Narrow Results

A highly efficient Monte Carlo method for the calculation of the density of states of classical spin systems is presented. As an application, we investigate the density of states Ω_{N(E, M)} of two- and three-dimensional Ising models with N spins as a function of energy E and magnetization M. For a fixed energy lower than a critical value E_c,N the density of states exhibits two sharp maxima at M = ± M_sp(E) which define the microcanonical spontaneous magnetization. An analysis of the form M_sp(E) ∝ (E_{c, ∞} - E)^β_ε yields very good results for the critical exponent β_ε, thus demonstrating that critical exponents can be determined by analyzing directly the density of states of finite systems.

The lowest-energy geometric and isomers of freestanding Co_n clusters (n = 2 - 10) and their corresponding magnetic moments have been studied using the Siesta code based on pseudopotential density-functional theory. The calculated results show that there are many isomers near the ground state. Different isomers hold different magnetic moment. The stability study shows that among the investigated clusters, the hexamer one is the most stable and is the magic cluster. Dissociation channels energy are also studied.

First-principles calculations were carried out to study the stability and electronic properties of native vacancy defects in the semiconducting ZnIn₂Te₄ (ZIT) and CdIn₂Te₄ (CIT). The Zn/Cd and In vacancies are acceptor defects, while the Te vacancy is donor defect. However, the In and Te vacancies dominate in the $n$-type and $p$-type semiconducting environments, respectively. The Te vacancy is not excited, so it could not compensate the majority of free carriers. The In vacancy prefers to be excited, which generates free hole carriers to compensate the majority of electron carriers. The Zn vacancy is rare in a typical semiconducting environment. Furthermore, all the vacancies induce localized defect states which may be trap centers for the free carriers. Accordingly, these native vacancy defects are destructive for the development of solar cells based on ZIT and CIT, so they should be avoided as much as possible during the growth process.

In this paper, we study the Polyakov loop and the $Z_2$ symmetry in the lattice $Z_2+\mathrm{\text{Higgs}}$ theory in four-dimensional space using Monte Carlo simulations. The results show that this symmetry is realized in the Higgs symmetric phase for large number of “temporal” lattice sites. To understand this dependence on the number of “temporal” sites, we consider a one-dimensional model by keeping terms of the original action corresponding to a single spatial site. In this approximation, the partition function can be calculated exactly as a function of the Polyakov loop. The resulting free energy is found to have the $Z_2$ symmetry in the limit of large temporal sites. We argue that this is due to $Z_2$ invariance as well as dominance of the distribution or density of states corresponding to the action.

We provide a conceptual unified description of the quantum properties of black holes (BH), elementary particles, de Sitter (dS) and Anti-de Sitter (AdS) string states.The conducting line of argument is the classical–quantum (de Broglie, Compton) duality here extended to the quantum gravity (string) regime (wave–particle–string duality). The semiclassical (QFT) and quantum (string) gravity regimes are respectively characterized and related: sizes, masses, accelerations and temperatures. The Hawking temperature, elementary particle and string temperatures are shown to be the same concept in different energy regimes and turn out the precise classical–quantum duals of each other; similarly, this result holds for the BH decay rate, heavy particle and string decay rates; BH evaporation ends as quantum string decay into pure (nonmixed) radiation. Microscopic density of states and entropies in the two (semiclassical and quantum) gravity regimes are derived and related, an unifying formula for BH, dS and AdS states is provided in the two regimes. A string phase transition towards the dS string temperature (which is shown to be the precise quantum dual of the semiclassical (Hawking–Gibbons) dS temperature) is found and characterized; such phase transition does not occurs in AdS alone. High string masses (temperatures) show a further (square root temperature behavior) sector in AdS. From the string mass spectrum and string density of states in curved backgrounds, quantum properties of the backgrounds themselves are extracted and the quantum mass spectrum of BH, dS and AdS radii obtained.

Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost forty years, cannot be applied in this case. Various strategies to overcome this so-called sign problem or complex action problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focusing on two more recent methods: dualization to worldline type of representations and the density-of-states approach.

Electrons, when scattered by static random disorder, form standing waves that can be imaged using scanning tunneling microscopy. Such interference patterns, observable by the recently developed technique of Fourier transform scanning tunneling spectroscopy (FT-STS), are shown to carry unique fingerprints characteristic of the electronic order present in a material. We exploit this feature of the FT-STS technique to propose a test for the nature of the enigmatic pseudogap phase in the high-T_c cuprate superconductors. Through their sensitivity to the quasiparticle spectra and coherence factors, the FT-STS patterns, in principle, carry enough information to unambiguously determine the nature of the condensate responsible for the pseudogap phenomenon. In practice, the absence of a detailed understanding of the scattering mechanism, together with the experimental uncertainties, prevent such an unambiguous determination. We argue, however, that the next generation of FT-STS experiments, currently underway, should be able to distinguish between the pseudogap dominated by the remnants of superconducting order from the pseudogap dominated by some competing order in the particle-hole channel. Using general arguments and detailed numerical calculations, we point to certain fundamental differences between the two scenarios and discuss the prospects for future experiments.

