arXiv subjects

J. Tworzydlo

Publications and source records attributed to J. Tworzydlo.

At least 37 records · Page 2Linked to original sources

arXiv2008

Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model

The Chalker-Coddington network model (introduced originally as a model for percolation in the quantum Hall effect) is known to map onto the two-dimensional Dirac equation. Here we show how the network model can be used to solve a scattering problem in a weakly doped graphene sheet connected to heavily doped electron reservoirs. We develop a numerical procedure to calculate the scattering matrix with the aide of the network model. For numerical purposes, the advantage of the network model over the honeycomb lattice is that it eliminates intervalley scattering from the outset. We avoid the need to include the heavily doped regions in the network model (which would be computationally expensive), by means of an analytical relation between the transfer matrix through the weakly doped region and the scattering matrix between the electron reservoirs. We test the network algorithm by calculating the conductance of an electrostatically defined quantum point contact and comparing with the tight-binding model of graphene. We further calculate the conductance of a graphene sheet in the presence of disorder in the regime where intervalley scattering is suppressed. We find an increase in conductance that is consistent with previous studies. Unlike the tight-binding model, the network model does not require smooth potentials in order to avoid intervalley scattering.

cond-mat.mes-hall↗

arXiv2008

Electronic shot noise in fractal conductors

By solving a master equation in the Sierpinski lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P ~ L^(d_f-2-alpha), with an exponent depending on the fractal dimension d_f and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I, which implies that the Fano factor F=P/2eI is scale independent. We obtain a value F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.

cond-mat.mes-hall↗

arXiv2007

Correspondence between Andreev reflection and Klein tunneling in bipolar graphene

Andreev reflection at a superconductor and Klein tunneling through an n-p junction in graphene are two processes that couple electrons to holes -- the former through the superconducting pair potential Delta and the latter through the electrostatic potential U. We derive that the energy spectra in the two systems are identical, at low energies E<<Delta and for an antisymmetric potential profile U(-x,y)=-U(x,y). This correspondence implies that bipolar junctions in graphene may have zero density of states at the Fermi level and carry a current in equilibrium, analogously to superconducting Josephson junctions. It also implies that nonelectronic systems with the same band structure as graphene, such as honeycomb-lattice photonic crystals, can exhibit pseudo-superconducting behavior.

cond-mat.mes-hall↗

arXiv2007

Anomalously large conductance fluctuations in weakly disordered graphene

We have studied numerically the mesoscopic fluctuations of the conductance of a graphene strip (width W large compared to length L), in an ensemble of samples with different realizations of the random electrostatic potential landscape. For strong disorder (potential fluctuations comparable to the hopping energy), the variance of the conductance approaches the value predicted by the Altshuler-Lee-Stone theory of universal conductance fluctuations. For weaker disorder the variance is greatly enhanced if the potential is smooth on the scale of the atomic separation. There is no enhancement if the potential varies on the atomic scale, indicating that the absence of backscattering on the honeycomb lattice is at the origin of the anomalously large fluctuations.

cond-mat.mes-hall↗

arXiv2007

Valley-isospin dependence of the quantum Hall effect in a graphene p-n junction

We calculate the conductance G of a bipolar junction in a graphene nanoribbon, in the high-magnetic field regime where the Hall conductance in the p-doped and n-doped regions is 2e^2/h. In the absence of intervalley scattering, the result G=(e^2/h)(1-cos Phi) depends only on the angle Phi between the valley isospins (= Bloch vectors representing the spinor of the valley polarization) at the two opposite edges. This plateau in the conductance versus Fermi energy is insensitive to electrostatic disorder, while it is destabilized by the dispersionless edge state which may exist at a zigzag boundary. A strain-induced vector potential shifts the conductance plateau up or down by rotating the valley isospin.

