigid exchange splitting represents edge magnetism
    Spin polarization is inserted as a uniform Δ rather than obtained self-consistently; used throughout Sec. III.B.
  • domain assumption BZ-averaged EPC strength g2_qλ
    Eq. (5) averages over k and orbital indices, removing k-dependence from the self-energy; momentum-dependent scattering is thereby neglected.
  • domain assumption Local Holstein coupling in central region, ballistic leads
    EPC is confined to the scattering region while leads are modeled as ideal reservoirs; this separation affects the phonon-assisted current.
  • standard math Standard NEGF/Landauer-Büttiker relations
    Retarded Green's function Eq. (11) and currents Eqs. (13)-(14) follow standard quantum transport theory (ref [35]).

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Cite this review

Pith. "Pith review of Lattice tuning of charge and spin transport in $\beta_{12}$-borophene nanoribbons." pith.science (2026). https://pith.science/paper/MUFQ6C6P

@misc{pith2026250722571,
  author       = {Pith},
  title        = {Pith review of: Lattice tuning of charge and spin transport in $\beta_12$-borophene nanoribbons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MUFQ6C6P}},
  note         = {Machine review of arXiv:2507.22571}
}
abstract

$\beta_{12}$-borophene nanoribbons (BNRs) exhibit magnetic zigzag edges, while other edge configurations are nonmagnetic. However, when the source, central, and drain regions of a logic device are all composed of zigzag BNRs (ZBNRs), the resulting spin polarization remains weak, unless a high voltage is applied. In this work, we demonstrate that lattice vibrations-introduced for example, via a thermal bath coupled to the central BNR-can enhance spin polarization in ZBNRs. This enhancement manifests as marked changes in the current-voltage characteristics, enabling direct experimental probing. In contrast, nonmagnetic edge configurations exhibit phonon-enhanced charge transport. We employ a tight-binding approach augmented with local electron-phonon interactions described by the Holstein model, and compute the phonon-renormalized Green's functions and transport currents using the Landauer-B\"{u}ttiker formalism. The mechanism is supported by analyzing both spinless and spinful electronic dispersions and the corresponding density of states. Compared to the phonon-free edges, structural distortions lead to anisotropic electron-phonon couplings, which significantly modify both charge and spin transport. These results position phonon as an effective tuning parameter for optimizing borophene-based logic devices via engineered edge configurations.

Figures

Figures reproduced from arXiv: 2507.22571 by the authors.

Figure 1
Figure 1. FIG. 1: (a) Atomic structure of FIG. 1. (a) Atomic structure of β12-bo 2D βborophene sheetindicating th [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic of the multiscale computational framework used in this work. First-principles (ab initio) calculations [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Local and total density of states (DOS) for (af) zigzag and (gi) lineline edge configurations o f 4 it lld lth f 4 llPl(b) d tthihl f th FIG. 3. Local and total density of states (DOS) for (a–f) zigzag and (g–i) line–line edge configurations of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: (a) illustrates the two-probe device structure employed in our nonequilibrium Green’s function calcu￾lations of electron transport through a zigzag-edge ω12- BNR. The scattering region consists of four supercells, each four fundamental unit cells wide; EPC is explic￾it…
Figure 6
Figure 6. Figure 6: FIG. 6. FIG5 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. tion p [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Two–probe setup used for the nonequilibrium Green’s-function calculations on a 4-unit-cell-wide and 4-supercell FIG. 6. (a) Two–probe setup used for the nonequilibrium Green’s-function calculations on a 4-unit-cell-wide and 4-supercell [PITH_FULL_IMAGE:f…
Figure 7
Figure 7. Figure 7: FIG. 7. Current–voltage characteristics, di!erential conductance and density of states for a 4-unit-cell-wide FIG. 7. Current–voltage characteristics, differential conductance and density of states for a 4-unit-cell-wide [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Representative ribbon geometries of FIG8Rttiibbtif [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Schematic illustration of armchair- and zigzag-edged FIG. 9. Schematic illustration of armchair- and zigzag-edged [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

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Works this paper leans on

64 extracted references · 58 canonical work pages

  1. [1]

    Phonon self-energy To incorporate e-ph interactions, we introduce the Hol- stein phonon self-energy. Transforming to the frequency domain, the lesser component of the phonon self-energy is given by Σ< ph(ω) = i 2N X q,λ g2 q,λ Z g< C (E) D<(ω − E) dE 2π , (D1) where the lesser phonon Green’s function is D<(ω) = −2πi nB(ω) δ(ω − ω0) − δ(ω + ω0) (D2) with n...

