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Cited by 780Topological Materials and PhenomenaQuantum and electron transport phenomenaSurface and Thin Film Phenomena

Aharonov–Bohm interference in topological insulator nanoribbons

Open access
Peng, Hailin, Lai, Keji, Kong, Desheng, Meister, Stefan, Chen, Yulin, Qi, Xiao-Liang, Zhang, Shou-Cheng, Shen, Zhi-Xun +1 more·2010·Nature Materials
DOI 10.1038/nmat2609
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Abstract

Topological insulators represent unusual phases of quantum matter with an insulating bulk gap and gapless edges or surface states. The two-dimensional topological insulator phase was predicted in HgTe quantum wells and confirmed by transport measurements. Recently, Bi(2)Se(3) and related materials have been proposed as three-dimensional topological insulators with a single Dirac cone on the surface, protected by time-reversal symmetry. The topological surface states have been observed by angle-resolved photoemission spectroscopy experiments. However, few transport measurements in this context have been reported, presumably owing to the predominance of bulk carriers from crystal defects or thermal excitations. Here we show unambiguous transport evidence of topological surface states through periodic quantum interference effects in layered single-crystalline Bi(2)Se(3) nanoribbons, which have larger surface-to-volume ratios than bulk materials and can therefore manifest surface effects. Pronounced Aharonov-Bohm oscillations in the magnetoresistance clearly demonstrate the coherent propagation of two-dimensional electrons around the perimeter of the nanoribbon surface, as expected from the topological nature of the surface states. The dominance of the primary h/e oscillation, where h is Planck's constant and e is the electron charge, and its temperature dependence demonstrate the robustness of these states. Our results suggest that topological insulator nanoribbons afford promising materials for future spintronic devices at room temperature.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper reports transport evidence for topological surface states in single-crystalline Bi₂Se₃ nanoribbons via periodic Aharonov–Bohm magnetoresistance oscillations. The dominant h/e period matches the nanoribbon cross-sectional area, indicating phase-coherent 2D surface conduction around the entire ribbon perimeter.

Key findings

  • Pronounced reproducible magnetoresistance oscillations with period 0.62 T were observed at 2 K; for the h/e AB effect this corresponds to an area of 6.7 × 10⁻¹⁵ m², in excellent agreement with the measured cross section S = w × t = 6.6 × 10⁻¹⁵ m².
  • FFT of dR/dB shows a prominent h/e oscillation and a weak second harmonic at h/2e; the primary h/e oscillation amplitude roughly scales with T⁻¹/² between 2 K and 20 K, and most oscillatory features persist up to 20 K.
  • The AB effect demonstrates that surface states cover the entire nanoribbon surface, including side walls, and remain phase coherent despite bulk conduction; the oscillation amplitude is on the order of the quantized conductance e²/h.
  • In additional devices, a narrow ribbon (200 nm × 50 nm) showed resistance minima at multiples of 0.4 T matching its cross section, while a wide ribbon (570 nm × 50 nm) showed aperiodic magnetoresistance reminiscent of universal conductance fluctuations.

Methods

  • Single-crystalline Bi₂Se₃ nanoribbons were synthesized by gold-catalyzed vapor–liquid–solid growth, with thicknesses of 25–100 nm and widths from 50 nm to several micrometers; EDX gave a Bi:Se atomic ratio of 2:3, and TEM/XRD confirmed single-crystalline rhombohedral Bi₂Se₃.
  • Four-point-probe devices were fabricated with Ti/Au Ohmic contacts; magnetoresistance was measured in a 9-T Quantum Design PPMS with a base temperature of 2 K.
  • Oscillatory components were analyzed by fast Fourier transform of dR/dB to separate them from slowly varying background.