cond-mat.mes-hall↗

arXiv2006

Valley filter and valley valve in graphene

It is known that the lowest propagating mode in a narrow ballistic ribbon of graphene may lack the twofold valley degeneracy of higher modes. Depending on the crystallographic orientation of the ribbon axis, the lowest mode mixes both valleys or lies predominantly in a single valley (chosen by the direction of propagation). We show, using a tight-binding model calculation, that a nonequilibrium valley polarization can be realized in a sheet of graphene, upon injection of current through a ballistic point contact with zigzag edges. The polarity can be inverted by local application of a gate voltage to the point contact region. Two valley filters in series may function as an electrostatically controlled ``valley valve'', representing a zero-magnetic-field counterpart to the familiar spin valve.

cond-mat.mes-hall↗

arXiv2006

Quantum-limited shot noise in graphene

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects), to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e^2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, three times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.

cond-mat.mes-hall↗

arXiv2006

How spin-orbit interaction can cause electronic shot noise

The shot noise in the electrical current through a ballistic chaotic quantum dot with N-channel point contacts is suppressed for N --> infinity, because of the transition from stochastic scattering of quantum wave packets to deterministic dynamics of classical trajectories. The dynamics of the electron spin remains quantum mechanical in this transition, and can affect the electrical current via spin-orbit interaction. We explain how the role of the channel number N in determining the shot noise is taken over by the ratio l_{so}/lambda_F of spin precession length l_{so} and Fermi wave length lambda_F, and present computer simulations in a two-dimensional billiard geometry (Lyapunov exponent alpha, mean dwell time tau_{dwell}, point contact width W) to demonstrate the scaling (lambda_F/l_{so})^{1/alpha tau_{dwell}} of the shot noise in the regime lambda_F << l_{so} << W.

cond-mat.mes-hall↗

arXiv2005

Stroboscopic model of transport through a quantum dot with spin-orbit scattering

We present an open version of the symplectic kicked rotator as a stroboscopic model of electrical conduction through an open ballistic quantum dot with spin-orbit scattering. We demonstrate numerically and analytically that the model reproduces the universal weak localization and weak anti-localization peak in the magnetoconductance, as predicted by random-matrix theory (RMT). We also study the transition from weak localization to weak anti-localization with increasing strength of the spin-orbit scattering, and find agreement with RMT.

cond-mat.mes-hall↗

arXiv2004

Exponential sensitivity to dephasing of electrical conduction through a quantum dot

According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish $\propto(τ_ϕ/τ_{D})^{p}$ when the dephasing time $τ_ϕ$ becomes small compared to the mean dwell time $τ_{D}$. Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression $\propto\exp(-τ_{E}/τ_ϕ)$ when $τ_ϕ$ drops below the Ehrenfest time $τ_{E}$. We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression $\propto\exp(-τ_{E}/τ_{D})$ in the absence of dephasing -- which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations.

cond-mat.mes-hall↗

arXiv2004

Coherent backscattering from a quantum dot is insensitive to the Ehrenfest time

This paper was withdrawn by the authors. The purpose of this paper was to provide conclusive evidence for the Ehrenfest-time-independence of weak localization, by means of a computer simulation of the coherent backscattering peak on very large systems. (Two orders of magnitude larger than we could reach in cond-mat/0405122 by studying weak localization directly.) We have decided to withdraw this paper, after Piet Brouwer convinced us that the one-to-one correspondence between weak localization and coherent backscattering can not be relied upon. For example, a reflection matrix with one half of its eigenvalues equal to 0 and the other half equal to 1 (hence without weak localization) would still show a coherent backscattering peak in a basis that is randomly related to its eigenbasis.

cond-mat.mes-hall↗

arXiv2004

Weak localization of the open kicked rotator

We present a numerical calculation of the weak localization peak in the magnetoconductance for a stroboscopic model of a chaotic quantum dot. The magnitude of the peak is close to the universal prediction of random-matrix theory. The width depends on the classical dynamics, but this dependence can be accounted for by a single parameter: the level curvature around zero magnetic field of the closed system.

