Dirac Electrons in a Magnetic Quantum Ring
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Dirac Electrons in a Magnetic Quantum Ring Dae Han Park and Nammee Kim
∗
Department of Physics, Soongsil University, Seoul 06978, Korea (Received 6 October 2020; revised 23 October 2020; accepted 2 November 2020) The electronic structure of a magnetic quantum ring in monolayer graphene is investigated analytically. The magnetic quantum ring is formed from inhomogeneous magnetic fields perpendicular to its monolayer plane, which are zero inside the ring and constant elsewhere. The low-energy spectra and the probability density of the magnetic edge states around the magnetic quantum ring are calculated analytically by solving the single-particle Dirac equation on a single K point with continuity of the wavefunctions across the boundaries of the magnetic quantum ring and without electron-electron interactions. The results are analyzed through a comparison with a magnetic quantum ring in a two-dimensional electron gas system, showing similar angular momentum transitions in the energy dispersion. These results indicate that electronic properties are often caused by the geometric shape of the system and have little to do with the base material. The qualitative energy spectra are confirmed analytically even if the solution of the Dirac Hamiltonian is limited by not including the detailed atomic arrangement of the material. Keywords: Electronic structure, Graphene monolayer, Magnetic quantum ring DOI: 10.3938/jkps.77.1233
I. INTRODUCTION Since October 2004 when the two-dimensional sheet of carbon atoms called graphene was prepared for the first time [1], the physics of two-dimensional Dirac-Weyl fermions has been a subject of great interest. One of the attractive aspects of the graphene problem is its massless Dirac spectrum at low-energy scales, which enables prominent transport behavior with a long mean free path and high carrier mobility [2, 3]. Mobilities of 10,000–15,000 cm2 /Vs have been routinely measured for exfoliated graphene on SiO2 -covered silicon wafers [4], and a mobility of 106 cm2 /Vs was reported for suspended graphene [5]. Linear energy dispersion is caused by the sublattice structure, which is the basis of graphene’s honeycomb lattice as it contains two carbon atoms and gives rise to an isospin degree of freedom in conjunction with a special band structure [6,7]. These characteristics have attracted the attention of the electron-device community, and there is a growing number of groups that have successfully fabricated graphene transistors [8]. Besides the potential of graphene as a new material for electron devices, there must also be fundamental research in basic science. Electrostatically controllable quantum structures, e.g., quantum wires, quantum dots, quantum rings, and quantum point contacts, using local gates are common in two-dimensional electron gas (2DEG) systems. In graphene, such quantum structures are designed ∗ E-mail:
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pISSN:0374-4884/eISSN:1976-8524
carefully by considering Klein tunneling and can also be formed by nonuniform magnetic fields [9–12].
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