Quantum oscillation signatures of the Bloch-Grüneisen temperature in the Dirac semimetal ${\mathrm{ZrTe}}_5$

The electron-phonon interaction is in many ways a solid state equivalent of quantum electrodynamics. Being always present, the e-p coupling is responsible for the intrinsic resistance of metals at finite temperatures, making it one of the most fundamental interactions present in solids. In typical metals, different regimes of e-p scattering are separated by a characteristic phonon energy scale—the Debye temperature. However, in metals harboring very small Fermi surfaces a new scale emerges—the Bloch-Grüneisen temperature. This is a temperature at which the average phonon momentum becomes comparable to the Fermi momentum of the electrons. Here we report sub-Kelvin transport and sound propagation experiments on the Dirac semimetal ${\mathrm{ZrTe}}_5$. The combination of the simple band structure with only a single small Fermi surface sheet allowed us to directly observe the Bloch-Grüneisen temperature and its consequences on electronic transport of a 3D metal in the limit where the small size of the Fermi surface leads to effective restoration of translational invariance of free space. Our results indicate that on entering this hydrodynamic transport regime, the viscosity of the Dirac electronic liquid undergoes an anomalous increase beyond the theoretically predicted $T^5$ temperature dependence. Extension of our measurements to strong magnetic fields reveal that, despite the dimensional reduction of the electronic band structure, the electronic liquid retains characteristics of the zero-field hydrodynamic regime up to the quantum limit. This is vividly reflected by an anomalous suppression of the amplitude of quantum oscillations seen in the Shubnikov-de Haas effect.