Rakesh P. Tiwari

Intrinsic anomalous Hall effect in type-II Weyl semimetals

Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation between the Weyl points vanishes, tilting of the conical spectrum could give rise to a finite anomalous Hall effect, if the tilts of the two cones are not identical.

Quantum pumping in graphene with a perpendicular magnetic field

We consider quantum pumping of Dirac fermions in a monolayer of graphene in the presence of a perpendicular magnetic field in the central pumping region. The two external pump parameters are electrical voltages applied to the graphene sheet on either side of the pumping region. We analyze this pump within scattering matrix formalism and calculate both pumped charge and spin currents. The predicted charge currents are of the order of 1000 nA, which is readily observable using current technology.

Magnetic superlattice with two-dimensional periodicity as a waveguide for spin waves

We describe a simple method of including dissipation in the spin-wave band structure of a periodic ferromagnetic composite, by solving the Landau-Lifshitz equation for the magnetization with the Gilbert damping term. We use this approach to calculate the band structure of square and triangular arrays of Ni nanocylinders embedded in an Fe host. The results show that there are certain bands and special directions in the Brillouin zone where the spin-wave lifetime is increased by more than an order of magnitude above its average value. Thus, it may be possible to generate spin waves in such composites which decay especially slowly, and propagate especially large distances, for certain frequencies and directions in k space.

A basis-set based Fortran program to solve the Gross-Pitaevskii equation for dilute Bose gases in harmonic and anharmonic traps

Abstract Inhomogeneous boson systems, such as the dilute gases of integral spin atoms in low-temperature magnetic traps, are believed to be well described by the Gross–Pitaevskii equation (GPE). GPE is a nonlinear Schrodinger equation which describes the order parameter of such systems at the mean field level. In the present work, we describe a Fortran 90 computer program developed by us, which solves the GPE using a basis set expansion technique. In this technique, the condensate wave function (order parameter) is expanded in terms of the solutions of the simple-harmonic oscillator (SHO) characterizing the atomic trap. Additionally, the same approach is also used to solve the problems in which the trap is weakly anharmonic, and the anharmonic potential can be expressed as a polynomial in the position operators x , y , and z . The resulting eigenvalue problem is solved iteratively using either the self-consistent-field (SCF) approach, or the imaginary time steepest-descent (SD) approach. Iterations can be initiated using either the simple-harmonic-oscillator ground state solution, or the Thomas–Fermi (TF) solution. It is found that for condensates containing up to a few hundred atoms, both approaches lead to rapid convergence. However, in the strong interaction limit of condensates containing thousands of atoms, it is the SD approach coupled with the TF starting orbitals, which leads to quick convergence. Our results for harmonic traps are also compared with those published by other authors using different numerical approaches, and excellent agreement is obtained. GPE is also solved for a few anharmonic potentials, and the influence of anharmonicity on the condensate is discussed. Additionally, the notion of Shannon entropy for the condensate wave function is defined and studied as a function of the number of particles in the trap. It is demonstrated numerically that the entropy increases with the particle number in a monotonic way. Program summary Title of program: bose.x Catalogue identifier: ADWZ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWZ_v1_0 Program obtainable from: CPC Program Library, Queens University of Belfast, N. Ireland Distribution format: tar.gz Computers: PCs/Linux, Sun Ultra 10/Solaris, HP Alpha/Tru64, IBM/AIX Programming language used: mostly Fortran 90 Number of bytes in distributed program, including test data, etc.: 27 313 Number of lines in distributed program, including test data, etc.: 28 015 Card punching code: ASCII Nature of physical problem: It is widely believed that the static properties of dilute Bose condensates, as obtained in atomic traps, can be described to a fairly good accuracy by the time-independent Gross–Pitaevskii equation. This program presents an efficient approach of solving this equation. Method of solution: The solutions of the Gross–Pitaevskii equation corresponding to the condensates in atomic traps are expanded as linear combinations of simple-harmonic oscillator eigenfunctions. Thus, the Gross–Pitaevskii equation which is a second-order nonlinear differential equation, is transformed into a matrix eigenvalue problem. Thereby, its solutions are obtained in a self-consistent manner, using methods of computational linear algebra. Unusual features of the program: None

Majorana Fermions from Landau Quantization in a Superconductor and Topological-Insulator Hybrid Structure

We show that the interplay of cyclotron motion and Andreev reflection experienced by massless-Dirac-like charge carriers in topological-insulator surface states generates a Majorana-particle excitation. On the basis of an envelope-function description of the Dirac-Andreev edge states, we discuss the kinematic properties of the Majorana mode and find them to be tunable by changing the superconductors chemical potential and/or the magnitude of the perpendicular magnetic field. Our proposal opens up new possibilities for studying Majorana fermions in a controllable setup.

Non-Abelian parafermions in time-reversal-invariant interacting helical systems

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of e/2, giving rise to a Josephson current with 8 pi periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as Z(4) parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.

Quantum Synchronization Blockade: Energy Quantization Hinders Synchronization of Identical Oscillators

Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization, is blocked. We demonstrate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with superconducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.

Model for the magnetoresistance and Hall coefficient of inhomogeneous graphene

Received 8 December 2008; revised manuscript received 24 February 2009; published 7 April 2009 We show that when bulk graphene breaks into n-type and p-type puddles, the in-plane resistivity becomes strongly field dependent in the presence of a perpendicular magnetic field even if homogeneous graphene has a field-independent resistivity. We calculate the longitudinal resistivity xx and Hall resistivity xy as a function of field for this system using the effective-medium approximation. The conductivity tensors of the individual puddles are calculated using a Boltzmann approach suitable for the band structure of graphene near the Dirac points. The resulting resistivity agrees well with experiment provided that the relaxation time is weakly field dependent. The calculated Hall resistivity has the sign of the carriers in the puddles occupying the greater area of the composite and vanishes when there are equal areas of n- and p-type puddles.

Robust quantum optimizer with full connectivity

A superconducting circuit of parametric oscillators realizes a robust quantum optimizer with full connectivity and zero overhead. Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. By leveraging the phenomenon of flux quantization, all-to-all connectivity with sufficient tunability to implement many relevant optimization problems is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the nondeterministic polynomial-time hard (NP-hard) and fully connected number partitioning problem in the presence of dissipation.

Localization and circulating currents in curved graphene devices

We calculate the energy spectrum and eigenstates of a graphene sheet that contains a circular deformation. Using time-independent perturbation theory with the ratio of the height and width of the deformation as the small parameter, we find that due to the curvature the wave functions for the various states acquire unique angular asymmetry.We demonstrate that the pseudomagnetic fields induced by the curvature result in circulating probability currents.