In Lanthanide based metals new electronic quasiparticles emerge from the interaction of f electrons with conduction electrons. They are called heavy fermion materials because of the highly enhanced effective mass of these quasiparticles. Great opportunities arise from the good control and tunability of these materials. As such heavy fermion materials provide outstanding access to study competing ground states and the quantum criticality associated with the zero temperature phase transition. Quantum criticality leads to novel states of matter and is discussed to underlie high temperature superconductivity.

The prototypical materials YbRh2Si2 features a quantum critical points which requires descriptions that go beyond the conventional order-parameter notion. Here, electronic structure studies played a key role to identify the intriguing physics of YbRh2Si2. I will discuss Hall effect measurements which find a reconstruction of the Fermi surface in the zero temperature limit. Furthermore, energy-over-temperature scaling deduced from the Hall effect measurements indicate that the fluctuations between the two different Fermi surface configurations is underlying the finite temperature quantum critical behavior.

The newly discovered heavy-fermion material YbNi4P2 appears to be one of the first examples of a truly continuous quantum phase transition from a ferromagnetic state to a paramagnetic state. Remarkably, this is in contrast to theoretical predictions which exclude ferromagnetic quantum critical points in metallic systems. However, these theoretical considerations are valid for two and three dimensional materials only. I will present electronic structure calculations in conjunction with quantum oscillation measurements. These comprehensive electronic structure studies reveal a quasi-one-dimensional electronic structure which might be the key to understand the presence of a ferromagnetic quantum critical point.