The origin of degeneracies and crossings in the 1d Hubbard model

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyse in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter-independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter-independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wavefunctions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter-independent symmetry.

The extended Enskog operator for simple fluids with continuous potentials: single particle and collective properties

We generalized the Enskog theory originally developed for the hard-sphere fluid to fluids with continuous potentials, such as the Lennard–Jones. We derived the expression for the k and ω dependent transport coefficient matrix which enables us to calculate the transport coefficients for arbitrary length and time scales. Our results reduce to the conventional Chapman–Enskog expression in the low density limit and to the conventional k dependent Enskog theory in the hard-sphere limit. As examples, the self-diffusion of a single atom, the vibrational energy relaxation, and the activated barrier crossing dynamics problem are discussed.

Photoluminescence of Sr(2-x)Ln(x)CeO(4+x/2) (Ln = Eu, Sm or Yb) prepared by a wet chemical method

A wet chemical route is developed for the preparation of Sr2CeO4 denoted the carbonate-gel composite technique. This involves the coprecipitation of strontium as fine particles of carbonates within hydrated gels of ceria (CeO2.xH(2)O, 40energy levels in the excited states in oxides. Efficient energy transfer occurs from Ce4+-O2- CT state to trivalent lanthanide ions (Ln(3+)) if the latter has CT excited states, leading to sensitizer-activator relation, through non-resonance process involving exchange interaction. Yb3+-substituted Sr2CeO4 does not show any line emission because the energy of Yb3+-O2- CT level is higher than that of the Ce4+-O2- CT level. Sr2-xEuxCeO4+x/2 shows white emission at xless than or equal to0.02 because of the dominant intensities of D-5(2)-F-7(0-3) transitions in blue-green region whereas the intensities of D-5(0)-F-7(0-3) transitions in orange-red regions dominate at concentrations xgreater than or equal to0.03 and give red emission. The appearance of all the emissions from D-5(2), D-5(1) and D-5(0) excited states to the F-7(0-3) ground multiplets of Eu3+ is explained on the basis of the shift from the hypersensitive electric-dipole to magnetic-dipole related transitions with the variation in site symmetry with increasing concentration of Eu3+. White emission of Sr2-x SmxCeO4+x/2 at xless than or equal to0.02 is due the co-existence of Ce4+-O2- CT emission and (4)G(4)(5/2)-H-6(J) Sm3+ transitions whereas only the Sm3+ red emission prevails for xgreater than or equal to0.03. The above unique changes in PL emission features are explained in terms of the changes in NNN environments of Ce4+. Quenching of Ce4+-O2- CT emission by other Ln(3+) is due to the ground state crossover arising out of the NNN interactions.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Simple theoretical analysis of the Fowler-Nordheim field emission from microstructures and quantum wires of optoelectronic materials

We present a simplified theoretical formulation of the Fowler-Nordheim field emission (FNFE) under magnetic quantization and also in quantum wires of optoelectronic materials on the basis of a newly formulated electron dispersion law in the presence of strong electric field within the framework of k.p formalism taking InAs, InSb, GaAs, Hg(1-x)Cd(x)Te and In(1-x)Ga(x) As(y)P(1-y) lattice matched to InP as examples. The FNFE exhibits oscillations with inverse quantizing magnetic field and electron concentration due to SdH effect and increases with increasing electric field. For quantum wires the FNFE increases with increasing film thickness due to the existence van-Hove singularity and the magnitude of the quantum jumps are not of same height indicating the signature of the band structure of the material concerned. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the field current varies in various manners with all the variables in all the limiting cases as evident from all the curves, the rates of variations are totally band-structure dependent. Under certain limiting conditions, all the results as derived in this paper get transformed in to well known Fowler-Nordheim formula. (C) 2011 Elsevier Ltd. All rights reserved.

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

Current rectification by a single ZnS nanorod probed using a scanning tunneling microscopic technique

We report on the rectification properties from a single ZnS nanorod measured using the UHV-SPM technique. The rectification behavior is evidenced from the current-voltage characteristics measured on a single ZnS nanorod. We propose a tunneling mechanism where the direct tunneling mechanism is dominant at lower applied bias voltages followed by resonant tunneling through discrete energy levels of the nanorod. A further increase in the bias voltage changes the tunneling mechanism to the Fowler-Nordheim tunneling regime enabling rectification behavior. Realizing rectification from a single ZnS nanorod may provide a means of realizing a single nanorod based miniaturized device.

