Electric and magnetic superlattices in trilayer graphene Salah Uddin a,b,n , K.S. Chan a,b a Department of Physics and Materials Science, City University of Hong Kong, Hong Kong b City University of Hong Kong, Shenzhen Research Institute, Shenzhen, PR China HIGHLIGHTS  We get the superlattice Ha- miltonian by using the Fourier transformation approach.  The potentials are converted into superlattice potentials by using Fourier series.  We examine the emergence of extra Dirac point using periodic electric potential.  We also examine the emergence of extra Dirac point using peri- odic vector potential.  A band gap is observed by ap- plying electric and vector poten- tial simultaneously. GRAPHICAL ABSTRACT article info Article history: Received 24 May 2015 Received in revised form 9 August 2015 Accepted 3 September 2015 Available online 6 September 2015 Keywords: Graphene Magnetic superlattice Band structure abstract The properties of one dimensional Kronig–Penney type of periodic electric and vector potential on ABC- trilayer graphene superlattices are investigated. The energy spectra obtained with periodic vector po- tentials shows the emergence of extra Dirac points in the energy spectrum with finite energies. For identical barrier and well widths, the original as well as the extra Dirac points are located in the k 0 y = plane. An asymmetry between the barrier and well widths causes a shift in the extra Dirac points away from the k 0 y = plane. Extra Dirac points having same electron hole crossing energy as that of the original Dirac point as well as finite energy Dirac points are generated in the energy spectrum when periodic electric potential is applied to the system. By applying electric and vector potential together, the sym- metry of the energy spectrum about the Fermi level is broken. A tunable band gap is induced in the energy spectrum by applying both electric and vector potential simultaneously with different barrier and well widths. & 2015 Elsevier B.V. All rights reserved. 1. Introduction The successful preparation of two-dimensional carbon materi- als, graphene, as well as bilayer and trilayer graphenes, [1–3] open up new research areas in condensed matter physics. The electrical and transport properties of graphene are significantly different from conventional semiconductors. In single layer graphene, charge carriers behave like “relativistic” chiral massless quasi- particles with the “light speed” equal to the Fermi velocity and possess a conical gapless dispersion close to the K and K′ points [4,5]. Apart from the above mentioned properties, graphene also displays an unconventional quantum Hall effect [6,7] and charge carriers with normal incidence in graphene are able to tunnel Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physe Physica E http://dx.doi.org/10.1016/j.physe.2015.09.001 1386-9477/& 2015 Elsevier B.V. All rights reserved. n Corresponding author at: Department of Physics and Materials Science, City University of Hong Kong, Hong Kong E-mail addresses: salahswati@yahoo.com (S. Uddin), apkschan@cityu.edu.hk (K.S. Chan). Physica E 75 (2016) 56–65