We examine the electronic states in the hole- and electron-doped cuprates by using the t-t′-t″-J model. Numerically exact diagonalization method is employed for a 20-site square lattice under twisted boundary conditions. The density of states in the underdoped region clearly shows a pseudogap behavior near the Fermi level in both hole and electron dopings. In hole doping, the edge of the pseudogap in the occupied side exhibits a large weight that comes from a flat band near k=(π,0). In contrast, the weight near the gap edge in electron doping is larger for the unoccupied side than for the occupied side.

First-principles density functional calculation of the total energy as a function of volume has been performed by the TB-LMTO approach for the ordered alloy FeRh in the anti-ferromagnetic state. We find that FeRh undergoes a structural phase transition from NaCl-type to tetragonal-type structure around 20.3 GPa which is in best agreement with the recent experimental observation. The calculations show that the energy of the antiferromagnetic ground state is lower than the one for the ferromagnetic state at ambient conditions.

We study density of states in the symmetrical and asymmetrical two-band periodic Anderson models at various band fillings with self-consistent calculation of the orbital occupancies. The application of the improved truncation approximation for irreducible Green functions that takes into account resonance broadening and band shifting inter-orbital exchange effects, resulted in the appearance of four spectral density moments and four- or five-subbands in the density of states depending upon the parameters of the model. It is shown that closing of the hybridization gap can occur as the result of doping, applied pressure, or change of the f-band width.

We present a universal relation between the densities of states near Van Hove singularities and the effective electron masses in 1-dimensional (1-D) materials. The relation can be utilized as a new method to determine the effective masses of charge carriers of 1-D materials in theoretical calculations and in experimental measurements. The calculated results, utilizing the relation for single-walled carbon nanotubes (SWCNTs), agree well with that of the conventional calculations when both approaches utilize the outputs of ab-initio density functional computations.

The mechanisms of the photoelectretic effect appearing on Ni intercalation GaSe were studied. The presence of the photoelectretic effect for such an object of investigation can be explained by the estimation that in Ni intercalated GaSe, the nonequilibrium electrons and holes excited by light occurred on an asymmetric potential well.

We evaluate analytically and numerically the density of states (DOS) and the heat capacity in a spherical quantum dot formed by a spherical thin barrier. The control of the spherical barrier thickness or the potential barrier height is found to cause the dimensional transition from the three-dimensional (3D) behavior to the quasi-zero dimensional (Q0D) behavior in the DOS and the heat capacity. When the barrier is thick enough, the DOS shows the Q0D-like behavior but when the barrier is thin enough to allow electrons to tunnel through it, the temperature dependence of the heat capacity exhibits quite a distinct behavior depending on the electron density. Explicit numerical plots are given in the low density regime.

Substituting Zn for Cu is known to rapidly quench superconductivity in the doped perovskites but the mechanism behind it is still not clearly understood. Single phase YBa₂(Cu_1-xZn_x)₃O_7-δ (x = 0.0 to 0.06) samples were synthesized and characterized using XRD, wet titration, resistivity, and ac susceptibility. Angle-integrated Valence Band Photoemission and Zn K-edge XAFS results clearly show that their oxygen stoichiometry (δ) changes on Zn substitution, thereby adversely affecting the density of free charge carriers and hence the normal state resistivity and the T_c. However, the observed changes in the two happen to be too large to be accounted for solely on the basis of changes in the oxygen stoichiometry δ. We find that the Zn cation acts as a strong "impurity" scattering centre in the YBCO lattice and causes local lattice distortion (LLD). It consequently induces local magnetic moment, seen in our dc susceptibility measurements. It is thus a composite of (Δδ), LLD and possibly also magnetic pair-breaking that is responsible for the rapid quenching of the superconductivity observed with Zn doping in this system.

