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The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can be used for two ends. First, it allows for a simple generalization of the Birkhoff theorem to Schwarzschild (A)de-Sitter spacetime. Second, it provides the means to construct an Abelian endomorphism group on the space of 2-forms. It is observed that taking the trace over this group element-wise induces a further Abelian group which may be identified with a tensor representation of conformal transformations, giving Einstein spacetimes access to their own conformal equivalence class. A further trace over the group yields the curvature invariants of the spacetime. The Kretschmann scalar becomes the topological Euler density, which may be linked in a simple way to the Hawking temperature of horizons., Comment: 19 pages, submitted to EPJ C

The associations between emergent physical phenomena (e.g., superconductivity) and orbital, charge, and spin degrees of freedom of $3d$ electrons are intriguing in transition metal compounds. Here, we successfully manipulate the superconductivity of spinel oxide Li$_{1\pm x}$Ti$_2$O$_{4-\delta}$ (LTO) by ionic liquid gating. A dome-shaped superconducting phase diagram is established, where two insulating phases are disclosed both in heavily electron-doping and hole-doping regions. The superconductor-insulator transition (SIT) in the hole-doping region can be attributed to the loss of Ti valence electrons. In the electron-doping region, LTO exhibits an unexpected SIT instead of a metallic behavior despite an increase in carrier density. Furthermore, a thermal hysteresis is observed in the normal state resistance curve, suggesting a first-order phase transition. We speculate that the SIT and the thermal hysteresis stem from the enhanced $3d$ electron correlations and the formation of orbital ordering by comparing the transport and structural results of LTO with the other spinel oxide superconductor MgTi$_2$O$_4$, as well as analysing the electronic structure by first-principles calculations. Further comprehension of the detailed interplay between superconductivity and orbital ordering would contribute to the revealing of unconventional superconducting pairing mechanism., Comment: 6 pages, 4 figures

High-field electrical transport and point-contact tunneling spectroscopy were used to investigate superconducting properties of the unique spinel oxide, LiTi$_2$O$_{4-\delta}$ films with various oxygen content. We find that the upper critical field $B_\mathrm{c2}$ gradually increases as more oxygen impurities are brought into the samples by carefully tuning the deposition atmosphere. It is striking that although the superconducting transition temperature and energy gap are almost unchanged, an astonishing isotropic $B_\mathrm{c2}$ up to $\sim$ 26 Tesla is observed in oxygen-rich sample, which is doubled compared to the anoxic sample and breaks the Pauli limit. Such anomalies of $B_\mathrm{c2}$ were rarely reported in other three dimensional superconductors. Combined with all the anomalies, three dimensional spin-orbit interaction induced by tiny oxygen impurities is naturally proposed to account for the remarkable enhancement of $B_\mathrm{c2}$ in oxygen-rich LiTi$_2$O$_{4-\delta}$ films. Such mechanism could be general and therefore provides ideas for optimizing practical superconductors with higher $B_\mathrm{c2}$.

We propose a new type of optical transistor for a broadband amplification of THz radiation. It is made of a graphene--superconductor hybrid, where electrons and Cooper pairs couple by Coulomb forces. The transistor operates via the propagation of surface plasmons in both layers, and the origin of amplification is the quantum capacitance of graphene. It leads to THz waves amplification, the negative power absorption, and as a result, the system yields positive gain, and the hybrid acts like an optical transistor, operating with the terahertz light. It can, in principle, amplify even a whole spectrum of chaotic signals (or noise), that is required for numerous biological applications., Comment: 7 pages, 3 figures

There is an ongoing debate about the relative importance of structural change versus doping charge carriers on the mechanism of superconductivity in Fe-based materials. Elucidating this issue is a major challenge since it would require a large number of samples where structure properties or the carrier density is systematically varied. FeSe, with its structural simplicity, is an ideal platform for addressing this question. It has been demonstrated that the superconductivity in this material can be controlled through crystal lattice tuning, as well as electronic structure manipulation. Here, we apply a high-throughput methodology to FeSe to systematically delineate the interdependence of its structural and electronic properties. Using a dual-beam pulsed laser deposition, we have generated FeSe films with a marked gradient in the superconducting transition temperature (below 2 K < Tc < 12 K) across 1 cm width of the films. The Tc gradient films display ~ 1% continuous stretch and compression in the out-of-plane and in-plane lattice constants respectively, triggering the continuous enhancement of superconductivity. Combining transport and angular-resolved photoemission measurements on uniform FeSe films with tunable Tc from 3 K to 14 K, we find that the electron carrier density is intimately correlated with Tc, i.e., it increases by a factor of 6 and ultimately surpasses the almost constant hole concentration. Our transmission electron microscope and band structure calculations reveal that rather than by shifting the chemical potential, the enhanced superconductivity is linked to the selective adjustment of the dxy band dispersion across the Fermi level by means of reduced local lattice distortions. Therefore, such novel mechanism provides a key to understand discrete superconducting phases in FeSe., Comment: 17 pages, 5 figures

This paper explores several types of income which have not been explored so far by authors who tackled income and wealth distribution using Statistical Physics. The main types of income we plan to analyze are income before redistribution (or gross income), income of retired people (or pensions), and income of active people (mostly wages). The distributions used to analyze income distributions are Fermi-Dirac distribution and polynomial distribution (as this is present in describing the behavior of dynamic systems in certain aspects). The data we utilize for our analysis are from France and the UK. We find that both distributions are robust in describing these varieties of income. The main finding we consider to be the applicability of these distributions to pensions, which are not regulated entirely by market mechanisms., Comment: Fermi-Dirac distribution, polynomial distribution, income distribution (other than disposable income)