Abstract
In this study, we report on the observation of de Haas-van Alphen-type quantum oscillations (QO) in the ultrasound velocity of NbP as well as `giant QO' in the ultrasound attenuation in pulsed magnetic fields. The difference of the QO amplitude for different acoustic modes reveals a strong anisotropy of the effective deformation potential, which we estimate to be as high as $9\,\mathrm{eV}$ for certain parts of the Fermi surface. Furthermore, the natural filtering of QO frequencies and the tracing of the individual Landau levels to the quantum limit allows for a more detailed investigation of the Fermi surface of NbP as was previously achieved by means of analyzing QO observed in magnetization or electrical resistivity.
Highlights
Probing the propagation of ultrasound in the quantum regime of electrons yields detailed information on the nature of electron-phonon interactions
We report on the measurements of quantum oscillations (QOs) in the ultrasound velocity and attenuation in a NbP single crystal in pulsed magnetic fields H c
V/v refers to the change√compared to the sound velocity at zero magnetic field v = Ceff /ρ, where Ceff is the effective elastic constant governing the respective mode [27] and ρ is the mass density (ρ = 6.52 g cm−3 for NbP [25]). v/v shows pronounced QOs with high harmonic content, whereas dominant frequencies and the size of the oscillation amplitudes strongly vary between the modes
Summary
Probing the propagation of ultrasound in the quantum regime of electrons yields detailed information on the nature of electron-phonon interactions. From a self-consistent treatment of ultrasound propagation as a stream of acoustic phonons interacting with an electron gas that is quantized into Landau levels (LLs) [3,4,5,6]. Both approaches yield the same result, namely, the amplitude of the QOs being dependent on the (effective) deformation potential k i =. Employing measurements of magnetoacoustic QOs, the deformation potential and its anisotropy have been experimentally determined for many metals and semimetals The connection to the microscopic picture can be understood intuitively by recalling that the probability for an electron in the kth band to be scattered by a phonon-mode corresponding to εi is proportional to ( k i )2 [3,4,5,6,7,8,9].
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