Zheyong Fan

We study Anderson localization in graphene with short-range disorder using the real-space Kubo-Greenwood method implemented on graphics processing units. Two models of short-range disorder, namely, the Anderson on-site disorder model and the vacancy defect model, are considered. For graphene with Anderson disorder, localization lengths of quasi-one-dimensional systems with various disorder strengths, edge symmetries, and boundary conditions are calculated using the real-space Kubo-Greenwood formalism, showing excellent agreement with independent transfer matrix calculations and superior computational efficiency. Using these data, we demonstrate the applicability of the one-parameter scaling theory of localization length and propose an analytical expression for the scaling function, which provides a reliable method of computing the two-dimensional localization length. This method is found to be consistent with another widely used method which relates the two-dimensional localization length to the elastic mean free path and the semiclassical conductivity. Abnormal behavior at the charge neutrality point is identified and interpreted to be caused by finite-size effects when the system width is comparable to or smaller than the elastic mean free path. We also demonstrate the finite-size effect when calculating the two-dimensional conductivity in the localized regime and show that a renormalization group beta function consistent with the one-parameter scaling theory can be extracted numerically. For graphene with vacancy disorder, we show that the proposed scaling function of localization length also applies. Lastly, we discuss some ambiguities in calculating the semiclassical conductivity around the charge neutrality point due to the presence of resonant states.

A classical SU(2) Einstein-Yang-Mills theory in (3+1)-dimensional anti-de Sitter spacetime is believed to be dual to a p-wave superconductor in (2+1)-dimensional flat spacetime. In order to calculate the superconducting coherence length ξ of the holographic superconductor near the superconducting phase transition point, we make a perturbative study of the gravity theory analytically. The superconducting coherence length ξ is found to be proportional to (1-T/Tc)-1/2 near the critical temperature Tc. We also obtain the magnetic penetration depth λ∝(Tc-T)1/2 by adding a small external homogeneous magnetic field. The results agree with the Ginzburg-Landau theory.

A d-wave holographic superconductor in the presence of a constant magnetic field is studied by the perturbation method. We obtain both droplet and triangular vortex lattice solutions. The results are the same as that of an s-wave holographic superconductor. The non-Abelian holographic superconductor with p+ip-wave background in the presence of a magnetic field is also studied. Unlike the d-wave and s-wave models, it is found that the non-Abelian model has only a droplet solution.

We study various aspects of the topological quantum computation scheme based on the non-Abelian anyons corresponding to fractional quantum hall effect states at filling fraction 5/2 using the Temperley-Lieb recoupling theory. Unitary braiding matrices are obtained by a normalization of the degenerate ground states of a system of anyons, which is equivalent to a modification of the definition of the 3-vertices in the Temperley-Lieb recoupling theory as proposed by Kauffman and Lomonaco. With the braid matrices available, we discuss the problems of encoding of qubit states and construction of quantum gates from the elementary braiding operation matrices for the Ising anyons model. In the encoding scheme where 2 qubits are represented by 8 Ising anyons, we give an alternative proof of the no-entanglement theorem given by Bravyi and compare it to the case of Fibonacci anyons model. In the encoding scheme where 2 qubits are represented by 6 Ising anyons, we construct a set of quantum gates which is equivalent to the construction of Georgiev.

A graphene antidot lattice, created by a regular perforation of a graphene sheet, can exhibit a considerable band gap required by many electronics devices. However, deviations from perfect periodicity are always present in real experimental setups and can destroy the band gap. Our numerical simulations, using an efficient linear-scaling quantum transport simulation method implemented on graphics processing units, show that disorder that destroys the band gap can give rise to a transport gap caused by Anderson localization. The size of the defect induced transport gap is found to be proportional to the radius of the antidots and inversely proportional to the square of the lattice periodicity. Furthermore, randomness in the positions of the antidots is found to be more detrimental than randomness in the antidot radius. The charge carrier mobilities are found to be very small compared to values found in pristine graphene, in accordance with recent experiments.

A systematics of excitation energy of the first 2+ state E21+ in even–even heavy nuclei (A⩾120) is studied in the NpNn scheme. It is found that a simple exponential function describes the dependence of E21+ values on NpNn values very well. In addition, the Z = 64 shell gap is reexamined by investigating the systematics of the 52⩽Z⩽66 region. It

It is known that a classical SU(2) Einstein-Yang-Mills theory in 3+1 dimensional anti-de Sitter spacetime can provide a holographic dual to a 2+1 dimensional time reversal symmetry breaking superconductor with a pseudogap. We study the properties of this holographic superconductor in the presence of an applied constant external magnetic field, neglecting backreaction on the geometry. The superconductor is immersed into a constant external magnetic field by adding a radially (the extra dimension) dependent magnetic field to the black hole. As for real superconductors, there is a critical magnetic field above which no superconductivity can appear. The continuity of the first derivative of the free energy difference between the superconducting phase and the normal phase at the critical temperature suggests that the superconducting phase transition with applied magnetic field is of second order.

Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for highly entangled states, but also for the corresponding quantum circuits creating these states. Simple quantum circuits for maximally (highly) entangled states are discovered for 3, 4, 5, and 6-qubit systems; and extension of the method to systems with more qubits is discussed. Among other results we have found explicit quantum circuits for maximally entangled 5 and 6-qubit circuits, with only 8 and 13 quantum gates respectively. One significant advantage of our method over previous ones is that it allows very simple construction of quantum circuits based on the quantum states found. Comment: 15 pages, 4 figures

A quantum phase transition may occur in a system at zero temperature when a controlling parameter is tuned towards a critical point. An important question is whether such a critical point exists in a particular system and how stable it is. Here, we identify the critical point of a quantum phase transition as a singular point in the affine algebraic variety of the characteristic equation for the Hamiltonian describing the system, with an unstable critical point being associated with an isolated singular point which has a finite Tjurina number. The theory is illustrated by studying a model system of zero-dimensional (finite) Heisenberg spin chain with an impurity, which exhibits a nontrivial first-order quantum phase transition. Both analytical and numerical calculations show that the quantum phase transition always exists when the impurity has a $Z_2$ symmetry but only remains in systems with an even number of spin sites when the $Z_2$ symmetry is broken.

ABSTRACT We propose a model of one-dimensional Heisenberg spin chain with a single local defect attached to one end of the spin chain which exhibits nontrivial quantum phase transition in the parameter space characterizing the local defect. By calculating the ground state energy, entanglement entropy, and total spin of the system using density matrix renormalization group, we found that a quantum phase transition, which is robust enough to survive in the thermodynamic limit, always exists when the defect is symmetric with respect to the spin chain. On the other hand, in the absence of this symmetry, the quantum phase transition only remains in systems with even number of spin sites. The quantum phase transition is characterized by crossover of two energy functions along with discontinuous total spin (in systems with even number of spin sites) and entanglement entropy at the critical point in the parameter space.

ABSTRACT We establish, through numerical calculations and comparisons with a recursive Green's-function based implementation of the Landauer-Büttiker formalism, an efficient method for studying Anderson localization in quasi-one-dimensional and two-dimensional systems using the Kubo-Greenwood formalism. Although the recursive Green's-function method can be used to obtain the localization length of a mesoscopic conductor, it is numerically very expensive for systems that contain a large number of atoms transverse to the transport direction. On the other hand, linear scaling has been achieved with the Kubo-Greenwood method, enabling the study of effectively two-dimensional systems. While the propagating length of the charge carriers will eventually saturate to a finite value in the localized regime, the conductances given by the Kubo-Greenwood method and the recursive Green's-function method agree before the saturation. The converged value of the propagating length is found to be directly proportional to the localization length obtained from the exponential decay of the conductance.

In this paper, a new nanostructure is proposed, namely, the knitted graphene-nanoribbon sheet (KGS), which consists of zigzag and/or armchair graphene nanoribbons. The knitting technology is introduced to graphene nanotechnology to produce large area graphene sheets. Compared with pristine graphene, the chirality of a knitted graphene-nanoribbon sheet is much more flexible and can be designed on demand. The mechanical properties of KGSs are investigated by molecular dynamics simulations, including the effect of vacancies. With hydrogen atoms saturating the ribbon edges, the structure (KGS + H) is found to be of significant mechanical robustness, whose fracture does not rely on the critical bonds. The fracture strain of KGS + H remains nearly unchanged as long as there remains a single defect-free graphene nanoribbon in the tensile direction. This graphene nano knitting technique is experimentally feasible, inspired by a recent demonstration by Fournier et al. [Phys. Rev. B, 2011, 84, 035435] of lifting a single molecular wire using a combined frequency-modulated atomic force and tunnelling microscope.

ABSTRACT We investigate the thermoelectric properties of ultrathin graphitic ZnO (0001) nanofilms based on first-principles calculations and Boltzmann transport theory. Staircase-like densities of states induced by quantum confinement in the nanofilms give rise to improved Seebeck coefficients and electrical conductivities. The optimized figure of merit for the single-layer graphitic ZnO (0001) nanofilm is estimated to be 0.6 at 300 K, which is about 120 times larger than that of bulk ZnO (0.005). Our results suggest that the graphitic ZnO (0001) nanofilms can be designed for high performance thermoelectric applications.

The thermoelectric performance of materials is dependent on the interplay or competition among three key components, the electrical conductivity, thermopower, and thermal conductivity, which can be written as integrals of a single function, the transport distribution function (TDF). Mahan and Sofo [Proc. Natl. Acad. Sci. USA 93, 7436 (1996)] found that, mathematically, the thermoelectric properties could be maximized by a delta-shaped transport distribution, which was associated with a narrow distribution of the energy of the electrons participating in the transport process. In this work, we revisited the shape effect of TDF on thermoelectric figure of merit. It is confirmed both heuristically and numerically that among all the normalized TDF the Dirac delta function leads to the largest thermoelectric figure of merit. Whereas, for the case of TDF being bounded, a rectangular-shape distribution is instead found to be the most favorable one, which could be achieved through nanoroute. Our results also indicate that high thermoelectric figure of merit is associated with appropriate violations of the Wiedemann-Franz law.

A systematics of excitation energy of the first 2+ state E21+ in even–even heavy nuclei (A⩾120) is studied in the NpNn scheme. It is found that a simple exponential function describes the dependence of E21+ values on NpNn values very well. In addition, the Z = 64 shell gap is reexamined by investigating the systematics of the 52⩽Z⩽66 region. It