The superconductivity of CaC6 as a function of pressure and of abundant Ca isotopes is revisited using DFT calculations on a 2c – double hexagonal superlattice. The introduction of superlattices is motivated by previous synchrotron absorption and Raman spectroscopy results on other superconductors that show evidence of superlattice vibrations at low (THz) frequencies. A 2c superlattice for CaC6 is illustrative of atomic orbital symmetry and periodicity, including bonding and antibonding s-orbital character implied by cosine modulated electronic bands. Inspection of the cosine band reveals that the cosine function has a small (meV) energy difference between bonding and antibonding regions relative to a midpoint non-bonding energy. Fermi surface nesting is apparent in an appropriately folded Fermi surface using a superlattice construct. Nesting relationships identify phonon vectors for conservation of energy and for phase coherency between coupled electrons at opposite sides of the Fermi surface. Detailed analysis of this Fermi surface nesting provides accurate estimates of the superconducting gaps for CaC6 with change in applied pressure. Recognition of superlattices within a rhombohedral or hexagonal representation provides consistent mechanistic insight on superconductivity and electron−phonon coupling in CaC6.

The electronic properties of calcium intercalated graphite (CaC6) as a function of pressure are revisited using density functional theory (DFT). The electronic band structures of CaC6, like many other layered superconducting materials, display cosine-shaped bands at or near the Fermi level (FL). Such bands encompass bonding/antibonding information with a strong connection to superconducting properties. Using an hexagonal cell representation for CaC6, construction of a double supercell in the c-direction effects six-folding in reciprocal space of the full cosine function, explicitly revealing the bonding/antibonding relationship divide at the cosine midpoint. Similarly, folding of the Fermi surface (FS) reveals physical phenomena relevant to electronic topological transitions (ETT) with application of pressure. For CaC6, the peak value for the superconducting transition temperature, Tc, occurs at about 7.5 GPa, near to the observed pressure of the calculated ETT. At this pressure, the radius of the nearly spherical Ca 4s-orbital FS coincides with three times the distance from the G centre point to the Brillouin zone (BZ) boundary of the 2c supercell (which is equal to half the identically defined distance for the primitive rhombohedral BZ). In addition, the ETT coincides with alignment of the non-bonding (inflection) point of the cosine band (the point at which the sign of the cosine amplitude modulation is reversed) with the FL. At other calculated pressure conditions, the Ca 4s-orbital FS undergoes topological changes that correspond and can be correlated to experimentally determined changes in Tc. The ETT is a key mechanism that circumscribes the known significant drop in Tc for CaC6 as a function of increasing pressure.

Generative Adversarial Networks (GANs) are powerful models for generative tasks but face significant challenges such as instability, mode collapse, and inefficient convergence. This paper introduces a theoretical framework leveraging Fermi-Dirac statistics, Ruppeiner geometry, phase transition dynamics, and graph theory to address these issues. The proposed theorems provide a robust mathematical foundation for enhancing GAN stability, diversity, and convergence. Experimental validation on the MNIST dataset demonstrates that the application of these theorems results in improved Inception Scores, reduced Fr´echet Inception Distances, and stable training dynamics, as indicated by Ruppeiner curvature analysis. The findings suggest that these theoretical insights offer a comprehensive solution to the persistent challenges in GAN training, paving the way for more reliable and effective generative models.

We propose that the coexistence of gapless Fermi arcs with the metal-insulator crossover of in-plane resistivity in strongly underdoped cuprates can be explained by the FL* fractionalized Fermi liquid nature of these systems and it is not due simply to disorder effects. The particle excitations of this FL* system derived from variants of the t-J model are: the gapless holon carrying charge with small Fermi momentum proportional to the doping, the gapful spinon carrying spin 1/2, gauge fluctuations coupling them and the hole as a spinon-holon bound state or resonance due to gauge binding with a Fermi surface respecting the topological Luttinger theorem. In our proposal Fermi arcs are determined by the hole resonance, whereas the metal-insulator crossover is dominated by spinon-spinon (with subleading holon-holon) gauge interactions and this dichotomy is able to explain their coexistence.

Starting from an overview of neutrino problems and a simplified survey of Fermi’s neutrino theory, it is shown why neutrinos are left-handed and why they seem to show an oscillatory behaviour between their flavours. After addressing the question how to assess the naked mass of the true elementary particles, it is hypothesized that the elementary constituents of the nuclear background energy and the cosmological background energy are the same. This allows to derive the magnitude of the quark’s “naked” mass from the polarization of the vacuum.