In the present work we theoretically develop a k⋅π model to calculate the carrier electronic structure for both n- and p-type SnTe. Here π is the momentum operator in the presence of the spin–orbit interaction. The work is an extension of the theory developed for n- and p-PbTe earlier by one of the authors to evaluate the Fermi energy and the density of states (DOS). We consider a six-level energy basis for SnTe, as proposed by Bernick and Kleinman. One set of calculations was done by diagonalizing the k⋅π Hamiltonian matrix for the band-edge states and treating the far bands using perturbation theory. In the second set we have rediagonalized the k⋅π Hamiltonian matrix for the band edge states, treating the first diagonalization as the basis. The far bands are, as usual, included through perturbation. We have compared the results of both the sets. Results obtained for n- and p-type SnTe are also compared with that of n- and p-type PbTe. The similarities and contrasts are discussed. An indirect comparison with the DOS of the metallic tin suggests that the calculations are fairly reasonable. The results are also compared with some recent results for SnTe.

Quantum mechanics manifests in experimental observations in several ways. Hauge et al. (1987) and Leavens et al. (1989) had pointed out that interference effects dominate a physical quantity called injectance. We show that, very paradoxically, the interference related term vanish in a quantum regime making semi-classical formula for injectance exact in this regime. This can have useful implications to experimentalists as semi-classical formulas are much more simple. There are other puzzling facts in this regime like an ensemble of particles that can be transmitted without any time delay or negative time delays.

The structural, elastic and electronic properties of O-doped and un-doped cubic Zr₃N₄ and Ti₃N₄ are studied by first principles calculations based on the density functional theory. The bulk and shear moduli, as well as Young's moduli, decrease after doping with oxygen, which is due to the lengthening of the metal-nitrogen bond as well as the inflation of the cell volume. The changes in elastic properties are consistent with available experimental results. Both nitrides change from brittle to ductile when doped with oxygen, and all materials can be regarded as being elastic isotropic. The band structure and density of states are calculated to discuss the electronic properties of O-doped cubic Zr₃N₄ and Ti₃N₄, the presence of oxygen has significant influence on the electronic structure near the Fermi level. The gap at Fermi level is vanished which confirms the metallic character when O is introduced into nitrides. It means that doping with oxygen will have important effects on the optical properties of Zr and Ti nitrides.

The equation for the electron Green's function of the fermionic Hubbard model, derived using the strong coupling diagram technique, is solved self-consistently for the near-neighbor form of the kinetic energy and for half-filling. In this case the Mott transition occurs at the Hubbard repulsion U_c ≈ 6.96t, where t is the hopping constant. The calculated spectral functions, density of states (DOS) and momentum distribution are compared with results of Monte Carlo simulations. A satisfactory agreement was found for U > U_c and for temperatures, at which magnetic ordering and spin correlations are suppressed. For U < U_c and lower temperatures the theory describes qualitatively correctly the positions and widths of spectral continua, variations of spectral shapes and occupation numbers with changing wave vector and repulsion. The locations of spectral maxima turn out to be close to the positions of δ-function peaks in the Hubbard-I approximation.

The conventional viewpoint of the strongly correlated electron metal-insulator transition is that a single band splits into two upper and lower Hubbard bands at the transition. Much work has investigated whether this transition is continuous or discontinuous. Here we focus on another aspect and ask the question of whether there are additional upper and lower Hubbard bands, which stretch all the way out to infinity — leading to an infinite single-particle bandwidth (or spectral range) for the Mott insulator. While we are not able to provide a rigorous proof of this result, we use exact diagonalization studies on small clusters to motivate the existence of these additional bands, and we discuss some different methods that might be utilized to provide such a proof. Even though the extra upper and lower Hubbard bands have very low total spectral weight, those states are expected to have extremely long lifetimes, leading to a nontrivial contribution to the transport density of states for $dc$ transport and modifying the high temperature limit for the electrical resistivity.

The ab initio computations have been performed to examine the structural, elastic, electronic and phonon properties of cubic $\mathrm{\text{La}}X$$(X=\mathrm{\text{Cd}}$, $\mathrm{\text{Hg}}$ and $\mathrm{\text{Zn}})$ compounds in the $B2$ phase. The optimized lattice constants, bulk modulus, and its pressure derivative and elastic constants are evaluated and compared with available data. Electronic band structures and total and partial densities of states (DOS) have been derived for $\mathrm{\text{La}}X$$(X=\mathrm{\text{Cd}}$, $\mathrm{\text{Hg}}$ and $\mathrm{\text{Zn}})$ compounds. The electronic band structures show metallic character; the conductivity is mostly governed by $\mathrm{\text{La}}$-$5d$ states for three compounds. Phonon-dispersion curves have been obtained using the first-principle linear-response approach of the density-functional perturbation theory. The specific heat capacity at a constant volume $C_V$ of $\mathrm{\text{La}}X$$(X=\mathrm{\text{Cd}}$, $\mathrm{\text{Hg}}$ and $\mathrm{\text{Zn}})$ compounds are calculated and discussed.