Gap Minimum Research Articles

Highly anisotropic superconducting gaps and possible evidence of antiferromagnetic order in FeSe single crystals

Specific heat has been measured in FeSe single crystals down to 0.414 K under magnetic fields up to 16 T. A sharp specific heat anomaly at about 8.2 K is observed and is related to the superconducting transition. Another jump of specific heat is observed at about 1.08 K which may either reflect an antiferromagnetic transition of the system or a superconducting transition arising from Al impurity. We would argue that this anomaly in low temperature region may be the long sought antiferromagnetic transition in FeSe. Global fitting in wide temperature region shows that the models with a single contribution with isotropic s-wave, anisotropic s-wave, and d-wave gap all do not work well, nor the two isotropic s-wave gaps. We then fit the data by a model with two components in which one has the gap function of $\Delta_0(1+\alpha cos2\theta)$. To have a good global fitting and the entropy conservation for the low temperature transition, we reach a conclusion that the gap minimum should be smaller than 0.15 meV ($\alpha$ = 0.9 to 1), indicating that the superconducting gap(s) are highly anisotropic. Our results are very consistent with the gap structure derived recently from the scanning tunneling spectroscopy measurements and yield specific heat contributions of about 32\% weight from the hole pocket and 68\% from the electron pockets.

Graphdiyne nanoribbons with open hexagonal rings: Existence of topological unprotected edge states

Using first principles calculations, we studied a new class of graphdiyne nanoribbons (GDYNR) with open hexagonal rings on the edges. To avoid the effects from dangling bond, hydrogen or oxygen atoms were absorbed on the edges. There are two kinds of GDYNR depending on the edge structures, armchair and zigzag. The electronic structures show that all of them are semiconductors. The band gap can be tuned by the width of GDYNR. As the width of nanoribbons increases, the energy gap decreases firstly and then increases, and reaches a minimum gap for both kinds. To understand the intriguing phenomenon, we constructed a tight-binding model for GDYNR and found that the existence of the minimum of the energy gap is due to the competition between the interaction within the two edges and the coupling in between. Furthermore, topological unprotected edge states are found in the band structure of a semi-infinite system by calculating surface Green's function. If GDYNR could be synthesized in experiments, it would be useful for the nanodevices in the future.

Creation of quasi-Dirac points in the Floquet band structure of bilayer graphene

We study the Floquet quasi-energy band structure of bilayer graphene when it is illuminated by two laser lights with frequencies and using Floquet theory. We focus on the dynamical gap formed by the conduction band with Floquet index = −1 and the valence band with Floquet index = +1 to understand how Dirac points can be formed. It is found that the dynamical gap does not have rotation symmetry in the momentum space, and quasi-Dirac points, where the conduction and valence bands almost touch, can be created when the dynamical gap closes along some directions with suitably chosen radiation parameters. We derive analytical expressions for the direction dependence of the dynamical gaps using Lowdin perturbation theory to gain a better understanding of the formation of quasi-Dirac points. When both radiations are circularly polarized, the gap can be exactly zero along some directions, when only the first and second order perturbations are considered. Higher order perturbations can open a very small gap in this case. When both radiations are linearly polarized, the gap can be exactly zero up to the fourth order perturbation and more than one quasi-Dirac point is formed. We also study the electron velocity around a dynamical gap and show that the magnitude of the velocity drops to values close to zero when the k vector is near to the gap minimum. The direction of the velocity also changes around the gap minimum, and when the gap is larger in value the change in the velocity direction is more gradual. The warping effect does not affect the formation of a Dirac point along the kx axis, while it prevents its formation when there is phase shift between the two radiations.

Numerical study of the rutile band structure by the Hartree–Fock–Roothaan method in the CO LCAO approximation using the cyclic cluster model

The technique for calculatingmaterial characteristicswith the aid of theHartree–Fock–Roothaan method in the CO LCAO approximation using the cyclic clustermodel is considered. The results of the numerical study are verified for the TiO2 system. The band gap minimum (2.9 eV) is calculated for the system under consideration.

