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In RuCl$_3$, inelastic neutron scattering and Raman spectroscopy reveal a continuum of non-spin-wave excitations that persists to high temperature, suggesting the presence of a spin liquid state on a honeycomb lattice. In the context of the Kitaev model, magnetic fields introduce finite interactions between the elementary excitations, and thus the effects of high magnetic fields - comparable to the spin exchange energy scale - must be explored. Here we report measurements of the magnetotropic coefficient - the second derivative of the free energy with respect to magnetic field orientation - over a wide range of magnetic fields and temperatures. We find that magnetic field and temperature compete to determine the magnetic response in a way that is independent of the large intrinsic exchange interaction energy. This emergent scale-invariant magnetic anisotropy provides evidence for a high degree of exchange frustration that favors the formation of a spin liquid state in RuCl$_3$., Comment: arXiv admin note: substantial text overlap with arXiv:1901.09245. Nature Physics

For an ideal topological insulator, the metallic surface states should be easy to measure using transport techniques; however, the bulk is not completely insulating. Improving the ‘leaky’ bulk state proves crucial for measuring the surface Dirac fermions, including correlation effects.

An understanding of the missing antinodal electronic excitations in the pseudogap state is essential for uncovering the physics of the underdoped cuprate high-temperature superconductors1–6. The majority of high-temperature experiments performed thus far, however, have been unable to discern whether the antinodal states are rendered unobservable due to their damping or whether they vanish due to their gapping7–18. Here, we distinguish between these two scenarios by using quantum oscillations to examine whether the small Fermi surface pocket, found to occupy only 2% of the Brillouin zone in the underdoped cuprates19–24, exists in isolation against a majority of completely gapped density of states spanning the antinodes, or whether it is thermodynamically coupled to a background of ungapped antinodal states. We find that quantum oscillations associated with the small Fermi surface pocket exhibit a signature sawtooth waveform characteristic of an isolated two-dimensional Fermi surface pocket25–32. This finding reveals that the antinodal states are destroyed by a hard gap that extends over the majority of the Brillouin zone, placing strong constraints on a drastic underlying origin of quasiparticle disappearance over almost the entire Brillouin zone in the pseudogap regime7–18. A careful study of quantum oscillations of single crystals of the cuprate superconductor YBCO placed under a magnetic field reveals a sawtooth behaviour that is reminiscent of two-dimensional electronic systems—in turn suggesting the existence of a so-called ‘hard antinodal gap’ in this system.