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Selection rules are of vital importance in determining the basic optical properties of atoms, molecules and semiconductors. They provide general insights into the symmetry of the system and the nature of relevant electronic states. A two-dimensional electron gas in a magnetic field is a model system where optical transitions between Landau levels (LLs) are described by simple selection rules associated with the LL indexN. Here we examine the inter-LL optical transitions of high-quality bilayer graphene by photocurrent spectroscopy measurement. We observed valley-dependent optical transitions that violate the conventional selection rules Δ|N| = ± 1. Moreover, we can tune the relative oscillator strength by tuning the bilayer graphene bandgap. Our findings provide insights into the interplay between magnetic field, band structure and many-body interactions in tunable semiconductor systems, and the experimental technique can be generalized to study symmetry-broken states and low energy magneto-optical properties of other nano and quantum materials.

 

Abstract The investigation of transport properties in normal liquid helium-3 and its topological superfluid phases provides insights into related phenomena in electron fluids, topological materials, and putative topological superconductors. It relies on the measurement of mass, heat, and spin currents, due to system neutrality. Of particular interest is transport in strongly confining channels of height approaching the superfluid coherence length, to enhance the relative contribution of surface excitations, and suppress hydrodynamic counterflow. Here we report on the thermal conduction of helium-3 in a 1.1  μ m high channel. In the normal state we observe a diffusive thermal conductivity that is approximately temperature independent, consistent with interference of bulk and boundary scattering. In the superfluid, the thermal conductivity is only weakly temperature dependent, requiring detailed theoretical analysis. An anomalous thermal response is detected in the superfluid which we propose arises from the emission of a flux of surface excitations from the channel.