    work page

  2. [2]

    with the self-energyΣC in- cluding contributions from the leads and phonons, ΣC = Σleads + Σphonons +

    Green’s functions and self-energies The total Green’s function for the central region is ob- tained from: GC = [z − HC − ΣC]−1 , z = ϵ + iη, , (D7) where HC is the Hamiltonian of the central region and η is a positive infinitesimal. with the self-energyΣC in- cluding contributions from the leads and phonons, ΣC = Σleads + Σphonons + . . . , (D8) For the l...

    work page

  3. [3]

    #$ℎ !! ! ! !

    and DST-SPARC, India (Ref. No. SPARC/2019- 2020/P1879/SL). The computations were enabled by resources provided by the National Academic Infras- tructure for Supercomputing in Sweden (NAISS) at UPPMAX (NAISS 2024/5-258) and at NSC and PDC (NAISS 2023/3-42) partially funded by the Swedish Re- search Council through grant agreement no. 2022-06725. B.S. also ...

    work page 2019

  4. [4]

    Zhao and J.-F

    C.-X. Zhao and J.-F. Jia, Stanene: A good platform for topological insulator and topological superconductor, Frontiers of Physics15, 53201 (2020)

    work page 2020

  5. [5]

    The EPC-driven en- hancement is further evidenced in the di!erential con- ductance profiles [Fig

    experiences the strongest EPC-driven improvement, largely mitigating the hybridization-induced suppression observed in the ballistic regime and restoring a nearly monotonic width-dependent trend. The EPC-driven en- hancement is further evidenced in the di!erential con- ductance profiles [Fig. 5(h)], which shift upward signifi- cantly compared to their balli...

    work page 2022

  6. [6]

    K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless dirac fermions in graphene, Nature438, 197 (2005)

    2005

  7. [7]

    W. B. L. Gao Yang, Lihua Li and M. C. Ng, Struc- ture of graphene and its disorders: a review, Science and Technology of Advanced Materials19, 613 (2018), pMID: 30181789

    work page 2018

  8. [8]

    Chaudhary, P

    V. Chaudhary, P. Neugebauer, O. Mounkachi, S. Lah- babi, and A. E. Fatimy, Phosphorene—an emerging two- dimensional material: recent advances in synthesis, func- tionalization, and applications, 2D Materials9, 032001 (2022)

    work page 2022

Show all 64 references
  1. [9]

    Naguib, M

    M. Naguib, M. W. Barsoum, and Y. Gogotsi, Ten years of progress in the synthesis and development of mxenes, Advanced Materials33, 2103393 (2021)

    2021

  2. [10]

    Molle and C

    H.J.Zandvliet,2-germanene,in Xenes,WoodheadPub- lishing Series in Electronic and Optical Materials, edited by A. Molle and C. Grazianetti (Woodhead Publishing,

  3. [11]

    M. A. Kharadi, G. F. A. Malik, F. A. Khanday, K. A. Shah, S. Mittal, and B. K. Kaushik, Review—silicene: From material to device applications, ECS Journal of Solid State Science and Technology9, 115031 (2020). 15

    2020

  4. [12]

    B. Feng, L. Chen, and K. Wu, Synthesis of borophene, in 2D Boron: Boraphene, Borophene, Boronene , edited by I. Matsuda and K. Wu (Springer International Publish- ing, Cham, 2021) pp. 51–72

    2021

  5. [13]

    B. Zhao, D. Shen, Z. Zhang, P. Lu, M. Hossain, J. Li, B.Li,andX.Duan,2dmetallictransition-metaldichalco- genides: Structures, synthesis, properties, and appli- cations, Advanced Functional Materials 31, 2105132 (2021)

    2021

  6. [14]

    C. Hou, G. Tai, Y. Liu, R. Liu, X. Liang, Z. Wu, and Z. Wu, Borophene pressure sensing for electronic skin and human-machine interface, Nano Energy97, 107189 (2022)

    2022

  7. [15]

    S. Roy, X. Zhang, A. B. Puthirath, A. Meiyazhagan, S. Bhattacharyya, M. M. Rahman, G. Babu, S. Susarla, S. K. Saju, M. K. Tran, L. M. Sassi, M. A. S. R. Saadi, J. Lai, O. Sahin, S. M. Sajadi, B. Dharmara- jan, D. Salpekar, N. Chakingal, A. Baburaj, X. Shuai, A. Adumbumkulath, ...

