Quantum oscillations in insulators with neutral Fermi surfaces

摘要

We develop a theory of quantum oscillations in insulators with an emergentfermi sea of neutral fermions minimally coupled to an emergent $U(1)$ gaugefield. As pointed out by Motrunich (Phys. Rev. B 73, 155115 (2006)), in thepresence of a physical magnetic field the emergent magnetic field develops anon-zero value leading to Landau quantization for the neutral fermions. Wefocus on the magnetic field and temperature dependence of the analogue of thede Haas-van Alphen effect in two- and three-dimensions. At temperatures abovethe effective cyclotron energy, the magnetization oscillations behave similarlyto those of an ordinary metal, albeit in a field of a strength that differsfrom the physical magnetic field. At low temperatures the oscillations evolveinto a series of phase transitions. We provide analytical expressions for theamplitude and period of the oscillations in both of these regimes and simpleextrapolations that capture well their crossover. We also describe oscillationsin the electrical resistivity of these systems that are expected to besuperimposed with the activated temperature behavior characteristic of theirinsulating nature and discuss suitable experimental conditions for theobservation of these effects in mixed-valence insulators and triangular latticeorganic materials.