Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony

T-Square Dependence of the Electronic Thermal Resistivity of Metallic Strontium Titanate

The temperature dependence of the phase space for electron-electron (e-e) collisions leads to a T-square contribution to electrical resistivity of metals. Umklapp scattering is identified as the origin of momentum loss due to e-e scattering in dense metals. However, in dilute metals like lightly doped strontium titanate, the origin of T-square electrical resistivity in the absence of umklapp events is yet to be pinned down. Here, by separating electron and phonon contributions to heat transport, we extract the electronic thermal resistivity in niobium-doped strontium titanate and show that it also displays a T-square temperature dependence. Its amplitude correlates with the T-square electrical resistivity. The Wiedemann-Franz law strictly holds in the zero-temperature limit, but not at finite temperature, because the two T-square prefactors are different by a factor of ≈3, like in other Fermi liquids. Recalling the case of ^{3}He, we argue that T-square thermal resistivity does not require umklapp events. The approximate recovery of the Wiedemann-Franz law in the presence of disorder would account for a T-square electrical resistivity without umklapp.

Boundary conductance in macroscopic bismuth crystals

The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary between the three-dimensional crystal and vacuum. The effect is absent in antimony, which has an identical crystal symmetry, a similar Fermi surface structure and equally ballistic carriers, but an inverted band symmetry and a topological invariant of opposite sign. Our observation confirms that the boundary interrupting the cyclotron orbits remains metallic in bismuth, which is in agreement with what was predicted by Azbel decades ago. However, the absence of the effect in antimony indicates an intimate link between band symmetry and this boundary conductance.

The topology of the surface states of a bismuth crystal remains an ongoing debate. Here, the authors observe surface electric conductivity with a magnetic field parallel to the two-dimensional boundary between the three-dimensional bismuth crystal and vacuum, but this effect is absent in antimony crystals indicating a link between band symmetry and boundary conductance.

Viscometry of Electron Fluids from Symmetry

When electrons flow as a viscous fluid in anisotropic metals, the reduced symmetry can lead to exotic viscosity tensors with many additional, nonstandard components. We present a viscometry technique that can, in principle, measure the multiple dissipative viscosities allowed in isotropic and anisotropic fluids alike. By applying representation theory to exploit the intrinsic symmetry of the fluid, our viscometry is also exceptionally robust to both boundary complications and ballistic effects. We present the technique via the illustrative example of dihedral symmetry, relevant in this context as the point symmetry of 2D crystals. Finally, we propose a present-day realizable experiment for detecting, in a metal, a novel hydrodynamic phenomenon: the presence of rotational dissipation in an otherwise isotropic fluid.