In a recent paper [B. Michon et al., Nat. Commun. (2023) 14:3033] optical conductivity experiments in cuprate superconductors were shown to display scaling properties consistent with the Marginal Fermi Liquid theory. Here we argue, that the temperature regime studied in these experiments does not allow to distinguish between Marginal Fermi Liquid and a Shrinking Fermi Liquid. In the latter scenario, which we recently proposed and which applies near a quantum critical point, dynamical fluctuations of the order parameter with short correlation length mediate a nearly isotropic scattering among the quasiparticles over the entire Fermi surface leading to strange-metal behavior. If the damping of these nearly local fluctuations increases by decreasing the temperature, the Fermi liquid regime shrinks and the strange-metal behavior is extended to the lowest temperatures. This Shrinking Fermi liquid scenario has many similarities and some differences with respect to the Marginal Fermi liquid theory. In particular, we show that the approximate scaling properties of the optical conductivity in some high-frequency regime predicted by the Shrinking Fermi liquid scenario account to a very good extend for the experimental data.

Quantum effects arising from manifestly broken time-reversal symmetry are investigated using time-dependent perturbation theory in a simple model. The forward time and the backward time Hamiltonians are taken to be different and hence the forward and backward amplitudes become unsymmetrical and are not complex conjugates of each other. The effects vanish when the symmetry breaking term is absent and ordinary quantum mechanical results such as Fermi Golden rule are recovered.

We discuss how the interaction of electrons with an overdamped optical phonon can give rise to a strange-metal behavior over extended temperature and frequency ranges. Although the mode has a finite frequency, an increasing damping shifts spectral weight to progressively lower energies so that, despite the ultimate Fermi liquid character of the system at the lowest temperatures and frequencies, the transport and optical properties of the electron system mimic a marginal Fermi liquid behavior. Within this shrinking Fermi liquid scenario, we extensively investigate the electron self-energy in all frequency and temperature ranges, emphasizing similarities and differences with respect to the marginal Fermi liquid scenario.

A procedure, dedicated to superconductivity, is extended to study the properties of interacting electrons in normal metals in the thermodynamic limit. Each independent-electron band is shown to split into two correlated-electron bands. Excellent agreement is achieved with Bethe's wave-function for the one-dimensional Hubbard model. The groundstate energy, reckoned for the two-dimensional Hubbard Hamiltonian, is found to be lower than values, obtained thanks to the numerical methods. This analysis applies for any spatial dimension and temperature.

An equation for the Fermi level of impurity isotropic semiconductors is considered when the bottom of the conduction band and the top of the valence band are at the center of the first Brillouin zone. The energy of charge carriers in the valence and conduction bands of semiconductors is considered taking into account the real positions of the top of the valence band and the bottom of the conduction band in the first Brillouin zone. A universal equation for determining the Fermi levels of impurity isotropic semiconductors is presented.

Recently Kawashima has reported that, when wetted with alkanes, several forms of graphite and single-layer graphene exhibit superconductor-like properties above room temperature under ambient pressure [AIP Adv. 2013, 3, 052132; arXiv:1612.05294; arXiv:1801.09376]. Under the assumption that these seemingly unlikely properties arise from the presence of paired electrons brought about by the alkane-wetting, we explored their implications to arrive at a probable mechanism for strong electron-pairing driven by Fermi surface nesting and acoustic phonon. This mechanism explains why alkane-wetting is essential for the graphene systems to become “superconductor-like” above room temperature and why the “T_c” of alkane-wetted pitch-based graphite fibers increases almost linearly from ~363 to ~504 K with increasing the molecular weight of alkane from heptane to hexadecane. It also provides a number of experimentally-verifiable predictions, the confirmation of which will provide a strong support for the superconductivity driven by Fermi surface nesting and acoustic phonon.