cond-mat.mes-hall↗

arXiv2004

Quantum-to-classical crossover of mesoscopic conductance fluctuations

We calculate the system-size-over-wave-length ($M$) dependence of sample-to-sample conductance fluctuations, using the open kicked rotator to model chaotic scattering in a ballistic quantum dot coupled by two $N$-mode point contacts to electron reservoirs. Both a fully quantum mechanical and a semiclassical calculation are presented, and found to be in good agreement. The mean squared conductance fluctuations reach the universal quantum limit of random-matrix-theory for small systems. For large systems they increase $\propto M^2$ at fixed mean dwell time $τ_D \propto M/N$. The universal quantum fluctuations dominate over the nonuniversal classical fluctuations if $N < \sqrt{M}$. When expressed as a ratio of time scales, the quantum-to-classical crossover is governed by the ratio of Ehrenfest time and ergodic time.

cond-mat.mes-hall↗

arXiv2003

Dynamical model for the quantum-to-classical crossover of shot noise

We use the open kicked rotator to model the chaotic scattering in a ballistic quantum dot coupled by two point contacts to electron reservoirs. By calculating the system-size-over-wave-length dependence of the shot noise power we study the crossover from wave to particle dynamics. Both a fully quantum mechanical and a semiclassical calculation are presented. We find numerically in both approaches that the noise power is reduced exponentially with the ratio of Ehrenfest time and dwell time, in agreement with analytical predictions.

cond-mat.mes-hall↗

arXiv2003

Scattering theory of plasmon-assisted entanglement transfer and distillation

We analyse the quantum mechanical limits to the plasmon-assisted entanglement transfer observed by E. Altewischer, M.P. van Exter, and J.P. Woerdman [Nature, 418, 304 (2002)]. The maximal violation S of Bell's inequality at the photodetectors behind two linear media (such as the perforated metal films in the experiment) can be described by two ratio's tau_1, tau_2 of polarization-dependent transmission probabilities. A fully entangled incident state is transferred without degradation for tau_1=tau_2, but a relatively large mismatch of tau_1 and tau_2 can be tolerated with a small reduction of S. We predict that fully entangled Bell pairs can be distilled out of partially entangled radiation if tau_1 and tau_2 satisfy a pair of inequalities.

quant-ph↗

arXiv2002

Quantum-optical communication rates through an amplifying random medium

We study the competing effects of stimulated and spontaneous emission on the information capacity of an amplifying disordered waveguide. At the laser threshold the capacity reaches a "universal" limit, independent of the degree of disorder. Whether or not this limit is larger or smaller than the capacity without amplification depends on the disorder, as well as on the input power. Explicit expressions are obtained for heterodyne detection of coherent states, and generalized for arbitrary detection scheme.

quant-ph↗

arXiv2001

The geometric order of stripes and Luttinger liquids

It is argued that the electron stripes as found in correlated oxides have to do with an unrecognized form of order. The manifestation of this order is the robust property that the charge stripes are at the same time anti-phase boundaries in the spin system. We demonstrate that the quantity which is ordering is sublattice parity, referring to the geometric property of a bipartite lattice that it can be subdivided in two sublattices in two different ways. Re-interpreting standard results of one dimensional physics, we demonstrate that the same order is responsible for the phenomenon of spin-charge separation in strongly interacting one dimensional electron systems. In fact, the stripe phases can be seen from this perspective as the precise generalization of the Luttinger liquid to higher dimensions. Most of this paper is devoted to a detailed exposition of the mean-field theory of sublattice parity order in 2+1 dimensions. Although the quantum-dynamics of the spin- and charge degrees of freedom is fully taken into account, a perfect sublattice parity order is imposed. Due to novel order-out-of-disorder physics, the sublattice parity order gives rise to full stripe order at long wavelength. This adds further credibility to the notion that stripes find their origin in the microscopic quantum fluctuations and it suggests a novel viewpoint on the relationship between stripes and high Tc superconductivity.

cond-mat.str-el↗

arXiv1999

Hierarchical model for the scale-dependent velocity of seismic waves

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.

cond-mat.dis-nn↗