Photophysical, electrochemical and solid state properties of diketopyrrolopyrrole based molecular materials: importance of the donor group

Diketopyrrolopyrrole (DPP) based molecular semiconductors have emerged as promising materials for high performance active layers in organic solar cells. It is imperative to comprehend the origin of such a property by investigating the fundamental structure property correlation. In this report we have investigated the role of the donor group in DPP based donor-acceptor- donor (D-A-D) structure to govern the solid state, photophysical and electrochemical properties. We have prepared three derivatives of DPP with varying strengths of the donor groups, such as phenyl (PDPP-Hex), thiophene (TDPP-Hex) and selenophene (SeDPP-Hex). The influence of the donor units on the solid state packing was studied by single crystal X-ray diffraction. The photophysical, electrochemical and density functional theory ( DFT) results were combined to elucidate the structural and electronic properties of three DPP derivatives. We found that these DPP derivatives crystallized in the monoclinic space group P21/c and show herringbone packing in the crystal lattice. The derivatives exhibit weak p-p stacking interactions as two neighboring molecules slip away from each other with varied torsional angles at the donor units. The high torsional angle of 32 degrees ( PDPP-Hex) between the phenyl and lactam ring results in weak intramolecular interactions between the donor and acceptor, while TDPP-Hex and SeDPP-Hex show lower torsional angles of 9 degrees and 12 degrees with a strong overlap between the donor and acceptor units. The photophysical properties reveal that PDPP-Hex exhibits a high Stokes shift of 0.32 eV and SeDPP- Hex shows a high molar absorption co-efficient of 33 600 L mol -1 1 cm -1 1 with a low band gap of similar to 2.2 eV. The electrochemical studies of SeDPP- Hex indicate the pronounced effect of selenium in stabilizing the LUMO energy levels and this further emphasizes the importance of chalcogens in developing new n-type organic semiconductors for optoelectronic devices.

New 4-(2-(4-alkoxyphenyl)-6-methoxypyridin-4-yl) benzonitriles: synthesis, liquid crystalline behavior and photo physical properties

A new series of luminescent 4-(2-(4-alkoxyphenyl)-6-methoxypyridin-4-yl) benzonitriles containing three ring systems, viz. methoxy pyridine, benzonitrile and alkoxy benzene with variable alkoxy chain length, with bent-core structures were synthesized as potential mesogens and characterized by spectral techniques. Their liquid crystalline behavior was investigated by polarizing optical microscopy (POM), differential scanning calorimetry (DSC) and variable temperature powder X-ray diffraction (PXRD) measurements. The study reveals that compounds with shorter chain lengths i.e. m = 4] exclusively exhibit the nematic phase while compounds with longer chain lengths i.e. m = 6-14 (only even)] show predominantly the orthorhombic columnar phase. Single crystal X-ray analysis of 4-(2-(4-butyloxy/octyloxyphenyl)-6-methoxypyridin-4-yl) benzonitriles reveals that they possess slightly non-planar unsymmetrical bent structures and their molecular packing consists of nonconventional H-bond interactions; it also explains the observed liquid crystalline phase. An optical study indicates that the title compounds are good blue emitting materials showing absorption and emission bands in the range 335-345 nm and 415-460 nm, respectively. An electrochemical study of 4-(2-(4-octyloxyphenyl)-6-methoxypyridin-4-yl) benzonitrile shows a band gap of 1.89 eV with HOMO and LUMO energy levels of -5.06 and -3.17 eV, respectively. Also, density functional theory (DFT) calculations confirm its optimized geometry, electronic absorption and frontier molecular orbital distributions.

Design and synthesis of new low band gap organic semiconductors for photovoltaic applications

Donor-acceptor (D-A) conjugated polymers have attracted a good deal of attention in recent years. In D-A systems, the introduction of electron withdrawing groups reduces E-g by lowering the LUMO levels whereas, the introduction of electron donating groups reduces E-g by raising the HOMO levels. Also, conjugated polymers with desired HOMO and LUMO energy levels could be obtained by the proper selection of donor and acceptor units. Because of this reason, D-A conjugated polymers are emerging as promising materials particularly for polymer light emitting diodes (PLEDs) and polymer solar cells (PSCs). We report the design and synthesis of four new narrow band gap donor-acceptor (D-A) conjugated polymers, PTCNN, PTCNF, PTCNV and PTCNO, containing electron donating 3,4-didodecyloxythiophene and electron accepting cyanovinylene units. The effects of further addition of electron donating and electron withdrawing groups to the repeating unit of a D-A conjugated polymer (PTCNN) on its optical and electrochemical properties are discussed. The studies revealed that the nature of D and A units as well as the extent of alternate D-A structure influences the optical and the electrochemical properties of the polymers. All the polymers are thermally stable up to a temperature of 300 degrees C under nitrogen atmosphere. The electrochemical studies revealed that the polymers possess low-lying HOMO energy levels and low-lying LUMO energy levels. In the UV-Vis absorption study, the polymer films displayed broad absorption in the wavelength region of 400-700 nm. The polymers exhibited low optical band gaps in the range 1.70 - 1.77 eV.