Silicon-based photodetectors, as low-cost and environmentally friendly optical sensors, are attractive. Also, their compatibility with complementary metal-oxide-semiconductor (CMOS) technology is advantageous for the development of silicon photonics systems. However, extending optical responsivity of silicon-based photodetectors to the mid-infrared (mid-IR) wavelength range remains challenging. In developing mid-IR infrared Schottky detectors, nanoscale metals are critical. Nonetheless, one key factor is the Fermi level pinning effect at the metal/silicon interface and the presence of metal-induced gap states (MIGS). Here, we demonstrate the utilization of the passivated surface layer on semiconductor materials as an insulating material in metal-insulator-semiconductor (MIS) contacts to mitigate the Fermi level pinning effect. The removal of Fermi level pinning effectively reduces the Schottky barrier height by 12.5% to 16%. The demonstrated devices exhibit a high responsivity of up to 234 μA/W at a wavelength of 2 μm, 48.2 μA/W at 3 μm, and 1.75 μA/W at 6 μm. The corresponding detectivities at 2 and 3 μm are 1.17×10^8 cm Hz^1/2 W^-1 and 2.41×10^7 cm Hz^1/2 W^-1, respectively. The expanded sensing wavelength range contributes to the application development of future silicon photonics integration platforms.

Abstract. Background: This paper investigates the propagation of behaviorally transmitted traits with negative effect on host fitness. Methods: We analyze equilibrium between genetically transmitted and behaviorally transmitted competing propagators and consider whether a behavioral propagator is linked to reproduction (e.g. vertical culture transmission), or not. We employ combined genetic and behavior-induced fitness components for hosts, while behavioral propagators have replication factors to distinguish from what’s good for the host (fitness). Results: A trait which spreads faster than its marginal host fitness contribution reduces population will establish itself. The often transient nature of laterally transmitted traits may be a defense against accumulation of deleterious traits. Laterally transmitted traits with high spreading rate often do not equalize with genetic traits, spreading outside natural selection of the hosts. Vertical transmission reduces replication rate and allows group selection against deleterious behaviorally transmitted traits. Competing mutually exclusive propagators contribute to inequality and altruism, but compete through adverse fitness since exclusivity assumes low conversion. Conclusion: Behaviorally transmitted traits, in some cases a tremendous advantage, may also be a significant problem in the development of societies.

In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. The doping-induced and concentration-dependent phase transition of zirconium dioxide under the influence of yttrium oxide was studied, after which the position of the Fermi level changes and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of -0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The calculations showed that ab initio research methods are capable of describing the mechanism of phase transitions of materials under the influence of alloying. That is, by optimizing the parameters of DFT calculations, it is possible to observe the effects of doping on other physical and chemical properties of materials, which are still beyond the scope of quantum chemical modeling. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.

We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_\mathrm{crit}$ of Thirring models in three dimensions. Only models with flavor number below $N_\mathrm{crit}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_\mathrm{crit}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_\mathrm{crit}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.

This paper brings to fruition recently found \cite{migdal2023exact} exact reduction of decaying turbulence in the Navier-Stokes equation in $3 + 1$ dimensions to a Number Theory problem of finding the statistical limit of the Euler ensemble. We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the \textbf{quantum} statistical theory of $N$ fermions on a ring, with an external field related to the random fractions of $\pi$. We find the solution of this system in the turbulent limit $N\to \infty, \nu \to 0$ in terms of a complex trajectory (instanton) providing a saddle point to the path integral over the density of these fermions. This results in an analytic formula for the observable correlation function of vorticity in wavevector space. This is a full solution of decaying turbulence from the first principle without approximations or fitted parameters. The energy spectrum decays as $k^{-\frac{7}{2}}$. We compute resulting integrals in \Mathematica{} and present effective index $n(t) = -t\partial_t \log E $ for the energy decay as a function of time Fig.\ref{fig::NPlot}. The asymptotic value of the effective index in energy decay $n(\infty) = \frac{5}{4}$, but the universal function $n(t)$ is neither constant nor linear.

In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. In this case, the position of the Fermi level changes abruptly, and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of - 0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.

In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three dimensional space defined by energy, temperature and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of large fermion systems with numerical simulation. As an example, we present energies for up to 50 noninteracting fermions and up to 20 interacting fermions at all temperatures and show good agreement with the analytical result for noninteracting case.

In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. A doping-induced and concentration-dependent phase transition in ZrO₂ under the influence of Y₂O₃ was discovered, due to which the position of the Fermi level changes and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of - 0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The results show that ab initio approaches are able to describe the mechanism of doping-induced phase transitions in (ZrO₂+Y₂O₃)-like systems, based on which it can be assumed that DFT calculations can also flawlessly evaluate other physical and chemical properties of YSZ, which have not yet been studied quantum chemical research. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.

