Fermi-Dirac Research Articles

Charge transport modelling of perovskite solar cells accounting for non-Boltzmann statistics in organic and highly-doped transport layers

We present a drift–diffusion model of a perovskite solar cell (PSC) in which carrier transport in the charge transport layers (TLs) is not based on the Boltzmann approximation to the Fermi–Dirac (FD) statistical distribution, in contrast to previously studied models. At sufficiently high carrier densities the Boltzmann approximation breaks down and the precise form of the density of states function (often assumed to be parabolic) has a significant influence on carrier transport. In particular, parabolic, Kane and Gaussian models of the density of states are discussed in depth and it is shown that the discrepancies between the Boltzmann approximation and the full FD statistical model are particularly marked for the Gaussian model, which is typically used to describe organic semiconducting TLs. Comparison is made between full device models, using parameter values taken from the literature, in which carrier motion in the TLs is described using (I) the full FD statistical model and (II) the Boltzmann approximation. For a representative TiO2/MAPI/Spiro device the behaviour of the PSC predicted by the Boltzmann-based model shows significant differences compared to that predicted by the FD-based model. This holds both at steady-state, where the Boltzmann treatment overestimates the power conversion efficiency by a factor of 27%, compared to the FD treatment, and in dynamic simulations of current–voltage hysteresis and electrochemical impedance spectroscopy. This suggests that the standard approach, in which carrier transport in the TLs is modelled based on the Boltzmann approximation, is inadequate. Furthermore, we show that the full FD treatment gives a more accurate representation of the steady-state performance, compared to the standard Boltzmann treatment, as measured against experimental data reported in the literature for typical TiO2/MAPI/Spiro devices.

Glauber P-representations for fermions

The Glauber-Sudarshan P-representation for bosons is well-known within quantum optics, and is widely applied to problems involving photon statistics. Less familiar, perhaps, is its fermionic counterpart, introduced by Cahill and Glauber. We present a derivation of both the bosonic and fermionic distributions and, in doing so, demonstrate the reason for the existence of two distinct fermionic forms and the relationship between these. We consider both single mode systems and also multiparticle systems with many modes. Expressions for the moments involving products of mode annihilation and creation operators are obtained. For simplicity only one type of boson or fermion will be considered, but generalising to more types is straightforward.

Generalized deep thermalization for free fermions

In noninteracting isolated quantum systems out of equilibrium, local subsystems typically relax to nonthermal stationary states. In the standard framework, information on the rest of the system is discarded, and such states are described by a generalized Gibbs ensemble (GGE), maximizing the entropy while respecting the constraints imposed by the local conservation laws. Here we show that the latter also completely characterize a recently introduced projected ensemble (PE), constructed by performing projective measurements on the rest of the system and recording the outcomes. By focusing on the time evolution of fermionic Gaussian states in a tight-binding chain, we put forward a random ensemble constructed out of the local conservation laws, which we call deep GGE (dGGE). For infinite-temperature initial states, we show that the dGGE coincides with a universal Haar random ensemble on the manifold of Gaussian states. For both infinite and finite temperatures, we use a Monte Carlo approach to test numerically the predictions of the dGGE against the PE. We study, in particular, the $k$ moments of the state covariance matrix and the entanglement entropy, finding excellent agreement. Our work provides a first step towards a systematic characterization of projected ensembles beyond the case of chaotic systems and infinite temperatures.

Edge states and SUSY in (2+1)-dimensional Maxwell Chern–Simons theory

In a [Formula: see text]-dimensional Maxwell–Chern–Simons theory coupled with a fermion and a scalar, which has [Formula: see text] SUSY in the absence of the boundary, supersymmetry is broken on the insertion of a spatial boundary. We show that only a subset of the boundary conditions allowed by the self-adjointness of the Hamiltonian can preserve partial ([Formula: see text]) supersymmetry, while for the remaining boundary conditions SUSY is completely broken. In the latter case, we demonstrate two distinct SUSY-breaking mechanisms. In one scenario, the SUSY-breaking boundary conditions are not consistent with the supersymmetry transformations. In another scenario, despite the boundary conditions being consistent with the SUSY transformations, unpaired fermionic edge states in the domain of the Hamiltonian leads to the breaking of the supersymmetry.