Energy gaps of graphene clusters: the first-principles calculations based on high-throughput screening

With the enumeration of the triangular lattice fragments, we have systematically investigated the graphene clusters (CnHm, n = 14 – 24) with various sizes and shapes, whose structural stabilities and electronic properties are studied by the Hückel molecular orbital (HMO) method and the first-principles calculation. According to the formation energies, we show the structural stabilities of the clusters are closely related to the shape and size, as well as the chemical potential of hydrogen. The energy gaps obtained from the HMO method are in the same trend with the ones calculated by the first-principles calculations, indicating the effective screening of the gap minimum and maximum in a fast speed. There is a general decreasing of the energy gaps with the size increment due to the quantum confinement, meanwhile, the gaps are also highly dependent on the shape of the clusters for those with the same number of carbon atom.

Ultralow Resistivity Ge:Sb heterostructures on Si Using Hydride Epitaxy of Deuterated Stibine and Trigermane.

The nonconventional deuterated stibine (SbD3) compound has been used for the first time in combination with trigermane (Ge3H8) to produce hyper-doped Ge-on-Si films with carrier concentrations n > 10(20) cm(-3) and record-low resistivities ρ = 1.8 × 10(-4) Ω cm. The growth takes place on Ge and Ge1-xSix buffered Si(100) wafers at ultralow temperatures (∼330 °C) at which Sb diffusion is negligible, leading to extremely flat atomic profiles of the constituents. The Sb substitution in the Ge lattice is determined by RBS channeling and corroborated by high-resolution XRD, which also reveal a systematic increase in lattice constant vs concentration, as expected due to the incorporation of the larger Sb. High-resolution TEM illustrates defect-free monocrystalline structures with device-quality morphologies. The electrical characteristics of the samples are measured using Hall effect and resistivity measurements combined with contactless infrared ellipsometry and are found to be consistent with an extrapolation of the bulk Ge:Sb properties to the high carrier concentrations achieved in our films. The Sb/Ge ratio in the doped layers is approximately the same as that in the precursor reaction mixture, indicating a highly efficient Sb incorporation afforded by the compatible reactivity of the molecules employed in this study. The resultant films are attractive for next generation germanium technologies that require low-resistance n+ junctions or a Fermi level that approaches the direct gap minimum in the conduction band, which drastically enhances the optical emission efficiency of n-type Ge.

The structural, electrical and optical properties of Mg-doped ZnO with different interstitial Mg concentration

Through first principle calculations, we studied the structural, electronic and optical properties of ZnO doped by interstitial Mg. With the increase of Mg content (x), the derivations of lattice parameters from the wurtzite ZnO become more and more significant. The Mg-doped ZnO with x below 15.79% is found to be n-type semiconductor. The minimum of energy band gap and light transmittance in high energy region (7.5–25 eV) decrease while the conductivity and refractive index increase with increasing x. Further increasing x up to 20%, the Mg-doped ZnO is found to be direct-band-gap semiconductor with great structural derivation from wurtzite phase. The light transmittance increases while the refractive index decreases with the increase of x due to the change of geometry and electronic structure. So, it’s concluded that the electronic and optical properties of ZnO doped by interstitial Mg may be greatly influenced by Mg content.

Interference effects in photoluminescence spectra of Cu2ZnSnS4 and Cu(In,Ga)Se2 thin films

Photoluminescence (PL) is commonly used for investigations of Cu2ZnSnS(e)4 [CZTS(e)] and Cu(In,Ga)Se2 (CIGS) thin film solar cells. The influence of interference effects on these measurements is, however, largely overlooked in the community. Here, it is demonstrated that PL spectra of typical CZTS absorbers on Mo/glass substrates can be heavily distorted by interference effects. One reason for the pronounced interference in CZTS is the low reabsorption of the PL emission that typically occurs below the band gap. A similar situation occurs in band gap graded CIGS where the PL emission originates predominantly from the band gap minimum located at the notch region. Based on an optical model for interference effects of PL emitted from a thin film, several approaches to reduce the fringing are identified and tested experimentally. These approaches include the use of measured reflectance data, a calculated interference function, use of high angles of incidence during PL measurements as well as the measurement of polarized light near the Brewster angle.