The work carried out first-principles calculations within the framework of density functional theory to study the structural stability of the CsSnI₃ compound and the influence of phase transitions on their electronic and optical properties. Using the GGA and SCAN functionals, the relaxed structures of the CsSnI₃ phases were obtained and their geometric characteristics were assessed. Using the Phonopy code based on VASP, calculations of phonon and thermodynamic properties were performed, and the temperatures of phase transitions of CsSnI₃ were determined. The temperature dependences of the thermodynamic parameters α-, β-, γ- and δ-phases of CsSnI₃ were analyzed. The trends in free energy, entropy, enthalpy, heat of formation energy and heat capacity were justified in terms of the pattern of changes in the total energy of the four phases of CsSnI₃ from VASP calculations. It is shown that at 0 K the non-perovskite structure of the CsSnI₃ compound (δ-CsSnI₃) is the most stable (followed by γ-CsSnI₃), and the tetragonal phase (β) is quite unstable, having the highest energy among the perovskite phases. It was revealed that at temperatures above 450 K the tetragonal phase becomes stable, and when the temperature drops, it transforms into the cubic phase (α-CsSnI₃). The phase transition between the β and γ phase of perovskite occurs in the range of 300-320 K, and at 320 K a black-yellow transformation of CsSnI₃ occurs in which the cubic phase (black perovskite) undergoes a phase transition to a non-perovskite conformation (yellow phase). The presence of temperature phase transitions between two orthorhombic phases of CsSnI₃ at 360 K was discovered, although direct transitions of the α⟷γ and γ⟷δ types have not yet been reported in any experiment, except for γ→δ transitions under the influence of moisture. Based on well-relaxed structures (from the SCAN calculations), the band gap widths for four CsSnI₃ phases were calculated and compared with experimental measurements. Electronic properties and Fermi level shifts as a result of phase transformations of CsSnI₃ were assessed using the HSE06 functional and machine learning prediction. The values of the complex dielectric constant and the refractive index of all phases of the CsSnI₃ were determined.

Based on the minimum conduction band edge caused by the minimum channel potential resulting from the quasi-3D scaling theory and the 3D density of state (DOS) accompanied by the Fermi-Dirac distribution function on the source and drain sides, a unified semiconductor-device-physics-based ballistic model is developed for the threshold voltage of modern multiple-gate (MG) transistors, including FinFET, W-gate MOSFET, and Nanosheet (NS) MOSFET. It is shown that the thin silicon, thin gate oxide, and high work function will alleviate the ballistic effects and resist the threshold voltage degradation. Besides, as the device dimension is further reduced to give rise to the 2D/1D DOS, the lowest conduction band edge is hence increased to resist the threshold voltage degradation. The nanosheet MOSFET exhibits the largest threshold voltage among the three transistors due to the smallest minimum conduction band edge caused by the quasi-3D minimum channel potential. Compared to P-type MOSFET (P-FET), the N-FET shows more threshold voltage because the electron has a more effective mass than the hole

This paper contains a comparative review of existing Zitterbewegung models. It attempts to synthesize them by offering a toy model containing an extra hypothesis of electromagnetic self-oscillation at the Fermi scale (10−15m). Inspired by Bell violation experiments, Zitterbewegung models and hydrodynamic walker studies, we revisit standing waves in quantum mechanics, echoing de Broglie-Bohm pilot wave theories. Starting with the electromagnetic self-oscillation hypothesis at the Fermi scale we propose an emergent and deductive hierarchical electron structure across multiple scales. The model spans Fermi, Compton (10−13m), Bohr (10−11m) and finally de Broglie (>10−10m). At the Fermi scale, the hypothesis is one of "source-free chiral light", known as the "zilch", emerging as a self-oscillating electromagnetic field at the Schwinger limit. This self-interaction of retarded potentials due to real relativistic delays is a generic self-oscillation of Liénard-Wiechert potentials. This primary Fermi oscillation accounts for charge and mass at the Fermi scale. It generates secondary stable "auto-orbits" dynamics at the Compton scale, manifesting as observable spin and other quantum properties of the usual Dirac zitterbewegung models. These zitter models account for known electron characteristics, including mass, charge, spin and g/2 anomalous factors up to 9 digits precision. We explain the de Broglie wavelength through Doppler-shifted Compton-scale standing waves, in the tradition of de Broglie. The framework extends to electron-positron pair production at the Schwinger limit, described as a result of natural light focusing in non-homogeneous media, utilizing René Thom’s catastrophe theory. This offers a new perspective on baryogenesis and matter emergence from electromagnetic fields. We dub this toy model the "sub-standard" model of the electron.