Electronic properties of bilayer graphene in a steady magnetic field

In this thesis, we consider the electronic properties of bilayer graphene in a steady, parallel magnetic field. Using the tight–binding model, and taking into account relevant tight–binding parameters, we find a new contribution to the electronic Hamiltonian describing the orbital effect of the magnetic field. We consider the effect of the magnetic field on the Lifshitz transition, in which the Fermi surface breaks up into separate pockets at very low energy, due to trigonal warping. We show that the predicted band structure is dramatically altered when taking the new magnetic field contribution into account. We consider the effect of the magnetic field on non–linear dynamics in the presence of an ac laser field and spatial inversion asymmetry. Bilayer graphene is particularly interesting from this point of view because inversion symmetry can be broken either through asymmetry of disorder, the presence of a substrate or through interlayer asymmetry induced by an external gate voltage, the latter yielding tunable non–linear properties. Using the Boltzmann transport equation, we determine the intraband contribution to the dc current, known as the magnetic ratchet effect, and the second harmonic current. We also take into account a perpendicular magnetic field component, which produces cyclotron motion and cyclotron resonance. We discuss the dependence of these non–linear currents on the polarisation of light, the direction of the in–plane field, and the cyclotron frequency.

Name dc:type.qualificationname

Ph.D.

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

Lancaster University

Year dc:date.issued

2018

Authors dc:creator

• Kheirabadi, Narjes
• McCann, Edward
• Falko, Vladimir