Strain-induced massless Dirac fermion state of the molecular conductor α-(BEDT-TTF)2I3

Uniaxial pressure can dramatically change the properties of low-dimensional systems and induce electronic phase transitions. The first-discovered molecular massless Dirac electron system α-(BEDT-TTF)2I3 has intensively been studied because of its unique features, such as the Fermi energy being very close to the Dirac point, strong electron correlation, and the quantum phase transition from the charge-ordered insulating state. However, the Dirac state is realized only under high pressure of 15 kbar, which limits the measurement of physical properties (e.g., experimental determination of band dispersion and density of states). Here, we demonstrate that the Dirac state of α-(BEDT-TTF)2I3 can be realized by applying uniaxial bending strain without confining it in a pressure cell. Uniaxial strain below 1% completely suppresses the metal–insulator transition observed at ambient pressure. Under strain, a characteristic temperature dependence of magnetoresistance associated with the formation of the n = 0 Landau level is observed, indicating the realization of the massless Dirac state.

Fermi–Dirac entropy as a measure of electron interactions

In this work, we analyzed two simple chemical reactions using Fermi–Dirac’s entropy defined in terms of the Löwdin’s occupation numbers, this definition of entropy has not been applied or explored enough in the field of quantum chemistry, in this vein, Fermi–Dirac’s entropy maybe a good option to perform works in which the main purpose will be the study or analysis of the effect of the electron interactions. The results presented in this work were complemented by the analysis of the kinetic energy, potential energy, and the variation of the electric potential, along the reaction path, the results obtained, suggest that Fermi-Driac’s entropy presented in this work can be a useful tool to perform and complement studies about electron–electron interactions.

Solving 2D and 3D Lattice Models of Correlated Fermions—Combining Matrix Product States with Mean-Field Theory

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature Tc for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work, we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: two- and three-dimensional materials comprised of weakly coupled correlated 1D fermions. This MPS+MF framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute Tc for superconductivity in 3D arrays of weakly coupled, doped, and repulsive Hubbard ladders. The MPS+MF framework thus enables the quantitative study of USC and high-Tc superconductivity—and potentially many more correlated phases—in fermionic Q1D systems based directly on their microscopic parameters, in ways inaccessible to previous methods. This approach further allows one to treat competing macroscopic orders, such as superconducting and insulating ones, on an equal footing. Benchmarks of the framework using auxiliary-field quantum Monte Carlo techniques show that the overestimation of, e.g., Tc due to its mean-field component, is near constant in microscopic parameters. These features of the MPS+MF approach to correlated fermions open up the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.13 MoreReceived 8 July 2022Revised 7 December 2022Accepted 3 January 2023DOI:https://doi.org/10.1103/PhysRevX.13.011039Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFermionsSuperconductivityPhysical Systems3-dimensional systemsStrongly correlated systemsUnconventional superconductorsTechniquesBosonizationDensity matrix renormalization groupMean field theoryCondensed Matter, Materials & Applied Physics

Magnetic and electrical properties of a heavy-fermion compound EuRh2Al8

We report the magnetic, thermodynamic, and electrical properties of ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$, a Eu-based heavy fermion member in the ${\mathrm{RT}}_{2}{\mathrm{X}}_{8}$ families with an orthorhombic $Pbam$ structure. Magnetization studies reveal multiple phase transitions in the single crystals, including two successive antiferromagnetic transitions at ${T}_{N1}\ensuremath{\sim}12.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{N2}\ensuremath{\sim}8.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. These two transitions are closely related to competing magnetic interactions in the Shastry-Sutherland lattice, which further give rise to another in-plane spin-flop transition at 1/3 of the full magnetization below 5 K when the applied magnetic field is higher than 6 T within the $ab$ plane. In addition to these, specific heat measurements in ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$ demonstrate a heavy fermion state with a large Sommerfeld coefficient $\ensuremath{\gamma}=393\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{mol}}^{\ensuremath{-}1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{K}}^{\ensuremath{-}2}$. Electrical transport measurement shows that its resistivity exhibits a ${T}^{2}$-dependence below ${T}_{N2}$ and a robust linear $T$-dependence above ${T}_{N1}$, which is also typical of a heavy fermion metal. Our work provides fundamental physical properties of ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$ and promotes understanding of the complex magnetic interactions and unusual spin correlations in the ${\mathrm{RT}}_{2}{\mathrm{X}}_{8}$ families.

