DFT calculation for the electronic properties and quantum capacitance of pure and doped Zr2CO2 as electrode of supercapacitors

Defect and doping are effective methods to modulate the physical and chemical properties of materials. In this report, we investigated the structural stability, electronic properties and quantum capacitance (Cdiff) of Zr2CO2 by changing the dopants of Si, Ge, Sn, N, B, S and F in the substitutional site. The doping of F, N, and S atoms makes the system undergo the semiconductor-to-conductor transition, while the doping of Si, Ge, and Sn maintains the semiconductor characteristics. The Cdiff of the doped systems are further explored. The B-doped system can be used as cathode materials, while the systems doped by S, F, N, Sn atoms are promising anode materials of asymmetric supercapacitors, especially for the S-doped system. The improved Cdiff mainly originates from Fermi-level shifts and Fermi-Dirac distribution by the introduction of the dopant. The effect of temperature on Cdiff is further explored. The result indicates that the maximum Cdiff of the studied systems gradually decreases with the increasing temperature. Our investigation can provide useful theoretical basis for designing and developing the ideal electrode materials for supercapacitors.

Impact of partially thermal electrons on the propagation characteristics of extraordinary mode in relativistic regime

On employing linearized Vlasov–Maxwell equations the solution of relativistic electromagnetic extraordinary mode is investigated for the wave propagating perpendicular to a uniform ambient magnetic field (in the presence of arbitrary magnetic field limit i.e., ω > Ω > k.v) in partially degenerate (i.e., for T F ≥ T and T ≠ 0) electron plasma under long wavelength limit (ω ≫ k.v). Due to the inclusion of weak quantum degeneracy the relativistic Fermi–Dirac distribution function is expanded under the relativistic limit ( m 0 2 c 2 2 p 2 < 1 $\frac{{m}_{0}^{2}{c}^{2}}{2{p}^{2}}{< }1$ ) to perform momentum integrations which generate the Polylog functions. The propagation characteristics and shifting of cutoff points of the extraordinary mode are examined in different relativistic density and magnetic field ranges. The novel graphical results of extraordinary mode in relativistic quantum partially degenerate (for μ T = 0 $\frac{\mu }{T}=0$ ), nondegenerate (for μ T ≈ − 1 $\frac{\mu }{T}\approx -1$ ) and fully/completely degenerate (for μ T ≈ $\frac{\mu }{T}\approx $ 1) environments are obtained and the previously reported results are retraced as well.

The Fermi–Dirac distribution provides a calibrated probabilistic output for binary classifiers

Binary classification is one of the central problems in machine-learning research and, as such, investigations of its general statistical properties are of interest. We studied the ranking statistics of items in binary classification problems and observed that there is a formal and surprising relationship between the probability of a sample belonging to one of the two classes and the Fermi–Dirac distribution determining the probability that a fermion occupies a given single-particle quantum state in a physical system of noninteracting fermions. Using this equivalence, it is possible to compute a calibrated probabilistic output for binary classifiers. We show that the area under the receiver operating characteristics curve (AUC) in a classification problem is related to the temperature of an equivalent physical system. In a similar manner, the optimal decision threshold between the two classes is associated with the chemical potential of an equivalent physical system. Using our framework, we also derive a closed-form expression to calculate the variance for the AUC of a classifier. Finally, we introduce FiDEL (Fermi–Dirac-based ensemble learning), an ensemble learning algorithm that uses the calibrated nature of the classifier’s output probability to combine possibly very different classifiers.

Electrons and holes in semiconductors

“Electrons and holes in semiconductors” applies band theory to electrons in the conduction band, and to holes in the valence band. Holes are described by an upside-down Fermi–Dirac distribution. An incorrect model (cinema-queue model) for a hole is discredited and replaced by a correct discussion. Both (conduction-band) electrons and (valence-band) holes are examples of quasi-particles. Both can be assigned their own group velocities and effective masses.

Summary of New Insight into Electron Transport in Metals

This paper gives a summary of a new insight into basic electron transport characteristics in crystalline elemental metals. The general expressions based on the Fermi-Dirac distribution of the effective density of the randomly moving electrons, their diffusion coefficient, drift mobility, and other characteristics, including the Einstein relation between diffusion coefficient and drift mobility, are presented. It is shown that the creation of the randomly moving electrons due to lattice atom vibrations produces the same number of electronic defects, which cause scattering of the randomly moving electrons and related transport characteristics.

The number of Dirac-weighted eigenvalues of Sturm-Liouville equations with integrable potentials and an application to inverse problems

In this paper, we further Meirong Zhang, et al.’s work by computing the number of weighted eigenvalues for Sturm-Liouville equations, equipped with general integrable potentials and Dirac weights, under Dirichlet boundary condition. We show that, for a Sturm-Liouville equation with a general integrable potential, if its weight is a positive linear combination of $n$ Dirac Delta functions, then it has at most $n$ (may be less than $n$, or even be $0$) distinct real Dirichlet eigenvalues, or every complex number is a Dirichlet eigenvalue; in particular, under some sharp condition, the number of Dirichlet eigenvalues is exactly $n$. Our main method is to introduce the concepts of characteristics matrix and characteristics polynomial for Sturm-Liouville problem with Dirac weights, and put forward a general and direct algorithm used for computing eigenvalues. As an application, a class of inverse Dirichelt problems for Sturm-Liouville equations involving single Dirac distribution weights is studied.

Work function seen with sub-meV precision through laser photoemission

Electron emission can be utilised to measure the work function of the surface. However, the number of significant digits in the values obtained through thermionic-, field- and photo-emission techniques is typically just two or three. Here, we show that the number can go up to five when angle-resolved photoemission spectroscopy (ARPES) is applied. This owes to the capability of ARPES to detect the slowest photoelectrons that are directed only along the surface normal. By using a laser-based source, we optimised our setup for the slow photoelectrons and resolved the slowest-end cutoff of Au(111) with the sharpness not deteriorated by the bandwidth of light nor by Fermi-Dirac distribution. The work function was leveled within ±0.4 meV at least from 30 to 90 K and the surface aging was discerned as a meV shift of the work function. Our study opens the investigations into the fifth significant digit of the work function.