We investigate the Fock-Darwin states of the massless chiral fermions confined in a graphitic parabolic quantum dot. In light of Klein tunneling, we analyze the condition for confinement of the Dirac fermions in a cylindrically symmetric potential. New features of the energy levels of the Dirac electrons as compared to the conventional electronic systems are discussed. We also evaluate the dipole-allowed transitions in the energy levels of the dots. We propose that in the high magnetic field limit, the band parameters can be accurately determined from the dipole-allowed transitions.

Abstract. We show how the problem of nontermination proving can be reduced to a question of underapproximation search guided by a safety prover. This reduction leads to new nontermination proving implementation strategies based on existing tools for safety proving. Our preliminary implementation beats existing tools. Furthermore, our approach leads to easy support for programs with unbounded nondeterminism.

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A phenomenological model defined in a two dimensional lattice is employed to investigate the d-wave superconductivity and the competing antiferromagnetic order in cuprate superconductors. Near the optimally doped regime, we show that it is possible to induce the spin density wave (SDW) and the accompanying charge density wave (CDW) orders with stripe modulations by applying a magnetic field. The periods of the magnetic field induced SDW and CDW are 8a and 4a, respectively. The spatial profiles of the local density of states (LDOS) at various bias energies have also been numerically studied. Near and beyond the energies of the vortex core states, we found that the LDOS may display the CDW stripe-like modulation throughout the whole magnetic unit cell. For energies closer to the zero bias, the stripes appear to be rather localized to the vortex. The intensity of the integrated spectrum of the LDOS shows that the strength of the stripe modulation is decaying away from the vortex core. This feature is in good agreement with STM experiments. The case for the magnetic-field induced SDW/CDW with 4-fold symmetry has also been studied. [3] seems to confirm the coexistence of the static charge modulation and the superconductivity on Bi 2 Sr 2 CaCu 2 O 8 (BSCCO) under a magnetic field. The authors reported that a four unit cell checkerboard pattern is localized in a small region around the vortex, and its intensity is exponentially decaying away from the vortex core. All these experiments indicate that the AF fluctuations could be pinned by the vortex cores and they may form a static SDW/charge-density-wave (CDW) like modulations in certain samples of cuprate superconductors. Theoretically, a number of works proposed that the observed checkerboard patterns could be explained by the SDW order with the two-dimensional (2D) [4,5,6] or stripe [7,8,9] modulations. Both the 2D-and stripe-SDW orders induced by the magnetic field are well known to have the accompanying CDW modulations. In particularly, the checkerboard pattern has been attributed to the superposition of stripe modulations of the CDW [7,10] oriented along x-and y-directions. In all these studies, the STM spectra obtained from the experiment have been directly interpreted in terms of the CDW order induced by the magnetic field. This is because that the conventional wisdom leads us to believe that the symmetry of the CDW order should be reflected in the STM spectra. On the other hand, the CDW order represents the charge density configuration in the ground state while the STM spectrum or the spatial distribution of the local density of states (LDOS) is determined by the behavior of the low-energy excitations in the system. It is therefore extremely interesting to know the difference between the CDW order and the spatial profile of the LDOS. This issue has not yet been addressed in the literature, and thus is the main purpose of the present paper.The phonemenological t − t ′ − U − V model defined in a 2D lattice and the Bogoliubov-de Gennes' equations will be used to n...

Several recent exact diagonalization calculations have established that the Anderson-Hubbard model has a disorder-induced zero bias anomaly (ZBA) (also called a disorder-induced pseudogap) in the density of states. In order to understand the physics of the ZBA, we study a simplified problem-an ensemble of two-site molecules with random site energies-for which analytical results are possible. For this ensemble, we examine how the ZBA forms in both the weakly correlated (mean field) and strongly correlated limits. In the weakly correlated case, the ZBA can be understood as the result of level repulsion between bonding and antibonding molecular orbitals. A similar level repulsion occurs in the strongly correlated case too, but a larger contribution to the ZBA comes from the suppression of a triplet excitation mode. This inherently many-body mechanism does not have a counterpart in mean-field models.

Quantum rings subjected to a Rashba spin-orbit coupling and an external magnetic field possess interesting magnetic properties. Specifically, the spectral linewidth of magnetic susceptibility is found to be independent of the ring geometry. For zero spin-orbit coupling it varies linearly with temperature and the slope is proportional to a scaling factor of material parameters. When the spin-orbit interaction is switched on, there is a turning temperature below which the spin-orbit coupling strength is directly measurable. The upper bound of the turning temperature is also investigated.

Based on the t − t ′ − U − V model with proper chosen parameters for describing the cuprate superconductors, it is found that near the optimal doping at low temperature (T ), only the pure d-wave superconductivity (dSC) prevails and the antiferromagnetic (AF) order is completely suppressed. At higher T , the AF order with stripe modulation and the accompanying charge order may emerge, and they could exist above the dSC transition temperature. We calculate the local differential tunnelling conductance (LDTC) from the local density of states (LDOS) and show that their energy variations are rather different from each other as T increases. Although the calculated modulation periodicity in the LDTC/LDOS and bias energy dependence of the Fourier amplitude of LDTC in the "pseudogap" region are in good agreement with the recent STM experiment [Vershinin et al., Science 303, 1995(2004], we point out that some of the energy dependent features in the LDTC do not represent the intrinsic characteristics of the sample.