Gaussian Quantum Systems and Kahler Geometrical Structure

In this article, we study the phase-space distribution of the quantum state as a framework to describe the different properties of quantum systems in continuous-variable systems. The natural approach to quantum systems is given the Gaussian Wigner representation, to unify the description of bosonic and fermionic quantum states, we study the structure of the Kahler space geometry as the geometry generated by three forms under the agreement conditions depended on the nature of the state bosonic or fermionic. Multimode light is studied, and we established that the Fock space vacuum corresponds to a certain homogeneous Gaussian state.

Symmetry-resolved entanglement of C2 -symmetric topological insulators

For a many-body system of arbitrary dimension, we consider fermionic ground states of noninteracting Hamiltonians invariant under a ${C}_{2}$ cyclic group. The absolute difference $\mathrm{\ensuremath{\Delta}}$ between the number of occupied symmetric and antisymmetric single-particle states is a topological invariant in this case. We prove lower bounds on the configurational and the number entropy based on this invariant. Entanglement entropies are particularly important for identifying topological phases protected by spatial symmetries because they lack gapless boundary modes in general. In topological crystalline insulators, the topological invariant $\mathrm{\ensuremath{\Delta}}$ and the entropy bounds can be directly determined from high-symmetry points in the Brillouin zone.

Solution of Density Profile Function of Trapped Fermi System

Starting from many-body theory, the density profile function of ideal Fermi systems in harmonic and delta traps are obtained under the quantum mechanics and thermodynamic statistical physics, respectively. The related thermodynamic properties are analyzed based on the Fermi-Dirac distribution and exact solution of the density profile function.

On the Zero Temperature Coefficient in Cryogenic FD-SOI MOSFETs

In this article, we propose an explanation of the origin of the zero-temperature coefficient (ZTC) in fully depleted-silicon on insulator (FD-SOI) MOSFETs capacitance curves from room to cryogenic temperature. It is demonstrated that the ZTC is a natural consequence of the Fermi–Dirac function controlling the carrier population. Moreover, based on transport analysis in linear region, it is proven that the ZTC point is preserved in the drain current transfer characteristics only if the mobility varies as the reciprocal temperature, i.e., if it is purely phonon scattering-limited. The inclusion of other defective scattering mechanisms dispels the ZTC point. Finally, the model developed is validated by some TCAD simulations down to deep cryogenic temperatures.

U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection

We develop a formalism for constructing particle-number-conserving Gaussian fermionic projected entangled pair states [U(1)-GfPEPS] and show that these states can describe ground states of band insulators and gapless fermions with band touching points. When using them as variational Ans\"{a}tze for two Dirac fermion systems ($\pi$-flux model on the square lattice and $[0,\pi]$-flux model on the kagome lattice), we find that the U(1)-GfPEPS, even with a relatively small bond dimension, can accurately approximate the Dirac Fermi sea ground states. By applying Gutzwiller projectors on top of these U(1)-GfPEPS, we obtain PEPS representation of U(1)-Dirac spin liquid states for spin-1/2 systems. With state-of-the-art tensor network numerics, the critical exponent in the spin-spin correlation function of the Gutzwiller-projected $\pi$-flux state is estimated to be $\eta \approx 1.7$.

