| dc.description.abstract | In recent years condensed matter physics is witnessing a rapid expansion of materials with
(massless) Dirac fermions as low-energy excitations, with examples ranging from graphene, topological insulators to Weyl semimetals (WSMs). These materials are named Dirac materials because the low-energy quasiparticles obey the Dirac equation, regardless of their origin. They have electronic and optical properties different from the conventional metals and (doped) semiconductors, which obey the nonrelativistic Schrödinger equation leading to quadratic spectra.
This dissertation is focused on the optics of Dirac materials, especially graphene and WSMs. We present systematic theoretical studies of both bulk and surface electromagnetic eigenmodes, or polaritons, in WSMs in the minimal model of two bands with two separated Weyl nodes. We derive the tensors of bulk and surface conductivity, taking into account all possible combinations of the optical transitions involving bulk and surface electron states. We show how information about Weyl semimetals’ electronic structure, such as the position and separation of Weyl nodes, Fermi energy, and Fermi arc surface states, can be unambiguously extracted from measurements of the dispersion, transmission, reflection, and polarization of electromagnetic waves. We also explore the potential of popular tip-enhanced optical spectroscopy techniques for studies of bulk and surface topological electron states in WSMs. Strong anisotropy, anomalous dispersion, and the optical Hall effect for surface polaritons launched by a nanotip provide information about Weyl node position and separation in the Brillouin zone, the value of the Fermi momentum, and the matrix elements of the optical transitions involving both bulk and surface electron states. Furthermore, from the theoretical point of view, we systematically study the inverse Faraday effect in graphene and WSMs. Both semiclassical and quantum theories are presented, with dissipation and finite-size effects included. We find that the magnitude of the effect can be much stronger in Dirac materials as compared to conventional semiconductors. Analytic expressions for the optically induced magnetization in the low-temperature limit are obtained.
Additionally, we study the dynamics of strongly coupled nanophotonic systems with time-variable parameters. The approximate analytic solutions are obtained for a broad class of open quantum systems, including a two-level fermion emitter strongly coupled to a multimode quantized electromagnetic field in a cavity with time-varying cavity resonances or the electron transition energy. The coupling of the fermion and photon subsystems to their dissipative reservoirs is included within the stochastic equation of evolution approach, equivalent to the Lindblad approximation in the master equation formalism. The analytic solutions for the quantum states and the observables are obtained under the approximation that the rate of parameter modulation and the amplitude of the frequency modulation are much smaller than the optical transition frequencies. At the same time, they can be arbitrary with respect to the generalized Rabi oscillation frequency, which determines the coherent dynamics. Therefore, our analytic theory can be applied to an arbitrary modulation of the parameters, both slower and faster than the Rabi frequency, for complete control of the quantum state. In particular, we demonstrate protocols for switching on and off the entanglement between the fermionic and photonic degrees of freedom, swapping between the quantum states, and decoupling the fermionic qubit from the cavity field due to modulation induced transparency. | en |
