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“Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines”. Barbier M, Vasilopoulos P, Peeters FM, Philosophical transactions of the Royal Society : mathematical, physical and engineering sciences 368, 5499 (2010). http://doi.org/10.1098/rsta.2010.0218
Abstract: We review the energy spectrum and transport properties of several types of one-dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on an SL is highly collimated. On the other hand, there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytical expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In the limit of δ-function barriers, the transmission T through and conductance G of a finite number of barriers as well as the energy spectra of SLs are periodic functions of the dimensionless strength P of the barriers, Graphic, with vF the Fermi velocity. For a KronigPenney SL with alternating sign of the height of the barriers, the Dirac point becomes a Dirac line for P = π/2+nπ with n an integer. In bilayer graphene, with an appropriate bias applied to the barriers and wells, we show that several new types of SLs are produced and two of them are similar to type I and type II semiconductor SLs. Similar to single-layer graphene SLs, extra Dirac points are found in bilayer graphene SLs. Non-ballistic transport is also considered.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.97
Times cited: 64
DOI: 10.1098/rsta.2010.0218
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“Extra Dirac points in the energy spectrum for superlattices on single-layer graphene”. Barbier M, Vasilopoulos P, Peeters FM, Physical review : B : condensed matter and materials physics 81, 075438 (2010). http://doi.org/10.1103/PhysRevB.81.075438
Abstract: We investigate the emergence of extra Dirac points in the electronic structure of a periodically spaced barrier system, i.e., a superlattice, on single-layer graphene, using a Dirac-type Hamiltonian. Using square barriers allows us to find analytic expressions for the occurrence and location of these new Dirac points in k space and for the renormalization of the electron velocity near them in the low-energy range. In the general case of unequal barrier and well widths the new Dirac points move away from the Fermi level and for given heights of the potential barriers there is a minimum and maximum barrier width outside of which the new Dirac points disappear. The effect of these extra Dirac points on the density of states and on the conductivity is investigated.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 211
DOI: 10.1103/PhysRevB.81.075438
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“Kronig-Penney model on bilayer graphene : spectrum and transmission periodic in the strength of the barriers”. Barbier M, Vasilopoulos P, Peeters FM, Physical review : B : condensed matter and materials physics 82, 235408 (2010). http://doi.org/10.1103/PhysRevB.82.235408
Abstract: We show that the transmission through single and double δ-function potential barriers of strength P=VWb/ℏvF in bilayer graphene is periodic in P with period π. For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behavior is found for the conductance. The spectrum of a periodic succession of δ-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2π. For P smaller than a critical value Pc, the spectrum exhibits two Dirac points while for P larger than Pc an energy gap opens. These results are extended to the case of a superlattice of δ-function barriers with P alternating in sign between successive barriers; the corresponding spectrum is periodic in P with period π.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 34
DOI: 10.1103/PhysRevB.82.235408
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“Dirac electrons in a Kronig-Penney potential: dispersion relation and transmission periodic in the strength of the barriers”. Barbier M, Vasilopoulos P, Peeters FM, Physical review : B : solid state 80, 205415 (2009). http://doi.org/10.1103/PhysRevB.80.205415
Abstract: The transmission T and conductance G through one or multiple one-dimensional, ä-function barriers of two-dimensional fermions with a linear energy spectrum are studied. T and G are periodic functions of the strength P of the ä-function barrier V(x,y)/ℏvF=Pä(x). The dispersion relation of a Kronig-Penney (KP) model of a superlattice is also a periodic function of P and causes collimation of an incident electron beam for P=2ðn and n integer. For a KP superlattice with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for P=(n+1/2)ð.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 93
DOI: 10.1103/PhysRevB.80.205415
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