By use of ultrasound studies we resolved magneto-acoustic quantum oscillation deep into the mixed state of the multiband nonmagnetic superconductor YNi2B2C. Below the upper critical field, only a very weak additional damping appears that can be well explained by the field inhomogeneity caused by the flux-line lattice in the mixed state. This is clear evidence for no or a vanishingly small gap for one of the bands, namely, the spheroidal α band. This contrasts de Haas-van Alphen data obtained by use of torque magnetometry for the same sample, with a rapidly vanishing oscillation signal in the mixed state. This points to a strongly distorted flux-line lattice in the latter case that, in general, can hamper a reliable extraction of gap parameters by use of such techniques. † This work is dedicated to the memory of Lev Petrovich Gor'kovThe observation of magnetic quantum oscillations is usually taken as evidence for the existence of a Fermi surface. The appearance of Landau levels in a magnetic field leads to an oscillating density of states at the Fermi level as a function of field. Experimentally, these oscillations can be detected in many thermodynamic and transport properties, with the most prominent being the de Haas-van Alphen (dHvA) effect in the magnetization. Consequently, the observation of dHvA oscillations in the mixed state of a superconductor first appeared as a surprise [1]. Below the upper critical field, B c2 , the opening of a superconducting gap and the corresponding disappearance of the entire Fermi surface seem to contradict the existence of such oscillations. Nevertheless, they were observed in many type-II superconductors ([2-4]
and references therein).Motivated by the experimental evidence, however, it subsequently was shown by a number of theoretical studies that this phenomenon may be understood in principle in a rather general context. Thereby, different models are used to explain the occurrence of quantum oscillations below B c2 [5-9], but it still remains unclear which of them is the most appropriate. Usually, the validity of these theories is tested by comparing the predicted additional damping of the quantum oscillations below B c2 with experiment. Such analysis gives as the main fit parameter the superconducting gap at zero temperature, ∆ 0 , a value that largely depends on the used model.With the proper theory at hand dHvA data could, in principle, yield information on the field and angular evolution of the superconducting gap, ∆. However, considerable ambiguity in ∆ is introduced not only by the various theoretical predictions but even more from varying, sometimes contradictory, experimental data. In particular, for YNi 2 B 2 C and LuNi 2 B 2 C highly controversial results were reported [4,[10][11][12][13][14][15][16][17][18]. Thereby, for the so-called α band, an additional damping of the dHvA signal was found either in line with the opening of a weak-coupling gap [11][12][13]15], or yielding an unexpectedly small gap [4,10,14,17,18], or even an abrupt vanishing of the oscillatio...