Properties of the chalcogenide-carbon nano tubes and graphene composite materials

Composite can deliver more than the individual elemental property of the material. Specifically chalcogenide- multi walled carbon nano tubes and chalcogenide- bilayer graphene composite materials could be interesting for the investigation, which have been less covered by the investigators. We describe micro structural properties of Se55Te25Ge20, Se55Te25Ge20 + 0.025% multi walled carbon nano tubes and Se55Te25Ge20 + 0.025% bilayer graphene materials. This gives realization of the alloying constituents inclusion/or diffusion inside the multi walled carbon nano tubes and bilayer graphene under the homogeneous parent alloy configuration. Raman spectroscopy, X-ray photoelectron spectroscopy, UV/Visible spectroscopy and Fourier transmission infrared spectroscopy have also been carried out under the discussion. A considerable core energy levels peak shifts have been noticed for the composite materials by the X-ray photoelectron spectroscopy. The optical energy band gaps are measured to be varied in between 1.2 and 1.3 eV. In comparison to parent (Se55Te25Ge20) alloy a higher infrared transmission has been observed for the composite materials. Subsequently, variation in physical properties has been explained on the basis of bond formation in solids. (C) 2014 Elsevier B. V. All rights reserved.

Narrow band gap conjugated polymer for improving the photovoltaic performance of P3HT:PCBM ternary blend bulk heterojunction solar cells

A new D-A structured conjugated polymer (PBDO-T-TDP) based on electron-rich benzo 1,2-b:4,5-b'] difuran (BDO) containing conjugated alkylthiophene side chains with an electron-deficient diketopyrrolopyrrole (DPP) derivative is designed and synthesized. The polymer shows a narrow band gap with broad UV-Visible absorption spectra, which is in contrast to that of the P3HT:PCBM binary blend. Furthermore, its energy levels can meet the energetic requirement of the cascaded energy levels of P3HT and PCBM. Therefore, PBDO-T-TDP is used as a sensitizer in P3HT: PCBM based BHJ solar cells and its effect on their photovoltaic properties was investigated by blending them together at various weight ratios. It is observed that the resulting ternary blend system exhibited a significant improvement in the device performance (similar to 3.10%) as compared with their binary ones (similar to 2.15%). Such an enhancement in the ternary blend system is ascribed to their balanced hole and electron mobility along with uniform distribution of PBDO-T-TDP in the blend system, as revealed by organic field effect transistors and AFM studies.

Electronic Structure of CH3NH3PbX3 Perovskites: Dependence on the Halide Moiety

A combination of measurements using photoelectron spectroscopy and calculations using density functional theory (DFT) was applied to compare the detailed electronic structure of the organolead halide perovskites CH3NH3PbI3 and CH3NH3PbBr3. These perovskite materials are used to absorb light in mesoscopic and planar heterojunction solar cells. The Pb 4f core level is investigated to get insight into the chemistry of the two materials. Valence level measurments are also included showing a shift of the valence band edges where there is a higher binding energy of the edge for the CH3NH3PbBr3 perovskite. These changes are supported by the theoretical calculations which indicate that the differences in electronic structure are mainly caused by the nature of the halide ion rather than structural differences. The combination of photoelectron spectroscopy measurements and electronic structure calculations is essential to disentangle how the valence band edge in organolead halide perovskites is governed by the intrinsic difference in energy levels of the halide ions from the influence of chemical bonding.

Self-assembled ZnO nanoparticles on ZnO microsheet: ultrafast synthesis and tunable photoluminescence properties

We report on the tunable photoluminescence characteristics of porous ZnO microsheets fabricated within 1-5 min of microwave irradiation in the presence of a capping agent such as citric acid, and mixture of citric acid with polyvinylpyrrolidone (PVP). The UV emission intensity reduces to 60% and visible emission increases tenfold when the molar concentration of citric acid is doubled. Further diminution of the intensity of UV emission (25%) is observed when PVP is mixed with citric acid. The addition of nitrogen donor ligands to the parent precursor leads to a red shift in the visible luminescence. The deep level emission covers the entire visible spectrum and gives an impression of white light emission from these ZnO samples. The detailed luminescence mechanism of our ZnO samples is described with the help of a band diagram constructed by using the theoretical models that describe the formation energy of the defect energy levels within the energy band structure. Oxygen vacancies play the key role in the variation of the green luminescence in the ZnO microsheets. Our research findings provide an insight that it is possible to retain the microstructure and simultaneously introduce defects into ZnO. The growth of the ZnO microsheets may be due to the self assembly of the fine sheets formed during the initial stage of nucleation.

Theoretical Insights to Niobium-Doped Monolayer MoS2-Gold Contact

We report a first principles study of the electronic properties for a contact formed between Nb-doped monolayer MoS2 and gold for different doping concentrations. We first focus on the shift of energy levels in band structure and the density of states with respect to the Fermi level for a geometrically optimized 5 x 5 MoS2 supercell for both pristine and Nb-doped structures. The doping is achieved by substituting Mo atoms with Nb atoms at random positions. It is observed that for an experimentally reported sheet hole doping concentration of (rho(2D)) 1.8 x 10(14) cm(-2), the pristine MoS2 converts to degenerate p-type semiconductor. Next, we interface this supercell with six layers of < 111 > cleaved surface of gold to investigate the contact nature of MoS2-Au system. By careful examination of projected band structure, projected density of states, effective potential and charge density difference, we demonstrate that the Schottky barrier nature observed for pure MoS2-Au contact can be converted from n-type to p-type by efficient Nb doping.