Limitations

  • Stated: bulk carriers remain present and can superimpose aperiodic universal conductance fluctuations and SdH-related background on the clean AB oscillations; high-field periodicity deteriorates slightly.
  • Stated: the phase-coherent length Lφ is likely around 0.5 µm at 2 K, so wider ribbons do not show clear AB periodicity; lower-temperature experiments are expected in the future.
  • Evident: the reported AB results were observed only in samples with relatively low total electron density ∼5 × 10¹³ cm⁻², while the total Hall density across samples ranged from 3 × 10¹³ to 2 × 10¹⁴ cm⁻².

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/nmat2609

Cites

26 of 26 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 20 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 2

    For fields 0.15 T < |B| < 2 T, pronounced and reproducible resistance oscillations with a period of 0.62 T are observed.

    “For fields 0.15T &lt; | B | &lt; 2T, pronounced and reproducible resistance oscillations with a period of 0.62T are observed.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 4

    The authors report the first transport measurement in this class of materials, based on the AB oscillations of the conductance associated with the topological surface states.

    “We report the first transport measurement in this class of materials, based on the AB oscillations of the conductance associated with the topological surface states.”
    Quote in the paperSubstantial claim
  • Findingreasoning
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 3

    The h/e oscillation amplitude roughly scales with T^-1/2 between 2 K and 20 K, where inelastic phonon scattering is negligible.

    “In Fig. 3b, the h/e oscillation amplitude roughly scales with T -1 / 2 between 2K and 20K, where the inelastic phonon scattering is negligible.”
    Quote in the paperSubstantial claim
  • Findingnone given
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 4

    The authors have fabricated topological insulator materials in nanoribbon form with large surface-to-volume ratios.

    “In conclusion, we have fabricated topological insulator materials in nanoribbon form, with large surface-tovolume ratios.”
    Quote in the paperSubstantial claim
  • Findingnone given
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    Results reported below are only observed in samples with relatively low total density ∼ 5 × 10^13 cm^-2.

    “Results reported below are only observed in samples with relatively low total density ∼ 5 × 10 13 cm -2 .”
    Quote in the paperSubstantial claim
  • May combine two claims. 22
  • Classified as probably not a substantial claim. 3

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 2

    The FFT of dR/dB shows a prominent h/e oscillation and a weak second harmonic at h/2e.

    “As shown in the inset of Fig. 2d, the prominent h/e oscillation and a weak second harmonic at h/ 2 e are better seen by taking the fast Fourier transform (FFT) of the derivative d R /d B”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 4

    The magnetoresistance of the wide ribbon (570 nm × 50 nm) does not display obvious periodicity, and its Fourier spectrum is reminiscent of the UCF effect.

    “On the other hand, the magnetoresistance of the wide ribbon (570nm × 50nm) in Fig. 4b does not display obvious periodicity, and the characteristics of its Fourier spectrum are reminiscent of the UCF effect.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 3

    The oscillation amplitude observed is on the order of the quantized conductance e^2/h, comparable to other quasi-1D nanostructures and disordered metal cylinders.

    “The oscillation amplitude observed in our experiment is on the order of the quantized conductance ( e 2 /h ), comparable to other quasi-1D nanostructures [25] and disordered metal cylinders [18].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [25] Hikami, S., Larkin, A. I. & Nagaoka, Y. Spin–orbit interaction and magnetoresistance in the 2 dimensional random system. Prog. Theor. Phys. 63, 707–710 (1980).

      Not checked in the free run.

    • cites [18] Fu, L. & Kane, C. L. Superconducting proximity effect and majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008). source

      Not checked in the free run.

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 4

    For the relatively narrow ribbon, well-defined resistance minima are observed at multiples of 0.4 T, and the inferred area from h/e flux quantization matches the cross-sectional area (200 nm × 50 nm) within measurement error bars.

    “For the relatively narrow ribbon in Fig. 4a, well defined resistance minima are observed at multiples of 0.4T except for weak shoulders at ∼ 0.8T. This period is better seen in the FFT plot. The inferred area from the h/e fl ux quantization again matches the cross sectional area (200nm × 50nm) well within the measurement error bars.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 2

    The 0.62 T period corresponds to an area of 6.7 × 10^-15 m^2, in excellent agreement with the measured cross-sectional area of the nanoribbon S = w × t = 6.6 × 10^-15 m^2.

