Quantum interference and Klein tunnelling in graphene heterojunctions
Open accessAbstract
The observation of oscillations in the conductance characteristics of narrow graphene p–n-junctions confirms their ability to collimate ballistic carriers. Moreover, the phase of these oscillations at low magnetic field suggests the occurrence of the perfect transmission of carriers normal to the junction as a direct result of the Klein effect. The observation of quantum conductance oscillations in mesoscopic systems has traditionally required the confinement of the carriers to a phase space of reduced dimensionality1,2,3,4. Although electron optics such as lensing5 and focusing6 have been demonstrated experimentally, building a collimated electron interferometer in two unconfined dimensions has remained a challenge owing to the difficulty of creating electrostatic barriers that are sharp on the order of the electron wavelength7. Here, we report the observation of conductance oscillations in extremely narrow graphene heterostructures where a resonant cavity is formed between two electrostatically created bipolar junctions. Analysis of the oscillations confirms that p–n junctions have a collimating effect on ballistically transmitted carriers8. The phase shift observed in the conductance fringes at low magnetic fields is a signature of the perfect transmission of carriers normally incident on the junctions9 and thus constitutes a direct experimental observation of ‘Klein tunnelling’10,11,12.
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This relativistic effect is attributed to positron or electron emission by a potential barrier when the barrier is sufficiently high.
“This relativistic effect is attributed to the positron or electron emission by a potential barrier when the barrier is sufficiently high (254)(255)(256).”
From Transport of Topological Semimetals (2019) · cites this paper as [256]
In the main text (page unavailable), the paper identifies Klein tunnelling as relativistic electrons passing through a potential barrier and describes perfect transmission at normal incidence. It does not attribute that effect to positron or electron emission by a sufficiently high barrier; its explanation concerns transmission and the absence of backscattering in graphene p–n junctions. (LLM, conf=0.84)
Experimental — accuracy not yet measuredNon-relativistic electrons in graphene monolayer obey the massless relativistic dispersion known as the Dirac cone, leading to realization of analogies to Zitterbewegung and Klein tunneling in low-energy condensed-matter physics and atom optics.
“Recently, the non-relativistic electrons in graphene monolayer were found to obey the massless relativistic dispersion known as the Dirac cone, leading to the realization of analogies to Zitterbewegung and Klein tunneling in low-energy condensed-matter physics and atom optics 4 -19 .”
From Observation of interaction-induced phenomena of relativistic quantum mechanics (2021) · cites this paper as [13]
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredRelativistic extensions of the Kronig-Penney model have been discussed by several authors, and the impact of relativity on band structure and localization, such as shrinkage of bulk bands with increasing band number, has been highlighted.
“Relativistic extensions of the Kronig-Penney model (also referred to as the Dirac-Kronig-Penney model) have been discussed by several authors (see, for instance, [65,66,67,68,69,70, 71,72,73,74,75,76] and references therein), and the impact of relativity on the band structure and localization, such as shrinkage of the bulk bands with increasing band number, have been highlighted on many occasions.”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [74]
The main text discusses relativistic tunnelling through graphene p–n junctions and a Berry-phase effect associated with its Dirac band structure. Searches for “Kronig-Penney,” “Dirac-Kronig-Penney,” and shrinking bulk bands found no passage in our copy addressing those claims. The supplied passages have no page numbers. (LLM, conf=0.76)
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- Authors
- Young, A. F., & Kim, P.
- Affiliations
- Columbia University (US)
- Corresponding author
- Kim, Philip
- Venue
- Nature Physics
- Published
- 2009-02-01
- Volume
- 5
- Issue
- 3
- Pages
- 222-226
- ISSN
- 1745-2473 (ISSN-L)
- 1745-2481
- OpenAlex
- W2021442722
- Semantic Scholar
- 10689593463be5aebaa119eb58d7eccd1645abf1
- Cited by
- 1,183
- References
- 31
- Citations by year
- 2026: 34 · 2025: 34 · 2024: 45 · 2023: 51 · 2022: 52 · 2021: 53 · 2020: 101 · 2019: 59 · 2018: 63 · 2017: 57 · 2016: 75 · 2015: 72 · 2014: 93 · 2013: 89 · 2012: 91
- FWCI
- 49.17
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Nature Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (FG02-05ER46215, DE‐FG02‐, DEFG0205ER46215)
- Office of Naval Research
- Division of Chemistry (0117752)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Graphene research and applications
- 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
- graphene heterojunctions, graphene p-n junctions, quantum interference, conductance oscillations, ballistic electron transport, electron interferometry, resonant cavity, phase shift
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