Abstract
It is shown that systems described by Harper’s equation exhibit a Dirac point at the center of the spectrum whenever the field parameter is a fraction of even denominator. The Dirac point is formed by the touching of two subbands at a single point in momentum space, and the physics around such point is characterized by the relative field only, as if the effective field were null at the reference value. Such behavior is consistent with the nesting property conjectured by Hofstadter, and its experimental verification would give support to such hypothesis.
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Acknowledgements
When one of us (FC) completed his PhD under Professor Gregory Wannier at the University of Oregon in 1972 and was planning to return to his home country, Chile, a well known physicist—actually, a Nobel Prize winner—remarked to him that if he wanted to build an academic career it was not sensible to try it in a country with no research tradition, nor established groups with appropriate funding and support as was the case of Chile then. Yet, at about the same time, a nuclear physicist of Hungarian origin, Michael Moravcsik, told him about the International Centre of Theoretical Physics (ICTP) in Trieste, Italy, precisely devoted to help young phycisists in developing countries building their scientific careers within their native community. Strongly commited to go back, he then returned to Chile, got in touch with the ICTP and travelled over the years to Italy several times to join the prestigious local Summer Workshop in Condensed Matter Physics. A most influential leader in this event was Professor Norman March, a well known scientist from England who spent every summer at the ICTP supporting the workshop organization and supervising research by attendants from all over the world, with exemplary devotion and commitement. He was widely respected by the community, and his constant availability, valuable counseling and advice helped making those events a remarkable opportunity for meeting first rate scientists, learning and doing quality research, to all attendants. It is then time to say, thank you Professor March.
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Claro, F., Robles, P. (2018). Graphene-Like Massless Dirac Fermions in Harper Systems. In: Angilella, G., Amovilli, C. (eds) Many-body Approaches at Different Scales. Springer, Cham. https://doi.org/10.1007/978-3-319-72374-7_4
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