arXiv subjects

L. Schweitzer

Publications and source records attributed to L. Schweitzer.

At least 19 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

Disordered two-dimensional electron systems with chiral symmetry

We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior of the density of states and the logarithmic scaling of the smallest Lyapunov exponents in the vicinity of the chiral quantum critical point in the band center at E=0. The observed peaks or depressions in the density of states, the distribution of the critical conductances, and the possible non-universality of the critical exponents for certain chiral unitary models are discussed.

cond-mat.dis-nn↗

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↗

arXiv2012

Scaling at chiral quantum critical points in two dimensions

We study the localization properties of electrons moving on two-dimensional bi-partite lattices in the presence of disorder. The models investigated exhibit a chiral symmetry and belong to the chiral orthogonal (chO), chiral symplectic (chS) or chiral unitary (chU) symmetry class. The disorder is introduced via real random hopping terms for chO and chS, while complex random phases generate the disorder in the chiral unitary model. In the latter case an additional spatially constant, perpendicular magnetic field is also applied. Using a transfer-matrix-method, we numerically calculate the smallest Lyapunov exponents that are related to the localization length of the electronic eigenstates. From a finite-size scaling analysis, the logarithmic divergence of the localization length at the quantum critical point at E=0 is obtained. We always find for the critical exponent κ, which governs the energy dependence of the divergence, a value close to 2/3. This result differs from the exponent κ=1/2 found previously for a chiral unitary model in the absence of a constant magnetic field. We argue that a strong constant magnetic field changes the exponent κwithin the chiral unitary symmetry class by effectively restoring particle-hole symmetry even though a magnetic field induced transition from the ballistic to the diffusive regime cannot be fully excluded.

cond-mat.dis-nn↗

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↗

arXiv2010

On the role of the symmetry parameter $β$ in the strongly localized regime

The generalization of the Dorokhov-Mello-Pereyra-Kumar equation for the description of transport in strongly disordered systems replaces the symmetry parameter $β$ by a new parameter $γ$, which decreases to zero when the disorder strength increases. We show numerically that although the value of $γ$ strongly influences the statistical properties of transport parameters $Δ$ and of the energy level statistics, the form of their distributions always depends on the symmetry parameter $β$ even in the limit of strong disorder. In particular, the probability distribution is $p(Δ)\sim Δ^β$ when $Δ\to 0$ and $p(Δ) \sim \exp (-cΔ^2)$ in the limit $Δ\to\infty$.

cond-mat.dis-nn↗

arXiv2010

Logarithmic scaling of Lyapunov exponents in disordered chiral two-dimensional lattices

We analyze the scaling behavior of the two smallest Lyapunov exponents for electrons propagating on two-dimensional lattices with energies within a very narrow interval around the chiral critical point at E=0 in the presence of a perpendicular random magnetic flux. By a numerical analysis of the energy and size dependence we confirm that the two smallest Lyapunov exponents are functions of a single parameter. The latter is given by ln L/ln xi(E), which is the ratio of the logarithm of the system width L to the logarithm of the correlation length xi(E). Close to the chiral critical point and energy |E| << E_0, we find a logarithmically divergent energy dependence lnxi(E)proporitonal to |\ln(E_0/|E|)|^{1/2}, where E_0 is a characteristic energy scale. Our data are in agreement with the theoretical prediction of M. Fabrizio and C. Castelliani [Nucl.\Phys.B 583, 542 (2000)] and resolve an inconsistency of previous numerical work.

cond-mat.dis-nn↗

arXiv2009

Narrow depression in the density of states at the Dirac point in disordered graphene

The electronic properties of non-interacting particles moving on a two-dimensional bricklayer lattice are investigated numerically. In particular, the influence of disorder in form of a spatially varying random magnetic flux is studied. In addition, a strong perpendicular constant magnetic field $B$ is considered. The density of states $ρ(E)$ goes to zero for $E\to 0$ as in the ordered system, but with a much steeper slope. This happens for both cases: at the Dirac point for B=0 and at the center of the central Landau band for finite $B$. Close to the Dirac point, the dependence of $ρ(E)$ on the system size, on the disorder strength, and on the constant magnetic flux density is analyzed and fitted to an analytical expression proposed previously in connection with the thermal quantum Hall effect. Additional short-range on-site disorder completely replenishes the indentation in the density of states at the Dirac point.

cond-mat.dis-nn↗

arXiv2008

Disorder-driven splitting of the conductance peak at the Dirac point in graphene

The electronic properties of a bricklayer model, which shares the same topology as the hexagonal lattice of graphene, are investigated numerically. We study the influence of random magnetic-field disorder in addition to a strong perpendicular magnetic field. We found a disorder-driven splitting of the longitudinal conductance peak within the narrow lowest Landau band near the Dirac point. The energy splitting follows a relation which is proportional to the square root of the magnetic field and linear in the disorder strength. We calculate the scale invariant peaks of the two-terminal conductance and obtain the critical exponents as well as the multifractal properties of the chiral and quantum Hall states. We found approximate values $ν\approx 2.5$ for the quantum Hall states, but $ν=0.33\pm 0.1$ for the divergence of the correlation length of the chiral state at E=0 in the presence of a strong magnetic field. Within the central $n=0$ Landau band, the multifractal properties of both the chiral and the split quantum Hall states are the same, showing a parabolic $f[α(s)]$ distribution with $α(0)=2.27\pm 0.02$. In the absence of the constant magnetic field, the chiral critical state is determined by $α(0)=2.14\pm 0.02$.