    “For the h/e AB effect, this period is associated with an area of 6 . 7 × 10 -15 m 2 , in excellent agreement with the measured cross sectional area of the nanoribbon S = w × t = 6 . 6 × 10 -15 m 2 (Fig. 2b).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 2

    At higher fields, the perfect periodicity deteriorates slightly, but a roughly linear relation of 0.6 T per resistance minimum still holds up to 9 T.

    “At higher fields (Fig. 2d), the perfect periodicity deteriorates slightly, but a roughly linear relation of 0.6T per resistance minimum still holds up to 9T.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    The as-grown Bi2Se3 nanoribbons have thicknesses of 25-100 nm and widths ranging from 50 nm to several micrometers.

    “Figure 1b shows a typical scanning electron microscopy (SEM) image of the as-grown Bi 2 Se 3 nanoribbons with thicknesses of 25-100nm and widths ranging from 50nm to several micrometers.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 3

    Most oscillatory features persist up to 20 K, beyond which the zero field resistance increases considerably, presumably due to phonon scattering.

    “As shown in Fig. 3a, most oscillatory features persist up to 20K, beyond which the zero field resistance increases considerably (inset of Fig. 3b), presumably due to phonon scattering.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 2

    At low magnetic fields |B| < 0.15 T, the weak anti-localization effect with a sharp cusp at zero field is seen, consistent with strong spin-orbit coupling in Bi2Se3.

    “At low magnetic fields | B | &lt; 0 . 15T, the weak anti-localization effect [24] with a sharp cusp at zero field is seen in Fig. 2c, consistent with the presence of strong spin-orbit coupling in Bi2Se3.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [24] Lee, P. A. & Stone, A. D. Universal conductance fluctuations in metals. Phys. Rev. Lett. 55, 1622–1625 (1985). source

      Not checked in the free run.

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    The total electron density measured by the Hall effect is between 3 × 10^13 and 2 × 10^14 cm^-2, with an effective Hall mobility ∼ 2 × 10^3 cm^2/Vs.

    “The total electron density measured by the Hall effect is between 3 × 10 13 to 2 × 10 14 cm -2 , with an effective Hall mobility ∼ 2 × 10 3 cm 2 /Vs extracted from the sheet resistance .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    EDX analysis reveals uniform chemical composition along the ribbon length with a Bi:Se atomic ratio of 2:3, indicating stoichiometric Bi2Se3 free of detectable impurities.

    “Energy-dispersive Xray spectroscopy (EDX) analysis reveals uniform chemical composition along the ribbon length with a Bi:Se atomic ratio of 2:3, indicating stoichiometric Bi 2 Se 3 free of detectable impurities.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingcitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 3

    The primary oscillation period corresponds to the Aharonov-Bohm h/e quantization, while the Altshuler-Aronov-Spivak (AAS) oscillation with h/2e period is suppressed.

    “Finally, the primary oscillation period corresponds to the Aharonov-Bohm h/e quantization, while the Altshuler-Aronov-Spivak (AAS) oscillation with h/ 2 e period [27, 28] originating from weak (anti) localization is suppressed.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [27] Berggren, K. F., Thornton, T. J., Newson, D. J. & Pepper, M. Magnetic depopulation of 1D subbands in a narrow 2D electron gas in a GaAs:AlGaAs heterojunction. Phys. Rev. Lett. 57, 1769–1772 (1986). source

      Not checked in the free run.

    • cites [28] Altshuler, B. L., Aronov, A. G. & Spivak, B. Z. The Aharonov–Bohm effect in disordered conductors. Jetp Lett. 33, 94–97 (1981).

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    Bi2Se3 and related materials have been proposed as three-dimensional topological insulators with a single Dirac cone on the surface and verified by angle-resolved photoemission spectroscopy experiments.

