Integrated optical Dirac physics via inversion symmetry breaking

This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. We show that the Dirac electrons behave in unusual ways in tunneling, confinement, and integer quantum Hall effect. We discuss the electronic properties of graphene stacks and show that they vary with stacking order and number of layers. Edge (surface) states in graphene are strongly dependent on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. We also discuss how different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

Recent theory predicted that the Quantum Spin Hall Effect, a fundamentally novel quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We have fabricated such sample structures with low density and high mobility in which we can tune, through an external gate voltage, the carrier conduction from n-type to the p-type, passing through an insulating regime. For thin quantum wells with well width d 6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e^2/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nm, is also independently determined from the magnetic field induced insulator to metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological protection, the total lack of scattering of electron waves by disorder, is perhaps the most fascinating and technologically important aspect of this material: it provides robustness that is otherwise known only for superconductors. However, unlike superconductivity and the quantum Hall effect, which necessitate low temperatures or magnetic fields, the immunity to disorder of topological insulators occurs at room temperature and without any external magnetic field. For this reason, topological protection is predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Recently, a large theoretical effort has been directed towards bringing the concept into the domain of photonics: achieving topological protection of light at optical frequencies. Besides the interesting new physics involved, photonic topological insulators hold the promise for applications in optical isolation and robust photon transport. Here, we theoretically propose and experimentally demonstrate the first photonic topological insulator: a photonic lattice exhibiting topologically protected transport on the lattice edges, without the need for any external field. The system is composed of an array of helical waveguides, evanescently coupled to one another, and arranged in a graphene-like honeycomb lattice. The chirality of the waveguides results in scatter-free, one-way edge states that are topologically protected from scattering.