arXiv subjects

W. Apel

Publications and source records attributed to W. Apel.

18 recordsLinked to original sources

arXiv2015

Merging of the Dirac points in electronic artificial graphene

Theory predicts that graphene under uniaxial compressive strain in an armchair direction should undergo a topological phase transition from a semimetal into an insulator. Due to the change of the hopping integrals under compression, both Dirac points shift away from the corners of the Brillouin zone towards each other. For sufficiently large strain, the Dirac points merge and an energy gap appears. However, such a topological phase transition has not yet been observed in normal graphene (due to its large stiffness) neither in any other electronic system. We show numerically and analytically that such a merging of the Dirac points can be observed in electronic artificial graphene created from a two-dimensional electron gas by application of a triangular lattice of repulsive antidots. Here, the effect of strain is modeled by tuning the distance between the repulsive potentials along the armchair direction. Our results show that the merging of the Dirac points should be observable in a recent experiment with molecular graphene.

cond-mat.mes-hall↗

arXiv2012

Landau level splitting due to graphene superlattices

The Landau level spectrum of graphene superlattices is studied using a tight-binding approach. We consider non-interacting particles moving on a hexagonal lattice with an additional one-dimensional superlattice made up of periodic square potential barriers, which are oriented along the zig-zag or along the arm-chair directions of graphene. In the presence of a perpendicular magnetic field, such systems can be described by a set of one-dimensional tight-binding equations, the Harper equations. The qualitative behavior of the energy spectrum with respect to the strength of the superlattice potential depends on the relation between the superlattice period and the magnetic length. When the potential barriers are oriented along the arm-chair direction of graphene, we find for strong magnetic fields that the zeroth Landau level of graphene splits into two well separated sublevels, if the width of the barriers is smaller than the magnetic length. In this situation, which persists even in the presence of disorder, a plateau with zero Hall conductivity can be observed around the Dirac point. This Landau level splitting is a true lattice effect that cannot be obtained from the generally used continuum Dirac-fermion model.

cond-mat.mes-hall↗

arXiv2011

Electric transport through circular graphene quantum dots: Presence of disorder

The electronic states of an electrostatically confined cylindrical graphene quantum dot and the electric transport through this device are studied theoretically within the continuum Dirac-equation approximation and compared with numerical results obtained from a tight-binding lattice description. A spectral gap, which may originate from strain effects, additional adsorbed atoms or substrate-induced sublattice-symmetry breaking, allows for bound and scattering states. As long as the diameter of the dot is much larger than the lattice constant, the results of the continuum and the lattice model are in very good agreement. We also investigate the influence of a sloping dot-potential step, of on-site disorder along the sample edges, of uncorrelated short-range disorder potentials in the bulk, and of random magnetic-fluxes that mimic ripple-disorder. The quantum dot's spectral and transport properties depend crucially on the specific type of disorder. In general, the peaks in the density of bound states are broadened but remain sharp only in the case of edge disorder.

cond-mat.mes-hall↗

arXiv2011

Energy gap in graphene nanoribbons with structured external electric potentials

The electronic properties of graphene zig-zag nanoribbons with electrostatic potentials along the edges are investigated. Using the Dirac-fermion approach, we calculate the energy spectrum of an infinitely long nanoribbon of finite width $w$, terminated by Dirichlet boundary conditions in the transverse direction. We show that a structured external potential that acts within the edge regions of the ribbon, can induce a spectral gap and thus switches the nanoribbon from metallic to insulating behavior. The basic mechanism of this effect is the selective influence of the external potentials on the spinorial wavefunctions that are topological in nature and localized along the boundary of the graphene nanoribbon. Within this single particle description, the maximal obtainable energy gap is $E_{\rm max}\propto π\hbar v_{\rm F}/w$, i.e., $\approx 0.12$\,eV for $w=$15\,nm. The stability of the spectral gap against edge disorder and the effect of disorder on the two-terminal conductance is studied numerically within a tight-binding lattice model. We find that the energy gap persists as long as the applied external effective potential is larger than $\simeq 0.55\times W$, where $W$ is a measure of the disorder strength. We argue that there is a transport gap due to localization effects even in the absence of a spectral gap.

cond-mat.mes-hall↗

arXiv2007

Heisenberg antiferromagnet with anisotropic exchange on the Kagome lattice: Description of the magnetic properties of volborthite