    2021

  8. [16]

    T. S. Miller, A. B. Jorge, T. M. Suter, A. Sella, F. Corà, and P. F. McMillan, Carbon nitrides: synthesis and char- acterization of a new class of functional materials, Phys. Chem. Chem. Phys.19, 15613 (2017)

    2017

  9. [17]

    Ashraf, S

    I. Ashraf, S. Rizwan, and M. Iqbal, A comprehen- sive review on the synthesis and energy applications of nano-structured metal nitrides, Frontiers in Materials7, 10.3389/fmats.2020.00181 (2020)

    2020

  10. [18]

    Lany, Semiconducting transition metal oxides, Journal of Physics: Condensed Matter27, 283203 (2015)

    S. Lany, Semiconducting transition metal oxides, Journal of Physics: Condensed Matter27, 283203 (2015)

    2015

  11. [19]

    Zhong, L

    Q. Zhong, L. Kong, J. Gou, W. Li, S. Sheng, S. Yang, P. Cheng, H. Li, K. Wu, and L. Chen, Synthesis of borophene nanoribbons on ag(110) surface, Phys. Rev. Mater. 1, 021001 (2017)

    2017

  12. [20]

    G. H. Gupta, S. Kadakia, D. Agiwal, T. Keshari, and S. Kumar, Borophene nanomaterials: synthesis and ap- plications in biosensors, Mater. Adv.5, 1803 (2024)

    2024

  13. [21]

    N. K. Arkoti and K. Pal, Improved selectivity of borophene sensor towards no2 gas with pei-zif-8 over- layer, Sensors and Actuators B: Chemical401, 135033 (2024)

    2024

  14. [22]

    C.Hou, G.Tai, Y.Liu,andX.Liu,Borophenegassensor, Nano Research15, 2537 (2022)

    2022

  15. [23]

    B. Peng, H. Zhang, H. Shao, Z. Ning, Y. Xu, G. Ni, H. Lu, D. W. Zhang, and H. Zhu, Stability and strength of atomically thin borophene from first principles calcu- lations, Materials Research Letters5, 399 (2017)

    2017

  16. [24]

    B. Feng, O. Sugino, R.-Y. Liu, J. Zhang, R. Yukawa, M. Kawamura, T. Iimori, H. Kim, Y. Hasegawa, H. Li, L. Chen, K. Wu, H. Kumigashira, F. Komori, T.-C. Chiang, S. Meng, and I. Matsuda, Dirac fermions in borophene, Phys. Rev. Lett.118, 096401 (2017)

    2017

  17. [25]

    Q. Li, L. Wang, H. Li, M. K. Y. Chan, and M. C. Hersam, Synthesis of quantum-confined borophene nanoribbons, ACS Nano18, 483 (2024)

    2024

  18. [26]

    B. N. Šoškić, J. Bekaert, C. Sevik, and M. V. Miloše- vić, Enhanced superconductivity of hydrogenated β12 borophene, Nano Letters24, 12650–12657 (2024)

    2024

  19. [27]

    Ezawa, Triplet fermions and dirac fermions in borophene, Phys

    M. Ezawa, Triplet fermions and dirac fermions in borophene, Phys. Rev. B96, 035425 (2017)

    2017

  20. [28]

    Jalali-Mola and S

    Z. Jalali-Mola and S. A. Jafari, Kinked plasmon disper- sion in borophene-borophene and borophene-graphene double layers, Phys. Rev. B98, 235430 (2018)

    2018

  21. [29]

    Orellana and R

    W. Orellana and R. H. Miwa,Feand Co adatoms on bi- layer borophene as single-atom catalysts for the oxygen- reduction reaction: A theoretical study, Phys. Rev. Appl. 21, 034008 (2024)

    2024

  22. [30]

    Y. Zhao, S. Zeng, C. Lian, Z. Dai, S. Meng, and J. Ni, Multigap anisotropic superconductivity in borophenes, Phys. Rev. B98, 134514 (2018)

    2018

  23. [31]

    Nakhaee, S

    M. Nakhaee, S. A. Ketabi, and F. M. Peeters, Tight- binding model for borophene and borophane, Phys. Rev. B 97, 125424 (2018)

    2018

  24. [32]

