The de Haas-van Alphen effect at a quantum critical point

Many heavy-fermion systems are close to a quantum critical point in that, as pressure is varied, the paramagnetic heavy-fermion phase becomes unstable to a magnetically ordered phase at zero temperature. The superconducting phases all occur within a narrow range of pressures centered around the quantum critical point. In materials such as UGe2, the paramagnetic phase is unstable to a ferromagnetically ordered phase. In this case, the heavy-fermion superconducting phase is contained within the ferromagnetic phase. We examine the effect of quantum critical fluctuations on the heavy quasi-particles, and how these effects are manifested in the de Haas-van Alphen oscillations. It is found that the non-linear field-dependence of the susceptibility becomes vitally important as the quantum critical point is approached, and can give rise to a logarithmic dependence of the quasi-particle mass on the applied field.