ABSTRACT
The phase diagram of an interacting two-dimensional electron system in a high magnetic field is enriched by the varying form of the effective Coulomb interaction, which depends strongly on the Landau level index. While the fractional quantum Hall states that dominate in the lower-energy Landau levels have been explored experimentally in a variety of two-dimensional systems, much less work has been done to explore electron solids owing to their subtle transport signatures and extreme sensitivity to disorder. Here, we use chemical potential measurements to map the phase diagram of electron solid states in N=2, N=3, and N=4 Landau levels in monolayer graphene. Direct comparison between our data and theoretical calculations reveals a cascade of density-tuned phase transitions between electron bubble phases up to two, three, or four electrons per bubble in the N=2, 3, and 4 Landau levels, respectively. Finite-temperature measurements are consistent with melting of the solids for T≈1 K.
ABSTRACT
Optical response of crystalline solids is to a large extent driven by excitations that promote electrons among individual bands. This allows one to apply optical and magneto-optical methods to determine experimentally the energy band gap -a fundamental property crucial to our understanding of any solid-with a great precision. Here it is shown that such conventional methods, applied with great success to many materials in the past, do not work in topological Dirac semimetals with a dispersive nodal line. There, the optically deduced band gap depends on how the magnetic field is oriented with respect to the crystal axes. Such highly unusual behavior is explained in terms of band-gap renormalization driven by Lorentz boosts which results from the Lorentz-covariant form of the Dirac Hamiltonian relevant for the nodal line at low energies.
ABSTRACT
We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N=2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the B-T phase diagram of the electron solid phase. The hierarchy of reentrant states suggests spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.
ABSTRACT
We investigate Weyl semimetals with tilted conical bands in a magnetic field. Even when the cones are overtilted (type-II Weyl semimetal), Landau-level quantization can be possible as long as the magnetic field is oriented close to the tilt direction. Most saliently, the tilt can be described within the relativistic framework of Lorentz transformations that give rise to a rich spectrum, displaying new transitions beyond the usual dipolar ones in the optical conductivity. We identify particular features in the latter that allow one to distinguish between semimetals of different types.