    Zhong, K

    H. Zhong, K. Huang, G. Yu, and S. Yuan, Electronic and mechanical properties of few-layer borophene, Phys. Rev. B 98, 054104 (2018)

    2018

  25. [33]

    S. Guo, Y. Wang, H. Qu, W. Zhou, Y. S. Ang, S. Zhang, and H. Zeng, Theoretical dissection of the electronic anisotropy and quantum transport of ultrascaled halo- genated borophene mosfets, Phys. Rev. Appl.21, 054016 (2024)

    2024

  26. [34]

    Chen, H.-Y

    Y.-J. Chen, H.-Y. Lu, F.-L. Shao, and P. Zhang, Predic- tion of two stable freestanding β12 borophanes: Struc- ture, electronic properties, and superconductivity, Phys- ical Review Materials7, 034004 (2023)

    2023

  27. [35]

    J. Liu, J. Wu, C. Chen, L. Han, Z. Zhu, and J. Wu, Negative differential resistance and magnetoresistance in zigzag borophene nanoribbons, International Journal of Modern Physics B32, 1850033 (2018)

    2018

  28. [36]

    Sun, X.-F

    C. Sun, X.-F. Wang, L.-P. Zhou, and Y.-S. Liu, The magnetism enhancement and spin transport in zigzag borophene nanoribbons edge-passivated by n atoms, Ap- plied Nanoscience10, 29–35 (2019)

    2019

  29. [37]

    T. C. Phong, H. V. Phuc, and L. T. T. Phuong, Electron– phonon coupling effect on the optical absorption of gated β12-borophene,PhysicalChemistryChemicalPhysics 26, 18983 (2024)

    2024

  30. [38]

    Gao, Q.-Z

    M. Gao, Q.-Z. Li, X.-W. Yan, and J. Wang, Prediction of phonon-mediated superconductivity in borophene, Phys- ical Review B95, 024505 (2017)

    2017

  31. [39]

    Smidstrup, T

    S. Smidstrup, T. Markussen, P. Vancraeyveld, J. Wellen- dorff, J. Schneider, T. Gunst, B. Verstichel, D. Stradi, P. A. Khomyakov, U. G. Vej-Hansen, M.-E. Lee, S. T. Chill, F. Rasmussen, G. Penazzi, F. Corsetti, A. Ojan- perä, K. Jensen, M. L. N. Palsgaard, U. Martinez, A. Blom...

    2019

  32. [40]

    Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, 2005)

    S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, 2005)

    2005

  33. [41]

    G. L. Goodvin, M. Berciu, and G. A. Sawatzky, Green’s function of the holstein polaron, Phys. Rev. B74, 245104 (2006)

    2006

  34. [42]

    Holstein, Studies of polaron motion: Part i

    T. Holstein, Studies of polaron motion: Part i. the molecular-crystal model, Annals of Physics8, 325 (1959)

    1959

  35. [43]

    Holstein, Studies of polaron motion: Part ii

    T. Holstein, Studies of polaron motion: Part ii. the “small” polaron, Annals of Physics8, 343 (1959)

    1959

  36. [44]

    Gunst, T

    T. Gunst, T. Markussen, K. Stokbro, and M. Brandbyge, First-principles method for electron-phonon coupling and electron mobility: Applications to two-dimensional ma- terials, Physical Review B93, 035414 (2016)

    2016

  37. [45]

    P. T. T. Le, T. C. Phong, and M. Yarmohammadi,β12- 16 borophene becomes a semiconductor and semimetal via a perpendicular electric field and dilute charged impurity, Physical Chemistry Chemical Physics21, 21790–21797 (2019)

    2019

  38. [46]

    L. T. T. Phuong, B. D. Hoi, and M. Yarmohammadi, Optical redshift and blueshift spectra in monolayerβ12- borophene: Inversion symmetry breaking effects, Phys. Rev. B106, 195409 (2022)

    2022

  39. [47]

    X.Zhang, J.Hu, Y.Cheng, H.Y.Yang, Y.Yao,andS.A. Yang, Borophene as an extremely high capacity elec- trode material for li-ion and na-ion batteries, Nanoscale 8, 15340 – 15347 (2016), cited by: 423; All Open Access, Green Open Access

    2016

  40. [48]

    See the Supplemental Materials at http://xxx.yyy.zzz for further details on the hopping parameters, the local den- sity of states for magnetic and non-magneticβ12-BNRs, and the transport properties of other non-magnetic con- figurations of β12-BNRs

  41. [49]