    “3D topological insulators with the simplest possible surface states consisting of a single Dirac cone, on the other hand, have been proposed theoretically [10] in stoichiometric compounds Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 , and topological surface states have been observed independently by angle-resolved photoemission spectroscopy (ARPES) experiments in Bi 2 Se 3 [11].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [10] Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007). source

      Not checked in the free run.

    • cites [11] Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    Such a high electron density indicates the existence of bulk carriers in the nanoribbons, while their contribution is suppressed compared with macroscopic samples.

    “Such a high electron density indicates the existence of bulk carriers in our nanoribbons, while their contribution is suppressed compared with macroscopic samples.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    Bi2Se3 has a simple band structure with a single Dirac cone on the surface and a large non-trivial bulk gap of 0.3 eV.

    “Among these materials, Bi 2 Se 3 , a narrow gap semiconductor for IR detectors and thermoelectric applications [13], has a simple band structure with a single Dirac cone on the surface and a large non-trivial bulk gap of 0.3eV [10, 11].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [10] Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007). source

      Not checked in the free run.

    • cites [11] Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 2

    For 2D states covering the entire surface, all phase coherent trajectories participating in quantum interference enclose the same area perpendicular to the B-field, leading to periodic magnetoresistance oscillations with a characteristic period ∆B = Φ0/S.

    “For the 2D states covering the entire surface, however, all phase coherent trajectories participating in the quantum interference enclose the same area perpendicular to the B -field (Fig. 2a). The low temperature transport therefore exhibits periodic magnetoresistance oscillations, a hallmark of the well-known Aharonov-Bohm (AB) effect [23], with a characteristic period of the external magnetic fi”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [23] Wyckoff, R. W. G. Crystal Structures (Krieger, 1986).

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    Despite extensive transport experiments on bulk Bi2Se3 since the 1970's, there has been no report of a conducting surface layer, and the predicted topological features have not been addressed.

    “However, despite extensive transport experiments on bulk Bi 2 Se 3 since the 1970's [19], there has been no report of a conducting surface layer, and the predicted topological features have not been addressed.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [19] Ando, T., Fowler, A. B. & Stern, F. Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 3

    The surface states not only exist on the top and bottom (0001) surfaces but also propagate coherently through the side walls of the nanoribbon.

    “Since full revolution around the perimeter of the ribbon is required for the interference effect, our result demonstrates that the surface states not only exist on the top and bottom (0001) surfaces but also propagate coherently through the side walls of the nanoribbon.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    Topological insulator surface states are topologically protected against all time-reversal-invariant perturbations, such as scattering by non-magnetic impurities, crystalline defects, and distortion of the surface itself.

    “These robust low-dimensional conducting states are topologically protected against all time-reversal-invariant perturbations, such as scattering by non-magnetic impurities, crystalline defects, and distortion of the surface itself.”
    Quote in the paperSubstantial claim0 of 6 sources checked
    • cites [1] Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006). source

      Not checked in the free run.

    • cites [2] König, M. et al. Quantum spin hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007). source

      Not checked in the free run.

    • cites [3] Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438–442 (2009). source

      Not checked in the free run.

    • cites [4] Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009). source

      Not checked in the free run.

    • cites [5] Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007). source

      Not checked in the free run.

    • cites [6] Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306 (2007). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 3

    The same T-dependence was observed in mesoscopic metal rings and explained by the averaging of conduction channels in the absence of inelastic scattering.

    “The same T-dependence was observed in mesoscopic metal rings and explained by the averaging of conduction channels in the absence of inelastic scattering [29].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [29] Bachtold, A. et al. Aharonov–Bohm oscillations in carbon nanotubes. Nature 397, 673–675 (1999). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 3

    The coherent motion of electrons through the side surface is highly nontrivial, providing further evidence for the topological robustness of the surface states.

    “Given that the side surface is terminated with dangling bonds and adjacent quasi-2D layers are predominantly linked by van der Waals coupling, the coherent motion of the electrons through the side surface is highly nontrivial, providing further evidence for the topological robustness of the surface states.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 4

    The phase coherent length Lφ in the nanoribbons is likely to be around 0.5 μm at 2 K, consistent with an order-of-magnitude estimate from SdH measurements.