cond-mat.mes-hall↗

arXiv2007

Critical conductance of the chiral 2d random flux model

The two-terminal conductance of a random flux model defined on a square lattice is investigated numerically at the band center using a transfer matrix method. Due to the chiral symmetry, there exists a critical point where the ensemble averaged mean conductance is scale independent. We also study the conductance distribution function which depends on the boundary conditions and on the number of lattice sites being even or odd. We derive a critical exponent $ν=0.42\pm 0.05$ for square samples of even width using one-parameter scaling of the conductance. This result could not be obtained previously from the divergence of the localization length in quasi-one-dimensional systems due to pronounced finite-size effects.

cond-mat.mes-hall↗

arXiv2007

Critical conductance of two-dimensional chiral systems with random magnetic flux

The zero temperature transport properties of two-dimensional lattice systems with static random magnetic flux per plaquette and zero mean are investigated numerically. We study the two-terminal conductance and its dependence on energy, sample size, and magnetic flux strength. The influence of boundary conditions and of the oddness of the number of sites in the transverse direction is also studied. We confirm the existence of a critical chiral state in the middle of the energy band and calculate the critical exponent nu=0.35 +/- 0.03 for the divergence of the localization length. The sample averaged scale independent critical conductance _c turns out to be a function of the amplitude of the flux fluctuations whereas the variance of the respective conductance distributions appears to be universal. All electronic states outside of the band center are found to be localized.

cond-mat.mes-hall↗

arXiv2006

Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

The critical two-terminal conductance $g_c$ and the spatial fluctuations of critical eigenstates are investigated for a disordered two dimensional model of non-interacting electrons subject to spin-orbit scattering (Ando model). For square samples, we verify numerically the relation $σ_c=1/[2π(2-D(1))] e^2/h$ between critical conductivity $σ_c=g_c=(1.42\pm 0.005) e^2/h$ and the fractal information dimension of the electron wave function, $D(1)=1.889\pm 0.001$. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent $ν=2.80\pm 0.04$ that governs the quantum phase transition.

cond-mat.mes-hall↗

arXiv2005

Universal Conductance and Conductivity at Critical Points in Integer Quantum Hall Systems

The sample averaged longitudinal two-terminal conductance and the respective Kubo-conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, $0.60\pm 0.02 e^2/h$ and $0.58\pm 0.03 e^2/h$, respectively. In the 2nd lowest Landau band, a critical conductance $0.61\pm 0.03 e^2/h$ is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value $1/2 e^2/h$. We argue that this difference is due to the multifractal structure of critical wavefunctions, a property that should generically show up in the conductance at quantum critical points.

cond-mat.mes-hall↗

arXiv2004

Levitation of the quantum Hall extended states in the $B\to$ 0 limit

We investigate the fate of the quantum Hall extended states within a continuum model with spatially correlated disorder potentials. The model can be projected onto a couple of the lowest Landau bands. Levitation of the $n=0$ critical states is observed if at least the two lowest Landau bands are considered. The dependence on the magnetic length $l_B=(\hbar/(eB))^{1/2}$ and on the correlation length of the disorder potential $η$ is combined into a single dimensionless parameter $\hatη=η/l_B$. This enables us to study the behavior of the critical states for vanishing magnetic field. In the two Landau band limit, we find a disorder dependent saturation of the critical states' levitation which is in contrast to earlier propositions, but in accord with some experiments.

cond-mat.mes-hall↗

arXiv2004

Comment on `Exact analytical solution for the generalized Lyapunov exponent of the two-dimensional Anderson localization'

In a recent publication, J. Phys.: Condens. Matt. 14 13777 (2002), Kuzovkov et. al. announced an analytical solution of the two-dimensional Anderson localisation problem via the calculation of a generalised Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalised states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy to use a generalised Lyapunov exponent for studying Anderson localisation.

cond-mat.dis-nn↗

arXiv2003

Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder

The fate of the current carrying states of a quantum Hall system is considered in the situation when the disorder strength is increased and the transition from the quantum Hall liquid to the Hall insulator takes place. We investigate a two-dimensional lattice model with spatially correlated disorder potentials and calculate the density of states and the localization length either by using a recursive Green function method or by direct diagonalization in connection with the procedure of level statistics. From the knowledge of the energy and disorder dependence of the localization length and the density of states (DOS) of the corresponding Landau bands, the movement of the current carrying states in the disorder--energy and disorder--filling-factor plane can be traced by tuning the disorder strength. We show results for all sub-bands, particularly the traces of the Chern and anti-Chern states as well as the peak positions of the DOS. For small disorder strength $W$ we recover the well known weak levitation of the critical states, but we also reveal, for larger $W$, the strong levitation of these states across the Landau gaps without merging. We find the behavior to be similar for exponentially, Gaussian, and Lorentzian correlated disorder potentials. Our study resolves the discrepancies of previously published work in demonstrating the conflicting results to be only special cases of a general lattice model with spatially correlated disorder potentials. To test whether the mixing between consecutive Landau bands is the origin of the observed floating, we truncate the Hilbert space of our model Hamiltonian and calculate the behavior of the current carrying states under these restricted conditions.

cond-mat.mes-hall↗

arXiv2002

Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms

We investigate a disordered two-dimensional lattice model for noninteracting electrons with long-range power-law transfer terms and apply the method of level statistics for the calculation of the critical properties. The eigenvalues used are obtained numerically by direct diagonalization. We find a metal-insulator transition for a system with orthogonal symmetry. The exponent governing the divergence of the correlation length at the transition is extracted from a finite size scaling analysis and found to be $ν=2.6\pm 0.15$. The critical eigenstates are also analyzed and the distribution of the generalized multifractal dimensions is extrapolated.

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