Ternary Alloyed ZnSexTe1–x Nanowires: Solution-Phase Synthesis and Band Gap Bowing

Ternary alloyed semiconductor nanostructures have attracted increasingly greater attention due to their unique physiochemical properties that may not be available in the parent binary systems. In this work, we report the solution–liquid–solid (SLS) growth of colloidal, uniform ZnSexTe1–x nanowires (NWs), the composition of which can be tuned over a wide range by manipulating the growth rate of multicomponent constituents. Two sets of ZnSexTe1–x NWs with high compositional homogeneities are synthesized by using zinc stearate (Zn(St)2) and diethyl zinc (Zn(Et)2) as the Zn precursor, respectively. The resultant NWs are systematically characterized with respect to the structure, composition, and optical band gap, and on the basis of these, the composition dependence of band gaps is extracted. Both sets of colloidal ZnSexTe1–x NWs are found to exhibit strong band bowing with the band gap minimum occurring at x = 0.30, which is consistent with the previously reported results based on ZnSexTe1–x bulk materials a...

Thermal evolution of the band edges of 6H-SiC: X-ray methods compared to the optical band gap

The band gap of semiconductors like silicon and silicon carbide (SiC) is the key for their device properties. In this research, the band gap of 6H-SiC and its temperature dependence were analyzed with silicon 2p X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES) and resonant inelastic X-ray scattering (RIXS) allowing for a separate analysis of the conduction-band minimum (CBM) and valence-band maximum (VBM) components of the band gap. The temperature-dependent asymmetric band gap shrinking of 6H-SiC was determined with a valence-band slope of +2.45×10−4eV/K and a conduction-band slope of −1.334×10−4eV/K. The apparent asymmetry, e.g., that two thirds of the band-gap shrinking with increasing temperature is due to the VBM evolution in 6H-SiC, is similar to the asymmetry obtained for pure silicon before. The overall band gap temperature-dependence determined with XAS and non-resonant XES is compared to temperature-dependent optical studies. The core-excitonic binding energy appearing in the Si 2p XAS is extracted as the main difference. In addition, the energy loss of the onset of the first band in RIXS yields to values similar to the optical band gap over the tested temperature range.

The factors contributing to the band gap bowing of the dilute nitride GaNP alloy

The factors contributing to the band gap bowing of the dilute nitride GaNP are analyzed. It is found that the band gap bowing is due to two factors. One is the coupling interaction between the N level and the Γ conduction band minimum of GaP. The other is the coupling interaction between the N level and the X conduction band minimum of GaP. We also estimate the band gap reduction due to each factor. It is found that the band gap bowing is mainly due to the coupling interaction between the N level and the Γ conduction band minimum of GaP.

Ab initio design of GaN-based photocatalyst: ZnO-codoped GaN nanotubes

ZnO-codoped GaN nanotubes are designed and studied for their application as photocatalyst on the basis of first-principles calculations. The codoped nanotubes are semiconducting with their band structures controllable by the doping concentration. It is found that the codoping and its effects on the band gaps strongly depend on the chirality of the nanotubes. For armchair nanotubes, the ZnO codoping prefers to the radial direction of the nanotube, and a minimum of band gap at 1.27 eV is achievable at the concentration of 31 at.%. For zigzag nanotubes, the codoping is energetically more stable in the axial direction, and a reduction of 21% in band gap can be obtained by optimizing the doping concentration. The calculated potentials of the conduction band bottoms of the codoped nanotubes are more negative than H2/H2O level, and those of their valence band tops are more positive than O2/H2O level. The calculated electronic properties of the codoped nanotubes evidence the widely tunable band gap, enhanced mobility, and better band edges' alignments, satisfying basic prerequisites as a new class of high efficiency photocatalysts for water splitting and other avenues of solar energy utilization.

