arXiv subjects

József Cserti

Publications and source records attributed to József Cserti.

31 records · Page 2Linked to original sources

arXiv2011

Effect of the band structure topology on the minimal conductivity for bilayer graphene with symmetry breaking

Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a two by two Hamiltonian. As an application we derive an analytical expression for the minimal conductivity tensor of bilayer graphene as a function of a complex parameter $w$ related to recently proposed symmetry breaking mechanisms resulting from electron-electron interaction or strain applied to the sample. The number of Dirac points changes with varying parameter w, this directly affect the minimal conductivity. Our analytic expression is confirmed using an independent calculation based on Landauer approach and we find remarkably good agreement between the two methods. We demonstrate that the minimal conductivity is very sensitive to the change of the parameter $w$ and the orientation of the electrodes with respect to the sample. Our results show that the minimal conductivity is closely related to the topology of the low energy band structure.

cond-mat.mes-hall↗

arXiv2010

Relation between Zitterbewegung and the charge conductivity, Berry curvature and the Chern number of multi band systems

We show that the charge conductivity for impurity free multi band electronic systems can be expressed in terms of the diagonal and non-diagonal elements of the Zitterbewegung amplitudes while the Berry curvature and the Chern number is related only to the diagonal elements. Thus, the phenomenon of the Zitterbewegung can no longer be viewed just as an interesting consequence of quantum physics but it has also an experimental relevance. Moreover, through several examples we demonstrate how efficient our approach is in the analytical calculation of the charge conductivity.

cond-mat.mes-hall↗

arXiv2010

Catastrophe optics of caustics in single and bilayer graphene: fine structure of caustics

We theoretically study the scattering of a plane wave of a ballistic electron on a circular n-p junction in single and bilayer graphene. We compare the exact wave function inside the junction to that obtained from a semiclassical formula developed in catastrophe optics. In the semiclassical picture short-wavelength electrons are treated as rays of particles that can get reflected and refracted at the n-p junction according to Snell's law with negative refraction index. We show that for short wavelength and close to caustics this semiclassical approximation gives good agreement with the exact results in the case of single-layer graphene. We also verify the universal scaling laws that govern the shrinking rate and intensity divergence of caustics in the semiclassical limit. It is straightforward to generalize our semiclassical method to more complex geometries, offering a way to efficiently design and model graphene-based electron-optical systems.

cond-mat.mes-hall↗

arXiv2008

Unified description of the Zitterbewegung for spintronic, graphene and superconducting systems

We present a unified treatment of Zitterbewegung phenomena for a wide class of systems including spintronic, graphene, and superconducting systems. We derive an explicit expression for the time-dependence of the position operator of the quasiparticles which can be decomposed into a mean part and an oscillatory term. The latter corresponds to the Zitterbewegung. To apply our result for different systems one needs to use only vector algebra instead of the more complicated operator algebra.

cond-mat.mes-hall↗

arXiv2006

Weak localization correction to the density of transmission eigenvalues in the presence of magnetic field and spin-orbit coupling for a chaotic quantum dot

We calculated the weak localization correction to the density of the transmission eigenvalues in the case of chaotic quantum dots in the framework of Random Matrix Theory including the parametric dependence on the magnetic field and spin-orbit coupling. The result is interpreted in terms of spin singlet and triplet Cooperon modes of conventional diagrammatic perturbation theory. As simple applications, we obtained the weak localization correction to the conductance, the shot noise power and the third cumulant of the distribution of the transmitted charge.

cond-mat.mes-hall↗

arXiv2006

Notes on the minimal longitudinal dc conductivity of perfect bilayer graphene

We calculated the minimal longitudinal conductivity in prefect single and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig et al. in Phys. Rev. B {\bf 50}, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain $σ^{\text min}_{xx}= (J π/2) e^2/h$ while from the other formula used in the above mentioned work we find $\barσ^{\text min}_{xx}= (4J/π) e^2/h$, where J=1 for single layer and J=2 for bilayer graphene. The two universal values are different although they are numerically close to each other. Our two results are in the same order of magnitude as that of experiments and for single layer case one of our result agrees many earlier theoretical predictions. However, for bilayer graphene only two studies are known with predictions for the minimal conductivity different from our calculated values. Similarly to the single layer case, the physical origin of the minimal conductivity in bilayer graphene is also rooted back to the intrinsic disorder induced by the Zitterbewegung which is related to the trembling motion of the electron.