The physics of intersecting thick to thin branes

We model four-dimensional junctions made out of intersections of co-dimension one brane living in higher-dimensional spacetimes through domain walls. We take a new look at the problem of localizing fermion states on brane junctions as a result of intersecting one thick brane to others sufficiently thin. All the branes intersect orthogonally to form a four-dimensional junction embedded in a higher-dimensional bulk. We discuss the effects of the Yukawa coupling and the proton decay on the restriction of the parameters that control the junction stability and the brane thickness which also define the bulk cosmological constant.

Entanglement transitions with free fermions

We use Majorana operators to study entanglement dynamics under random free fermion unitary evolution and projective measurements in one dimension. For certain choices of unitary evolution, namely, those which swap neighboring Majorana operators, and measurements of neighboring Majorana bilinears, one can map the evolution to the statistical model of completely packed loops with crossings (CPLC) and study the corresponding phase diagram. We generalize this model using the language of fermionic Gaussian states to a general free fermion unitary evolution acting on neighboring Majorana operators and numerically compute its phase diagram. We find that both the Goldstone and area-law phases persist in this new phase diagram, but with a shifted phase boundary. One important qualitative aspect of the new phase boundary is that even for the case of commuting measurements, the Goldstone phase persists up to a finite nonzero measurement rate. This is in contrast with the CPLC, in which noncommuting measurements are necessary for realizing the Goldstone phase. We also numerically compute the correlation length critical exponent at the transition, which we find to be near to that of the CPLC, and give a tentative symmetry-based explanation for some differences in the phase transition line between the CPLC and generalized models.

A New Route to Symmetries through the Extended Dirac Equation

A new route to the Dirac equation and its symmetries is outlined on the basis of the four-vector representation of the Lorentz group (LG). This way permits one to linearize the first Casimir operator of the LG in terms of the energy–momentum four-vector and enables one to derive an extended Dirac equation that naturally reveals the SU(2) symmetry in connection with an isospin associated with the LG. The procedure gives a spin-one-half fermion doublet, which we interpret as the electron and neutrino or the up-and-down quark doublet. Similarly, the second Casimir operator can be linearized by invoking an abstract isospin that is not connected with the LG, but with the two basic empirical fermion types. Application of the spinor helicity formalism yields two independent singlet and triplet fermion states—which we interpret as being related to U(1) and the lepton, respectively—to the SU(3) symmetry group of the three colors of the quarks. The way in which we obtain these results indicates the genuine yet very different physical natures of these basic symmetries. This new notion does not need the idea of grand unification. However, by still combining them in the product group SU(4)=SU(3)⊗U(1) and then further combining all groups into SU(2)⊗SU(4), one may get a symmetry scheme that perhaps supports the notion of unification by the group SU(8). We also argue that the simpler SO(4) group—instead of SU(4)—seems more appropriate for achieving unification.

Simulating Majorana zero modes on a noisy quantum processor

The simulation of systems of interacting fermions is one of the most anticipated applications of quantum computers. The most interesting simulations will require a fault-tolerant quantum computer, and building such a device remains a long-term goal. However, the capabilities of existing noisy quantum processors have steadily improved, sparking an interest in running simulations that, while not necessarily classically intractable, may serve as device benchmarks and help elucidate the challenges to achieving practical applications on near-term devices. Systems of non-interacting fermions are ideally suited to serve these purposes. While they display rich physics and generate highly entangled states when simulated on a quantum processor, their classical tractability enables experimental results to be verified even at large system sizes that would typically defy classical simulation. In this work, we use a noisy superconducting quantum processor to prepare Majorana zero modes (MZMs) as eigenstates of the Kitaev chain Hamiltonian, a model of non-interacting fermions. Our work builds on previous experiments with non-interacting fermionic systems. Previous work demonstrated error mitigation techniques applicable to the special case of Slater determinants. Here, we show how to extend these techniques to the case of general fermionic Gaussian states, and demonstrate them by preparing MZMs on systems of up to seven qubits.