We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbour exchange couplings on the kagome net, i.e. with coupling J in one lattice direction and couplings J' along the other two directions. For J/J' > 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground states: a ferrimagnetic state for J/J' < 1/2 and a large manifold of canted spin states for J/J' > 1/2. To include quantum effects self-consistently, we investigate the Sp(N) symmetric generalisation of the original SU(2) symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp(N) symmetric model depends on a parameter kappa that measures the importance of quantum effects. Our numerical calculations reveal that in the kappa-J/J' plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short- and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp(N) phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerised version of the original spin-1/2 model leads us to suggest that in the limit of strong anisotropy, J/J' >> 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition.

cond-mat.str-el↗

arXiv2006

Spatially anisotropic Heisenberg Kagome antiferromagnet

In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite has recently been the subject of experimental studies [Hiroi et al.,2001]. It has been suggested that the magnetic properties of this material are described by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic exchange couplings. We report on investigations of the Sp(N) symmetric generalisation of this model in the large N limit. We obtain a detailed description of the dependence of possible ground states on the anisotropy and on the spin length S. A fairly rich phase diagram with a ferrimagnetic phase, incommensurate phases with and without long range order and a decoupled chain phase emerges.

cond-mat.str-el↗

arXiv2005

Fractional minima in the conductivity of the quantum-Hall-system under microwaves

We analyse theoretically the conductivity of a quantum Hall system exposed to microwave radiation. We find that whenever microwave frequency and cyclotron frequency are commensurate, there is a {\em resonance} in the longitudinal conductivity. This resonance has the form of the derivative of a Lorentz function; precisely at the center of the resonance, the microwave induced conductivity vanishes. Between the resonances there are maxima and minima, the depths and precise positions of which depend on the microwave amplitude and the scattering rate of the impurities. We demonstrate the existence of these resonances by a microscopic, analytical calculation of the conductivity in lowest order in the microwave intensity and show here that the conductivity is independent of the microwave polarization, linear or circular. We then discuss the general case and predict minima in the longitudinal conductivity corresponding to fractional values of the microwave frequency divided by the cyclotron frequency.

cond-mat.mes-hall↗

arXiv2002

Single-hole dynamics in the t-J model

The quasi-particle weight of a single hole in an antiferromagnetic background is studied in the semiclassical approximation. We start from the t-J model, generalize it to arbitrary spin S by employing an appropriate coherent state representation for the hole, and derive an effective action for the dynamics in the long-wavelength low-energy limit. In the same limit, we find an expression for the single-hole Green's function which we evaluate in an 1/S expansion. Our approach has the advantage of being applicable in one and in two dimensions. We find two qualitatively different results in these two cases: while in one dimension our results are compatible with a vanishing quasi-particle weight, this weight is found to be finite in two dimensions, indicating normal quasi-particle behavior of the hole in this last case.

cond-mat.str-el↗

arXiv2000

Nuclear Spin Relaxation for Higher Spin

We study the relaxation of a spin I that is weakly coupled to a quantum mechanical environment. Starting from the microscopic description, we derive a system of coupled relaxation equations within the adiabatic approximation. These are valid for arbitrary I and also for a general stationary non--equilibrium state of the environment. In the case of equilibrium, the stationary solution of the equations becomes the correct Boltzmannian equilibrium distribution for given spin I. The relaxation towards the stationary solution is characterized by a set of relaxation times, the longest of which can be shorter, by a factor of up to 2I, than the relaxation time in the corresponding Bloch equations calculated in the standard perturbative way.

cond-mat.mes-hall↗

arXiv1998

Spin relaxation in quantum Hall systems

We study the spin relaxation in an interacting two--dimensional electron gas in a strong magnetic field for the case that the electron density is close to filling just one Landau sub--level of one spin projection, i.e., for filling factor near one. Assuming the relaxation to be caused by scattering with phonons, we derive the kinetic equations for the electron's spin--density which replace the Bloch equations in our case. These equations are non--linear and their solution depends crucially on the filling factor and on the temperature of the phonon bath. In the limit of zero temperature and for filling factor 1, the solution relaxes asymptotically with a power law inversely proportional to time, instead of following the conventional exponential behavior.

cond-mat.mes-hall↗

arXiv1998

Path Integral for Composite Fermions in the Half-Filled Lowest Landau Level

We consider electrons in two dimensions in a strong magnetic field at half filling of the lowest Landau level using the Chern-Simons approach. Starting from a lattice Hamiltonian for the electrons, we derive a path integral (PI) formulation for the composite fermions (CF) which respects the order of the operators. We use a time lattice with intermediate times in order to have a PI expressed in density fluctuations. This formulation reveals that there is no infrared (IR) singularity in the grand-canonical potential in lowest order perturbation theory.

