Browsing by Author "Hakioǧlu, T."
Now showing 1 - 7 of 7
Results Per Page
Sort Options
Item Open Access The action-angle Wigner function: A discrete, finite and algebraic phase space formalism(2000) Hakioǧlu, T.; Tepedelenlioǧlu, E.The action-angle representation in quantum mechanics is conceptually quite different from its classical counterpart and motivates a canonical discretization of the phase space. In this work, a discrete and finite-dimensional phase space formalism, in which the phase space variables are discrete and the time is continuous, is developed and the fundamental properties of the discrete Weyl-Wigner-Moyal quantization are derived. The action-angle Wigner function is shown to exist in the semi-discrete limit of this quantization scheme. A comparison with other formalisms which are not explicitly based on canonical discretization is made. Fundamental properties that an action-angle phase space distribution respects are derived. The dynamical properties of the action-angle Wigner function are analysed for discrete and finite-dimensional model Hamiltonians. The limit of the discrete and finite-dimensional formalism including a discrete analogue of the Gaussian wavefunction spread, viz. the binomial wavepacket, is examined and shown by examples that standard (continuum) quantum mechanical results can be obtained as the dimension of the discrete phase space is extended to infinity.Item Open Access Canonical-covariant Wigner function in polar form(OSA - The Optical Society, 2000) Hakioǧlu, T.The two-dimensional Wigner function was investigated in polar canonical coordinates. The covariance properties under the action of affine canonical transformations were derived. The polar canonical phase-space representations were considered important for paraxial optical systems as well as other systems in which a rotational symmetry around a particular axis was present.Item Open Access CDW-Exciton Condensate Competition and a Condensate Driven Force(Physical Society of Japan, 2016) Özgün, E.; Hakioǧlu, T.We examine the competition between the charge-density wave (CDW) instability and the excitonic condensate (EC) in spatially separated layers of electrons and holes. The CDW and the EC order parameters (OPs), described by two different mechanisms and hence two different transition temperatures TcCDWand TcEC,are self-consistently coupled by a microscopic mean field theory. We discuss the results in our model specifically focusing on the transition-metal dichalcogenides which are considered as the most typical examples of strongly coupled CDW/EC systems with atomic layer separations where the electronic energy scales are large with the critical temperatures in the range TcEC∼ TcCDW∼ 100-200 K. An important consequence of this is that the excitonic energy gap, hence the condensed free energy, vary with the layer separation resulting in a new type of force FEC . We discuss the possibility of this force as the possible driver of the structural lattice deformation observed in some TMDCs with a particular attention on the 1T-TiSe2 below 200 K.Item Open Access Electronic structure, insulator-metal transition and superconductivity in K-ET2X salts(1998) Ivanov V.A.; Ugolkova, E.A.; Zhuravlev, M.Ye.; Hakioǧlu, T.The electronic structure and superconductivity of layered organic materials based on the bis(ethylenedithio)tetrathiafulvalene molecule (BEDT-TTF, hereafter ET) with essential intra-ET correlations of electrons are analysed. Taking into account the Fermi surface topology, the superconducting electronic density of states (DOS) is calculated for a realistic model of K-ET2X salts. A d-symmetry of the superconducting order parameter is obtained and a relation is found between its nodes on the Fermi surface and the superconducting phase characteristics. The results are in agreement with the measured non-activated temperature dependences of the superconducting specific heat and NMR relaxation rate of central 13C atoms in ET. © 1998 John Wiley & Sons, Ltd.Item Open Access Landau quantization of two-dimensional heavy holes, energy spectrum of magnetoexcitons and Auger-recombination lines(2013) Podlesny I.V.; Moskalenko, S.A.; Hakioǧlu, T.; Kiselyov, A.A.; Gherciu L.The Landau quantization of the two-dimensional (2D) heavy holes, its influence on the energy spectrum of 2D magnetoexcitons, as well as their optical orientation are studied. The Hamiltonian of the heavy holes is written in two-band model taking into account the Rashba spin-orbit coupling (RSOC) with two spin projections, but with nonparabolic dispersion law and third-order chirality terms. The most Landau levels, except three with m=0,1,2, are characterized by two quantum numbers m-3 and m for m≥3 for two spin projections correspondingly. The difference between them is determined by the third-order chirality. Four lowest Landau levels (LLLs) for heavy holes were combined with two LLLs for conduction electron, which were taken the same as they were deduced by Rashba in his theory of spin-orbit coupling (SOC) based on the initial parabolic dispersion law and first-order chirality terms. As a result of these combinations eight 2D magnetoexciton states were formed. Their energy spectrum and the selection rules for the quantum transitions from the ground state of the crystal to exciton states were determined. On this base such optical orientation effects as spin polarization and magnetoexciton alignment are discussed. The continuous transformation of the shake-up (SU) into the shake-down (SD) recombination lines is explained on the base of nonmonotonous dependence of the heavy hole Landau quantization levels as a function of applied magnetic field. © 2013 Elsevier B.V. All rights reserved.Item Open Access A measurable force driven by an excitonic condensate(American Institute of Physics Inc., 2014) Hakioǧlu, T.; Özgün, E.; Günay, M.Free energy signatures related to the measurement of an emergent force (≈10-9N) due to the exciton condensate (EC) in Double Quantum Wells are predicted and experiments are proposed to measure the effects. The EC-force is attractive and reminiscent of the Casimir force between two perfect metallic plates, but also distinctively different from it by its driving mechanism and dependence on the parameters of the condensate. The proposed experiments are based on a recent experimental work on a driven micromechanical oscillator. Conclusive observations of EC in recent experiments also provide a strong promise for the observation of the EC-force. © 2014 AIP Publishing LLC.Item Open Access Weakly Anisotropic Noncentrosymmetric Superconductors with Radial Line Nodes and the Origin of the Anomalous Thermodynamic Data(Physical Society of Japan, 2017) Günay, M.; Hakioǧlu, T.; Sömek, H. H.In noncentrosymmetric superconductors (NCSs), the inversion symmetry (IS) is most commonly broken by an antisymmetric spin-orbit coupling (SOC). Removing the spin degeneracy and splitting the Fermi surface (FS) into two branches. A two component condensate is then produced mixing an even singlet and an odd triplet. When the triplet and the singlet strengths are comparable, the pair potential can have rich nodes. The angular line nodes (ALNs) are associated with the point group symmetries of the anisotropic lattice structure and they are widely studied in the literature. When the anisotropy is weak, other types of nodes can be present which then affect differently the low temperature properties. Here, we focus on the weakly anisotropic NCSs and the line nodes which survive in the limit of full isotropy. We study the topology of these radial line nodes (RLNs) and show that it is characterized by the Z2 index similar to the quantum-spin-Hall Insulators. From the thermodynamic perspective, the RLNs cause, even in the topological phases, an exponentially suppressed low temperature behaviour which can be mistaken by nodeless s-wave pairing, thus, providing an explanation to a number of recent experiments with contraversial pairing symmetries. In the rare case when the RLN is on the Fermi surface, the exponential suppression is replaced by a linear temperature dependence. The RLNs are difficult to detect, and for this reason, they may have escaped experimental attention. We demonstrate that Andreev conductance measurements with clean interfaces can efficiently identify the weakly anisotropic (WA) conditions where the RLNs are expected to be found.