Discussion for the enhanced understanding of the photoelectric effect

The photoelectric effect is a crucial phenomenon that contributed to the emergence of modern physics. Even, it is widely used in various fields of physics, such as spectroscopy, image sensing, and particle physics. Albeit its significance in physics, most of the textbooks illuminate a limited perspective focusing on the particle nature of light. This study aims to provide a more productive account of the photoelectric effect from a holistic viewpoint relevant to various fields of physics. This study examines the various fields of physics, from electromagnetics to modern physics, including quantum mechanics such as Fermi–Dirac statistics and light quantum theory. We also suggest extending the quantum mechanics to consider factors influencing the photoelectric effect experiment, such as both anode and cathode materials, geometric considerations of apparatus, and various kinds of interaction between quantum particles. To understand the mechanism of the photoelectric effect deeply, students should be aware of various fields of physics and connect them. The discussions in this study provide more productive ways of understanding the photoelectric effect.

Real-space entanglement spectra of lowest Landau level projected fractional quantum Hall states using Monte Carlo methods

Real-space entanglement spectrum (RSES) of a quantum Hall (QH) wavefunction gives a natural route to infer the nature of its edge excitations. Computation of RSES becomes expensive with an increase in the number of particles and included Landau levels (LL). RSES can be efficiently computed using Monte Carlo (MC) methods for trial states that can be written as products of determinants such as the composite fermion (CF) and parton states. This computational efficiency also applies to the RSES of lowest Landau level (LLL) projected CF and parton states; however, LLL projection to be used here requires approximations that generalize the Jain Kamilla (JK) projection. This work is a careful study of how this approximation should be made. We identify the approximation closest in spirit to JK projection and perform tests of the approximations involved in the projection by comparing the MC results with the RSES obtained from computationally expensive but exact methods. We present the techniques and use them to calculate the exact RSES of the exact LLL projected bosonic Jain $2/3$ state in bipartition of systems of sizes up to $N=24$ on the sphere. For the lowest few angular momentum sectors of the RSES, we present evidence to show that MC results closely match the exact spectra. We also discuss other plausible projection schemes. We also calculate the exact RSES of the unprojected fermionic Jain $2/5$ state obtained from the exact diagonalization of the Trugman-Kivelson Hamiltonian in the two lowest LLs on the sphere. By comparing with the RSES of the unprojected $2/5$ state from Monte Carlo methods, we show that the latter is practically exact.

Dual gate AlGaN/GaN MOS-HEMT biosensor for electrical detection of biomolecules-analytical model

This paper proposes an analytical model for a dual gate AlGaN/GaN Metal oxide semiconductor-high-electron-mobility transistor (MOS-HEMT) biosensor for electrical detection of neutral species such as Biotin, Keratin, ChOx, and Zein. When only one subband is occupied and the AlGaN layer is assumed to have been fully ionized, the Fermi–Dirac statistic and 2D state density are used to produce a self-consistent calculation of the carrier density in the quantum well at the interface. It is done by analyzing the impact of biomolecule concentration by inserting a biomolecule of appropriate dielectric permittivity in the cavity area beneath the gate region. The impact of cavity length has been analyzed on the sensor’s performance. The proposed device significantly changes the channel potential, transconductance, drain current, and threshold voltage. Dual gate structures offer superior resistance to short channel effects. Due to enhanced transport characteristics, high carrier mobility, drain current, and a variety of other factors, double gate MOS HEMT outperforms single-gate MOS HEMT. The maximal transconductance, drain on sensitivity, and the maximal drain current that has been attained in this work is 0.017 s, 0.22 and 0.129 mA, respectively, for biomolecule concentration, N b = 3 × 1012. Among all the biomolecules used in this study, Keratin has achieved the maximum shift in threshold voltage and transconductance of 0.4 V and 0.016 s. The increase in current for Keratin, Biotin, Zein, and ChOx is 0.67%, 78%, 17%, and 42%, respectively, from single to dual gate AlGaN/GaN MOS-HEMT. SiO2, Al2O3, and HfO2 oxides have been compared by filling them in the left side of the cavity. Dual gate AlGaN/GaN MOS-HEMT biosensor presents an opportunity to develop robust, low-cost, specific detection and analysis of neutral biomolecule. The analytical model provides good results for drain current according to the comparison of simulation and analytical model findings.