Multipole transitions beyond the dipole approximation apply when the Bohr radius of the quantum state is larger or comparable to the excitation wavelength. This is rarely the case for atoms or quantum dots. However, in the quantum Hall regime, wave functions can be extended to a length scale comparable to optical wavelengths, and the coherence is topologically protected against dephasing. Consequently, multipole transitions become possible. Motivated by this, we study the light-matter interaction in graphene in the quantum Hall regime, manifested as the photocurrent (PC).

In the first part of the thesis, we experimentally study the PC in graphene in the quantum Hall regime. Prominent PC oscillations as a function of gate voltage on samples’ edges are observed with minimal obscurations and noise. These oscillation amplitudes form an envelope which depends on the strength of the magnetic field, as does the PCs’ power dependence and their saturation behavior. We explain these experimental observations through a model using optical Bloch equations, incorporating relaxations through acoustic-, optical-phonons and Coulomb interactions. The simulated PC agrees with our experimental results, leading to a unified understanding of the chiral PC in graphene at various magnetic field strengths, and providing hints for the occurrence of a sizable carrier multiplication.

In the second part, we theoretically study the light-matter interaction beyond dipole, manifested as a PC. Inspired by the seminal gedankenexperiment by Laughlin which describes the charge transport in quantum Hall systems via the pumping of flux, we propose an optical scheme which probes and manipulates quantum Hall systems in a similar way: When light containing orbital angular momentum interacts with electronic Landau levels, it acts as a flux pump which radially moves the electrons through the sample. We investigate this effect for a graphene system with Corbino geometry, and calculate the radial current in the absence of any electric potential bias. Remarkably, the current is robust against the disorder, and in the weak excitation limit, the current shows a power-law scaling with intensity characterized by the novel exponent 2/3.