Anisotropic superconducting order parameters in the iron pnictide superconductors

The symmetry and structure of the superconducting gap in the Fe-based superconductors are the central issues for understanding these novel materials. So far the experimental data and theoretical models have been highly controversial. Some experiments favor two or more isotropic gaps, others indicate strong anisotropy and even nodes. In this paper we present the experimental data of low temperature specific heat to illustrate that the superconducting gap is anisotropic. In the case of optimally doped 122, the gap minimum may appear as point nodes or small segment of nodal lines, while in the FeTe0.55Se0.45 it may appear on the electron pockets with the gap minimum along the Γ-Z (Fe-Fe bond) direction.

A Deterministic Reduction for the Gap Minimum Distance Problem

Determining the minimum distance of a linear code is one of the most important problems in algorithmic coding theory. The exact version of the problem was shown to be NP-complete by Vardy. The gap version of the problem was shown to be NP-hard for any constant factor under a randomized reduction in an earlier work. It was shown in the same paper that the minimum distance problem is not approximable in randomized polynomial time to the factor 2log1-ϵn unless NP ⊆ RTIME(2polylog(n)). In this paper, we derandomize the reduction and thus prove that there is no deterministic polynomial time algorithm to approximate the minimum distance to any constant factor unless P=NP. We also prove that the minimum distance is not approximable in deterministic polynomial time to the factor 2log1-ϵn unless NP ⊆ DTIME(2polylog(n)). As the main technical contribution, for any constant 2/3 <; ρ <; 1, we present a deterministic algorithm that given a positive integer s , runs in time poly(s) and constructs a code C of length poly(s) with an explicit Hamming ball of radius ρd(C), such that the projection at the first s coordinates sends the codewords in the ball surjectively onto a linear subspace of dimension s , where d(C) denotes the minimum distance of C. The codes are obtained by concatenating Reed-Solomon codes with Hadamard codes.

Conduction-Band Tailing of Ce-Doped TiO2 Visible-Light-Driven Photocatalyst: The Essential Role of Oxygen Vacancy

The varied electronic structure of Ce-doped TiO 2 was probed with x-ray absorption spectra at O K -, Ce L -, Ti L -edge, and Ti K -edges. We expose the essential role of existed oxygen vacancies in band gap narrowing of Ce-doped TiO 2 and deduce the mechanism in detail by charge transfer and covalent hybridization. Oxygen vacancies would release electrons behind the Ce 4 f state, inducing the mixing valence characteristic of the Ce ions (Ce 3+ /Ce 4+ ) doped in TiO 2 . Oxygen defect state thus hybridizes with Ce 4 f state (Ce 3+ /Ce 4+ ) constructing an impurity band below the conduction band, causing a tailing of the conduction band minimum and narrowing of band gap of TiO 2 . As Ce-doped TiO 2 annealed in an oxidized atmosphere, filling up oxygen vacancies, the absorption edge in the O K -edge x-ray absorption spectrum is shifted to higher energy as compared with that for the un-treated sample, indicating the drastic diminution of band-gap-narrowing effect. This study evidences the existed oxygen vacancy is critical to mediate the impurity band formation and band gap narrowing of Ce-doped TiO 2 . The phenomenon should also be emphasized in TiO 2 doped with other elements.

Ab Initio Multireference Investigation of Disjoint Diradicals: Singlet versus Triplet Ground States

We present improved virtual orbital (IVO) complete active space (CAS) configuration interaction (IVO-CASCI) and IVO-CASCI-based multireference Møller-Plesset perturbation theory (MRMPPT) calculations with an aim to elucidate the electronic structure of tetramethyleneethane (TME) in its lowest singlet and triplet state and to quantify their order and extent of splitting. The potential surfaces of singlet and triplet states for the twisting of TME are also studied. We found that the triplet state is higher in energy than the singlet one in the whole range of twisting angles with the energy gap minimum at a twisting angle of about 45°. Harmonic vibrational frequencies of TME have also been calculated for both the states. We also report the ground to first excited triplet state transition energies. Our results are analyzed with respect to the results available in the literature to illustrate the efficacy of our methods employed. We also demonstrate that the spin character of the ground state of disjoint, TME-like diradicals can be manipulated by using appropriate selection of annulenic spacer to separate the allyl groups of TME.