    Xing, Z.-H

    E.-F. Xing, Z.-H. Niu, G.-P. Zhang, C.-K. Wang, G. Chen, and Y. Song, First principles design of mul- tifunctional spintronic devices based on super nar- row borophene nanoribbons, Scientific Reports 15, 10.1038/s41598-025-87132-2 (2025)

    2025 doi

  42. [50]

    Kaasbjerg, K

    K. Kaasbjerg, K. S. Thygesen, and K. W. Jacobsen, Phonon-limited mobility inn-type single-layer mos2 from first principles, Physical Review B85, 115317 (2012)

    2012

  43. [51]

    G. D. Mahan, Many-Particle Physics (Springer US, 2000)

    2000

  44. [52]

    M. Yarmohammadi, Strain effects on the optical con- ductivity of gapped graphene in the presence of holstein phonons beyond the dirac cone approximation, AIP Ad- vances6, 085008 (2016)

    2016

  45. [53]

    Q. Gao, Z. Hu, and L. Chen, Strain-tunable electronic properties of 2d-b9: a borophene allotrope with mechan- ical flexibility, Journal of Physics: Condensed Matter37, 175501 (2025)

    2025

  46. [54]

    Wakabayashi, Electronic transport properties of nanographite ribbon junctions, Physical Review B 64, 10.1103/physrevb.64.125428 (2001)

    K. Wakabayashi, Electronic transport properties of nanographite ribbon junctions, Physical Review B 64, 10.1103/physrevb.64.125428 (2001)

    2001 doi

  47. [55]

    Kumar, G

    P. Kumar, G. Singh, R. Bahadur, Z. Li, X. Zhang, C. I. Sathish, M. R. Benzigar, T. K. A. Tran, N. T. Padman- abhan, S. Radhakrishnan, J. C. Janardhanan, C. A. Biji, A. J. Mathews, H. John, E. Tavakkoli, R. Murugavel, S.Roy, P.M.Ajayan,andA.Vinu,Theriseofborophene, Progress in ...

    2024

  48. [56]

    Davoudiniya and K

    M. Davoudiniya and K. Mirabbaszadeh, Effects of strain and electric fields on the electronic transport proper- ties of single-layerβ12-borophene nanoribbons, Physical Chemistry Chemical Physics23, 18647–18658 (2021)

    2021

  49. [57]

    Davoudiniya and K

    M. Davoudiniya and K. Mirabbaszadeh, Quantum trans- port along the armchair and zigzag edges of β12- borophene nanoribbons in the presence of a zeeman mag- netic field and dilute charged impurities, Physical Chem- istry Chemical Physics23, 26285–26295 (2021)

    2021

  50. [58]

    Chakrabarty, A

    S. Chakrabarty, A. H. M. A. Wasey, R. Thapa, and G. P. Das, Origin of spin polarization in an edge boron doped zigzag graphene nanoribbon: a potential spin filter, Nan- otechnology 29, 345203 (2018)

    2018

  51. [59]

    D. H. Lee and J. D. Joannopoulos, Simple scheme for surface-band calculations. ii. the green’s function, Phys. Rev. B23, 4997 (1981)

    1981

  52. [60]

    Ding and J

    Y. Ding and J. Ni, Electronic structures of sil- icon nanoribbons, Applied Physics Letters 95, 10.1063/1.3211968 (2009)

    2009 doi

  53. [61]

    Y.-L. Song, Y. Zhang, J.-M. Zhang, and D.-B. Lu, Ef- fects of the edge shape and the width on the structural and electronic properties of silicene nanoribbons, Applied Surface Science256, 6313–6317 (2010)

    2010

  54. [62]

    Fang, S.-L

    D.-Q. Fang, S.-L. Zhang, and H. Xu, Tuning the elec- tronic and magnetic properties of zigzag silicene nanorib- bons by edge hydrogenation and doping, RSC Advances 3, 24075 (2013)

    2013

  55. [63]

    M. P. L. Sancho, J. M. L. Sancho, J. M. L. Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface green functions, Journal of Physics F: Metal Physics15, 851 (1985)

    1985

  56. [9386]

    and DST-SPARC, India (Ref. No. SPARC/2019- 2020/P1879/SL). The computations were enabled by resources provided by the National Academic Infras- tructure for Supercomputing in Sweden (NAISS) at UPPMAX (NAISS 2024/5-258) and at NSC and PDC (NAISS 2023/3-42) partially funded by t...

    2019

Pith tools

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