cond-mat.mes-hall↗

arXiv2006

Two-dimensional electron scattering in regions of nonuniform spin-orbit coupling

We present a theoretical study of elastic spin-dependent electron scattering caused by a nonuniform Rashba spin-orbit coupling strength. Using the spin-generalized method of partial waves the scattering amplitude is exactly derived for the case of a circular shape of scattering region. We found that the polarization of the scattered waves are strongly anisotropic functions of the scattering angle. This feature can be utilized to design a good all-electric spin-polarizer. General properties of the scattering process are also investigated in the high and low energy limits.

cond-mat.mes-hall↗

arXiv2006

Rashba billiards

We study the energy levels of non-interacting electrons confined to move in two-dimensional billiard regions and having a spin-dependent dynamics due to a finite Rashba spin splitting. The Green's function for such Rashba billiards is constructed analytically and used to find the area and perimeter contributions to the density of states, as well as the smooth counting function. We show that, in contrast to systems with spin-rotational invariance, Rashba billiards always possess a negative energy spectrum. A semi-classical analysis is presented to interpret the singular behavior of the density of states at certain negative energies. Our detailed analysis of the spin structure of Rashba billiards reveals a finite out-of-plane spin projection for electron eigenstates.

cond-mat.mes-hall↗

arXiv2005

Non-universal behavior of the parity effect in monovalent atomic wires

We propose a mixed analytical-ab-initio method for the accurate calculation of the conductance in monovalent atomic wires. The method relies on the most general formula for ballistic transport through a monovalent wire, whose parameters can be determined from first-principles calculations. Our central result is the demonstration of the highly non-universal behavior of the conductance, which depends on the fine details of the contacts to the leads. We are therefore able to reconcile a large number of the apparently contradictory results that have recently appeared in the literature.

cond-mat.mes-hall↗

arXiv2004

Electronic and spin properties of Rashba billiards

Ballistic electrons confined to a billiard and subject to spin--orbit coupling of the Rashba type are investigated, using both approximate semiclassical and exact quantum--mechanical methods. We focus on the low--energy part of the spectrum that has negative eigenvalues. When the spin precession length is smaller than the radius of the billiard, the low--lying energy eigenvalues turn out to be well described semiclassically. Corresponding eigenspinors are found to have a finite spin polarization in the direction perpendicular to the billiard plane.

cond-mat.mes-hall↗

arXiv2003

A simple model for the vibrational modes in honeycomb lattices

The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbors are represented by springs connecting them. A short and necessary introduction of the lattice structure is presented. The dynamical matrix of the vibrational modes is then derived, and its eigenvalue problem is solved analytically. The solution may provide deeper insight into the nature of the vibrational modes. Numerical results for the vibrational frequencies are presented. To show that how effective our method used for the case of honeycomb lattice is, we also apply it to triangular and square lattice structures. A few suggested problems are listed in the concluding section.

cond-mat.mes-hall↗

arXiv2002

Tunable Lyapunov exponent in inverse magnetic billiards

The stability properties of the classical trajectories of charged particles are investigated in a two dimensional stadium-shaped inverse magnetic domain, where the magnetic field is zero inside the stadium domain and constant outside. In the case of infinite magnetic field the dynamics of the system is the same as in the Bunimovich billiard, i.e., ergodic and mixing. However, for weaker magnetic fields the phase space becomes mixed and the chaotic part gradually shrinks. The numerical measurements of the Lyapunov exponent (performed with a novel method) and the integrable/chaotic phase space volume ratio show that both quantities can be smoothly tuned by varying the external magnetic field. A possible experimental realization of the arrangement is also discussed.

cond-mat.mes-hall↗

arXiv2001

Perturbation of infinite networks of resistors

The resistance between arbitrary nodes of infinite networks of resistors is studied when the network is perturbed by removing one bond from the perfect lattice. A connection is made between the resistance and the lattice Green's function of the perturbed network. Solving Dyson's equation the Green's function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Numerical results are presented for a square lattice. Our method of the lattice Green's function in studying resistor networks can also be applied in the field of random walks as well as electrical and mechanical breakdown phenomena in insulators, thin films and modern ceramics.

cond-mat.dis-nn↗