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Abstract:

We identify an unusual mechanism for quantum oscillations in nodal semimetals, driven by a single pair of Landau levels periodically closing their gap at the Fermi energy as a magnetic field is varied. These `zero Landau level' quantum oscillations (ZQOs) appear in the nodal limit where the zero-field Fermi volume vanishes, and have distinctive periodicity and temperature dependence. We link the Landau spectrum of a two-dimensional (2D) nodal semimetal to the Rabi model, and show by exact solution that across the entire Landau fan, pairs of opposite-parity Landau levels are intertwined in a `serpentine' manner. We propose 2D surfaces of topological crystalline insulators as natural settings for ZQOs, and comment on implications for anomaly physics in 3D nodal semimetals.

Abstract:

We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak but non-zero interaction strength $U_0$, and spin spiral order at larger $U_0$, separated by a narrow window of trivial insulator. We introduce a simplified model capturing essential features of the WTe$_2$ band structure, in which the two phases may be viewed as distinct valley ferromagnetic orders. We link the competition between the two phases to the orbital structure of the electronic wavefunctions at the Fermi surface and hence its proximity to the underlying gapped Dirac point in WTe$_2$. We briefly discuss collective modes of the two excitonic states, and comment on implications for experiments.