Approximated solution on the properties of the scavenging gap during precipitation using harmonic mean method

Wet deposition refers to both natural and artificial processes where particles are scavenged by atmospheric hydrometeors. Below-cloud atmospheric particles are removed by raindrops via Brownian diffusion, interception, and impaction. The overall scavenging coefficient has a broad and distinctive minimum for aerosol penetration between 0.1 and several micrometers in diameter. In this study, the approximated analytical solution for most penetrating particle size during precipitation was obtained. Brownian diffusion and interception were considered under the assumption of the inertial impaction can be neglected in this study conditions. Both the minimum collection efficiency and minimum scavenging coefficient particle size were estimated using the harmonic mean type approximation, with the solution compared to the numerically calculated results. The approximated results were comparable with the numerical solutions. The results showed that collection efficiency diameter is a function of terminal velocity and the collection mechanisms included. When considering Brownian diffusion and interception, most penetrating particle size increases as drop diameter increases, which shows a contrary to the study of Wang (1978) and this shows that most penetrating particle size depends on collection efficiency mechanism, flow velocity and collector diameter. Consequently, this study analytically approximated general type-solutions for scavenging gap particle size and minimum collection efficiency during precipitation.

Angle-resolved photoemission observation of the superconducting-gap minimum and its relation to the nesting vector in the phonon-mediated superconductorYNi2B2C

We have performed ultrahigh-resolution angle-resolved photoemission spectroscopy to directly study the large superconducting (SC) gap anisotropy of YNi 2 B 2 C. We succeed in measuring momentum (k) dependence of SC gap for individual Fermi surface (FS) sheets, which demonstrates complexity of SC gap in a phonon-mediated superconductor. Within measured k regions on FS sheets, we find a pointlike minimum of SC gap, whose k positions can be connected by the known nesting vector. This shows close correlation between the nesting vector and node formation.

Evidence from anisotropic penetration depth for a three-dimensional nodal superconducting gap in single-crystallineBa(Fe1−xNix)2As2

The London penetration depth, $\lambda$, is directly related to the density, $n_{s}$, of the Cooper pairs ($\lambda^{2}\propto 1/n_{s}$) and its variation with temperature provides valuable insight into the pairing mechanism. Here we study the evolution with doping of the temperature dependence of the in-plane ($\lambda_{ab}$) and out-of-plane ($\lambda_{c}$) penetration depths in single crystals of electron-doped Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$. As is the case for other pnictides, $\lambda(T) \sim T^n$ over the whole doping range and this behavior extends down to at least $T=T_c/100$, setting a very small upper limit on the gap minimum. Furthermore, in the overdoped regime: 1) the exponent $n$ becomes substantially smaller than 2, which is incompatible with the models that explain power-law behavior to be due to scattering; 2) the exponent $n$ becomes anisotropic, with $\lambda_{c}(T)$ showing a clear $T$-linear behavior over a large temperature interval. These findings suggest that in the overdoped regime the superconducting gap in iron-based pnictide superconductors develops nodal structure, which unlike in the cuprates, cannot be understood within a two-dimensional picture.

Full configuration-interaction study of the metal-insulator transition in model systems

The precursor of the Metal-Insulator transition is studied at ab-initio level in equally-spaced Lin and Ben linear chains. In particular, large-size Full Configuration-Interaction (FCI) calculations (up to one billion determinants for Li8 and half a billion for Be5) have been performed. At FCI level, it is possible to take into account the different nature of the electronic wavefunction at the different internuclear distances. Several indicators of the Metal-Insulator transition (minimum of the Koopmans energy gap, maximum of the localization and polarizability tensors) are considered and discussed. In is shown that the three considered properties indicate a Metal-Insulator transition at distances that are in remarkable agreement.