cond-mat.mes-hall↗

arXiv1998

Effective Hamiltonians for holes in antiferromagnets: a new approach to implement forbidden double occupancy

A coherent state representation for the electrons of ordered antiferromagnets is used to derive effective Hamiltonians for the dynamics of holes in such systems. By an appropriate choice of these states, the constraint of forbidden double occupancy can be implemented rigorously. Using these coherent states, one arrives at a path integral representation of the partition function of the systems, from which the effective Hamiltonians can be read off. We apply this method to the t-J model on the square lattice and on the triangular lattice. In the former case, we reproduce the well-known fermion-boson Hamiltonian for a hole in a collinear antiferromagnet. We demonstrate that our method also works for non-collinear antiferromagnets by calculating the spectrum of a hole in the triangular antiferromagnet in the self-consistent Born approximation and by comparing it with numerically exact results.

cond-mat.str-el↗

arXiv1998

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the 1/k^2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level.

cond-mat.mes-hall↗

arXiv1996

Hopf term and the effective Lagrangian for the Skyrmions in a two-dimensional electron gas at small g-factor

We study interacting electrons in two dimensions moving in the lowest Landau level under the condition that the Zeeman energy is much smaller than the Coulomb energy and the filling factor is one. In this case, Skyrmion quasiparticles play an important role. Here, we present a simple and transparent derivation of the corresponding effective Lagrangian. In its kinetic part, we find a non-zero Hopf term the prefactor of which we determine rigorously. In the Hamiltonian part, we calculate, by means of a gradient expansion, the Skyrmion-Skyrmion interaction completely up to fourth order in spatial derivatives.

cond-mat.mes-hall↗

arXiv1995

Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations

We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length $ξ$, the susceptibility at the ordering wavevector $χ(\bf Q)$, and the spin stiffness $ρ$ clearly reflects the existence of two temperature regimes -- a high temperature regime $T > T_{th}$, in which the disordering effect of vortices is dominant, and a low temperature regime $T < T_{th}$, where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For $T > T_{th}$, a satisfactory fit of the data is achieved, if the temperature dependence of $ξ$ and $χ(\bf Q)$ is assumed to be of the form predicted by the Kosterlitz--Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around $T_{th} \simeq 0.28$.

cond-mat↗

arXiv1994

Electrons in a Strong Magnetic Field on a Disk

The problem of interacting electrons moving under the influence of a strong magnetic field in two dimensions on a finite disk is reconsidered. First, the results of exact diagonalizations for up to $N=9$ electrons for Coulomb as well as for a short--range interaction are used in the search for a peculiar ground state corresponding to filling factor $1/3$. Not for the Coulomb, but only for the short--range interaction, can the $1/3$--state be safely identified amongst the spectra of various filling factors close to $1/3$. Second, the propositions of the concept of quasiparticles, as used in the hierarchical theory, are examined in view of the exact results for the disk geometry. Whereas the theory for the quasiholes is in complete accordance with the spectra, for the quasielectrons, finite size corrections make an analysis difficult. For the quasielectron energy, an extrapolation to $N \rightarrow \infty$ is given and compared with the corresponding extrapolations of three different proposals for trial wave functions. While the limiting value for the best trial wave function is very close to the limit of the exact results, the behavior of the finite size corrections of the exact energies and of the trial wave functions, respectively, is qualitatively rather different.

cond-mat↗

arXiv1994

The Heisenberg antiferromagnet on a triangular lattice: topological excitations

We study the topological defects in the classical Heisenberg antiferromagnet in two dimensions on a triangular lattice (HAFT). While the topological analysis of the order parameter space indicates that the defects are of $Z_2$ type, consideration of the energy leads us to a description of the low--energy stationary points of the action in terms of $\pm$ vortices, as in the planar XY model. Starting with the continuum description of the HAFT, we show analytically that its partition function can be reduced to that of a 2--dimensional Coulomb gas with logarithmic interaction. Thus, at low temperatures, the correlation length is determined by the spinwaves, while at higher temperatures we expect a crossover to a Kosterlitz--Thouless type behaviour. The results of recent Monte Carlo calculations of the correlation length are consistent with such a crossover.

cond-mat↗

arXiv1993

A comparison of FQHE quasi-electron trial wave functions on the disk

The various proposals for FQHE quasi-electron trial wave functions are reconsidered. In a short-range model for the electronic interaction, the energy expectation values of four different trial wave functions are calculated at filling factor $\frac{1}{3}$ for up to ten electrons in the disk geometry. Jain's trial wave function displays the lowest energy expectation value.

cond-mat↗