    “Thus the phase coherent length L φ in our nanoribbons is likely to be around 0.5 µ m at 2K, consistent with an order-of-magnitude estimate from SdH measurements.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 2

    Neither bulk-related effect could result in B-periodicity over the large field range in this experiment; therefore the AB effect in Bi2Se3 nanoribbons indisputably manifests the existence of conducting surface states.

    “Nevertheless, neither of these bulk-related effects could result in B-periodicity over the large field range in this experiment. Therefore, the AB effect in Bi 2 Se 3 nanoribbons indisputably manifests the existence of the conducting surface states”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [10] Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007). source

      Not checked in the free run.

    • cites [11] Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Interpretationreasoning
    § Aharonov-Bohm interference in topological insulator nanoribbons · p. 1

    Quasi-1D nanoribbons with large surface-to-volume ratios provide excellent geometries for probing the transport properties of surface states.

    “Quasi-1D nanoribbons, with their large surface-to-volume ratios, provide excellent geometries for probing the transport properties of surface states.”
    Quote in the paperSubstantial claim
24 of 24

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The 1/2 in the flux period is interpreted as indicative of a π Berry's phase.

    “The 1 2 is interpreted as it is in the case of topological insulator nanoribbons (Peng et al. , 2010) as indicative of a π Berry's phase (Bardarson et al. , 2010; Zhang and Vishwanath, 2010).”

    From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Peng et al., 2010

  • Aharonov-Bohm oscillations have been measured in topological insulator nanoribbons.

    “the transport measurement of AharonovBohm oscillations in topological insulator nanoribbons (43)”

    From Three-Dimensional Topological Insulators (2011) · cites this paper as [43]

Cites

Flagged first, then by citations

Research works printed but not linked: 4

  1. Raghu, S., Chung, S. B., Qi, X. L. & Zhang, S. C. Collective modes of a helical liquid. Preprint at &lt;http://arxiv.org/abs/0909.2477&gt; (2009). · arXiv
  2. Wyckoff, R. W. G. Crystal Structures (Krieger, 1986).
  3. Hikami, S., Larkin, A. I. & Nagaoka, Y. Spin–orbit interaction and magnetoresistance in the 2 dimensional random system. Prog. Theor. Phys. 63, 707–710 (1980).
  4. Altshuler, B. L., Aronov, A. G. & Spivak, B. Z. The Aharonov–Bohm effect in disordered conductors. Jetp Lett. 33, 94–97 (1981).

Cited by

Sorted by citations

Authors
Peng, H., Lai, K., Kong, D., Meister, S., Chen, Y., Qi, X.-L., Zhang, S.-C., Shen, Z.-X., & Cui, Y.
Affiliations
  • Peking University (CN)
  • Stanford University (US)
  • SLAC National Accelerator Laboratory (US)
Corresponding author
Cui, Yi
ORCID
Venue
Nature Materials
Publisher
Springer Science and Business Media LLC
Published
2009-12-13
Volume
9
Issue
3
Pages
225-229
ISSN
  • 1476-1122 (ISSN-L)
  • 1476-4660
DOI
10.1038/nmat2609
OpenAlex
W2103022637
Semantic Scholar
83fa33368f9268ad693b08d5950248ba6adf0561
Cited by
780
References
26
Citations by year
2026: 14 · 2025: 22 · 2024: 21 · 2023: 38 · 2022: 25 · 2021: 33 · 2020: 41 · 2019: 35 · 2018: 51 · 2017: 57 · 2016: 47 · 2015: 69 · 2014: 79 · 2013: 86 · 2012: 79
FWCI
30.06
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Materials (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Surface and Thin Film Phenomena
Keywords
topological insulators, Aharonov-Bohm oscillations, topological surface states, quantum interference, magnetoresistance, coherent electron transport, time-reversal symmetry, spintronics, surface-to-volume ratio

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