Charged plasma and Fermi liquid are two distinct states of electronic matter intrinsic to dilute two-dimensional electron systems at elevated and low temperatures, respectively. Probing their thermodynamics represents challenge because of lack of an adequate technique. Here, we report a thermodynamic method to measure the entropy per electron in gated structures. Our technique appears to be three orders of magnitude superior in sensitivity to a.c. calorimetry, allowing entropy measurements with only 10⁸ electrons. This enables us to investigate the correlated plasma regime, previously inaccessible experimentally in two-dimensional electron systems in semiconductors. In experiments with clean two-dimensional electron system in silicon-based structures, we traced entropy evolution from the plasma to Fermi liquid regime by varying electron density. We reveal that the correlated plasma regime can be mapped onto the ordinary non-degenerate Fermi gas with an interaction-enhanced temperature-dependent effective mass. Our method opens up new horizons in studies of low-dimensional electron systems.

We report thermodynamic magnetization measurements of two-dimensional electrons in several high-mobility Si metal-oxide-semiconductor field-effect transistors. We provide evidence for an easily polarizable electron state in a wide density range from insulating to deep into the metallic phase. The temperature and magnetic field dependence of the magnetization is consistent with the formation of large-spin droplets in the insulating phase. These droplets melt in the metallic phase with increasing density and temperature, though they survive up to large densities.

In this paper, we present novel experimental evidence for the odd-parity nematic superconductivity in high-quality single crystals of doped topological insulator ${\mathrm{Sr}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$. The x-ray diffraction shows that the grown single crystals are either weakly stretched or compressed uniaxially in the basal plane along one of the crystal axis. We show that in the superconducting state, the upper critical magnetic field $H_{c2}$ has a twofold rotational symmetry and depends on the sign of the strain: in the stretched samples the maximum of $H_{c2}$ is achieved when the in-basal-plane magnetic field is transverse to the strain axis, while in the compressed samples this maximum is observed when the field is along the strain direction. This result is naturally explained within a framework of the odd-parity nematic superconductivity coupled to the strain. Magnetoresistance in the normal state is independent of the current direction and also has a twofold rotational symmetry that demonstrates the nematicity of the electronic system in the normal state.

We study the diffusive electron-electron interaction correction to conductivity by analyzing simultaneously ${\rho }_{xx}$ and ${\rho }_{xy}$ for disordered 2D electron systems in Si in a tilted magnetic field. Tilting the field is shown to be a straightforward tool to disentangle spin and orbital effects. In particular, by changing the tilt angle we prove experimentally that in the field range $g{\mu }_{B}B>k_{B}T$ the correction depends on the modulus of the magnetic field rather than on its direction, which is expected for a system with isotropic $g$ factor. In the high-field limit, the correction behaves as $\ln \left(B\right)$, as expected theoretically [Lee and Ramakrishnan, Phys. Rev. B 26, 4009 (1982)]. Our data prove that the diffusive electron-electron interaction correction to conductivity is not solely responsible for the huge and temperature-dependent magnetoresistance in a parallel field, typically observed in Si-MOSFETs.

Bismuth chalcogenides are the most studied 3D topological insulators. As a rule, at low temperatures, thin films of these materials demonstrate positive magnetoresistance due to weak antilocalization. Weak antilocalization should lead to resistivity decrease at low temperatures; in experiments, however, resistivity grows as temperature decreases. From transport measurements for several thin films (with various carrier density, thickness, and carrier mobility), and by using a purely phenomenological approach, with no microscopic theory, we show that the low-temperature growth of the resistivity is accompanied by growth of the Hall coefficient, in agreement with the diffusive electron-electron interaction correction mechanism. Our data reasonably explain the low-temperature resistivity upturn.