Evidence for charging effects in an open dot at zero magnetic field

We have measured the low-temperature transport properties of an open quantum dot formed in a clean one-dimensional channel. At zero magnetic field, continuous and periodic oscillations superimposed upon ballistic conductance steps are observed when the conductance through the dot G exceeds 2e²/h. We ascribe the observed conductance oscillations to evidence for charging effects in an open dot. This is supported by the evolution of the oscillating features for G>2e²/h as a function of both temperature and barrier transparency.     

Magnetopumping current in graphene Corbino pump

We study conductance and adiabatic pumped charge and spin currents in a graphene quantum pump with Corbino geometry in the presence of an applied perpendicular magnetic field. Pump is driven by the periodic and out of phase modulations of the magnetic field and an electrostatic potential applied to the ring area of the pump. We show that Zeeman splitting, despite its smallness, suppresses conductance and pumped current oscillations at zero doping. Moreover, quite considerable spin conductance and pumped spin current are generated at low dopings due to Zeeman splitting. We find that pumped charge and spin currents increase by increasing the magnetic field, with small oscillations, until they are suppressed due to the effect of nonzero doping and Zeeman splitting.     

Transport evidence of 3D topological nodal-line semimetal phase in ZrSiS

Topological nodal-line semimetal is a new emerging material, which is viewed as a three-dimensional (3D) analog of graphene with the conduction and valence bands crossing at Dirac nodes, resulting in a range of exotic transport properties. Herein, we report on the direct quantum transport evidence of the 3D topological nodal-line semimetal phase of ZrSiS with angular-dependent magnetoresistance (MR) and the combined de Hass-van Alphen (dHvA) and Shubnikov-de Hass (SdH) oscillations. Through fitting by a two-band model, the MR results demonstrate high topological nodal-line fermion densities of approximately 6×10²¹ cm⁻³ and a perfect electron/hole compensation ratio of 0.94, which is consistent with the semi-classical expression fitting of Hall conductance Gxy and the theoretical calculation. Both the SdH and dHvA oscillations provide clear evidence of 3D topological nodal-line semimetal characteristic.     

Selecting wave function states in open quantum dots

We study how wave function scarring in an open quantum dot is influenced as the strength of its environmental coupling is varied and show evidence for groups of wave function scars that recur periodically with gate voltage. The precise form of these scars is found to evolve with gate voltage, which we discuss in terms of the properties of the semi-classical orbits that give rise to the scars. We also provide convincing experimental evidence for a correlation between the scars and the oscillations observed in the conductance when the gate voltage is varied.     

Tunable quantum dot resonator embedded in a quantum wire

Combined quantum wire and quantum dot system is theoretically predicted to show unique conductance properties associated with Coulomb interactions. We use a split gate technique to fabricate a quantum wire containing a quantum dot with two tunable potential barriers in a two-dimensional electron gas. We observe the effects of the quantum dot cavity on the electron transport through the quantum wire, such as Coulomb oscillations near the pinch-off voltage and periodic conductance oscillations on the first conductance plateau.     

Eigenvalues and eigenfunctions of a clover plate

We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories. The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows that it has both integrable and chaotic regions. Examples of the stable and the unstable periodic orbits in the geometry are presented. We numerically solve the biharmonic equation for the flexural vibrations of the Clover shaped plate with clamped boundary conditions. The first few hundred eigenvalues and the eigenfunctions are obtained using a boundary elements method. The Fourier transform of the eigenvalues show strong peaks which correspond to ray periodic orbits. However, the peaks corresponding to the shortest stable periodic orbits are not stronger than the peaks associated with unstable periodic orbits. We also perform statistics on the obtained eigenvalues and the eigenfunctions. The eigenvalue spacing distribution P(s) shows a strong peak and therefore deviates from both the Poisson and the Wigner distribution of random matrix theory at small spacings because of the C_4v symmetry of the Clover geometry. The density distribution of the eigenfunctions is observed to agree with the Porter-Thomas distribution of random matrix theory. Received 12 February 2001 and Received in final form 17 April 2001     

Semiclassical Asymptotics for Weakly Nonlinear Bloch Waves

We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB–analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.     

Conductance oscillations of a spin-orbit stripe with polarized contacts

We investigate the linear conductance of a stripe of spin-orbit interaction in a 2D electron gas; that is, a 2D region of length l\ell along the transport direction and infinite in the transverse one in which a spin-orbit interaction of Rashba type is present. Polarization in the contacts is described by means of Zeeman fields. Our model predicts two types of conductance oscillations: Ramsauer oscillations in the minority spin transmission, when both spins can propagate, and Fano oscillations when only one spin propagates. The latter are due to the spin-orbit coupling with quasibound states of the non propagating spin. In the case of polarized contacts in antiparallel configuration Fano-like oscillations of the conductance are still made possible by the spin orbit coupling, even though no spin component is bound by the contacts. To describe these behaviors we propose a simplified model based on an ansatz wave function. In general, we find that the contribution for vanishing transverse momentum dominates and defines the conductance oscillations. Regarding the oscillations with Rashba coupling intensity, our model confirms the spin transistor behavior, but only for high degrees of polarization. Including a position dependent effective mass yields additional oscillations due to the mass jumps at the interfaces.     

Semiclassical theory of transport in antidot lattices

Motivated by a recent experiment by Weiss et al. [Phys. Rev. Lett. 70, 4118 (1993)], we present a detailed study of quantum transport in large antidot arrays whose classical dynamics is chaotic. We calculate the longitudinal and Hall conductivities semiclassically starting from the Kubo formula. The leading contribution reproduces the classical conductivity. In addition, we find oscillatory quantum corrections to the classical conductivity which are given in terms of the periodic orbits of the system. These periodic-orbit contributions provide a consistent explanation of the quantum oscillations in the magnetoconductivity observed by Weiss et al. We find that the phase of the oscillations with Fermi energy and magnetic field is given by the classical action of the periodic orbit. The amplitude is determined by the stability and the velocity correlations of the orbit. The amplitude also decreases exponentially with temperature on the scale of the inverse orbit traversal time/T . The Zeeman splitting leads to beating of the amplitude with magnetic field. We also present an analogous semiclassical derivation of Shubnikov-de Haas oscillations where the corresponding classical motion is integrable. We show that the quantum oscillations in antidot lattices and the Shubnikov-de Haas oscillations are closely related. Observation of both effects requires that the elastic and inelastic scattering lengths be larger than the lengths of the relevant periodic orbits. The amplitude of the quantum oscillations in antidot lattices is of a higher power in Planck's constant and hence smaller than that of Shubnikov-de Haas oscillations. In this sense, the quantum oscillations in the conductivity are a sensitive probe of chaos.This paper is dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

Effect of boundary conditions on quantum-anti-dots in the presence of a magnetic field

Many people have studied the conductance properties through an array of anti-dots, especially since the observation of Weiss oscillations. In most cases, however, in which the recursive Greenźs functions are used on a spatial lattice, periodic boundary conditions are employed. In this paper, we analyse the effects of boundary conditions and magnetic field on the conductance behavior in a number of anti-dot-shaped, GaAs/AlGaAs 2DEG quantum systems. The effect of periodic boundary conditions causes a reduction in the overall conductance. The effect of changing the boundary conditions is more profound for lower numbers of anti-dots.     

Transition between synchronization and chaos in doped GaAs/AlAs superlattices

The transition between chaotic and periodic regimes in spontaneous current oscillations of weakly coupled, doped GaAs/AlAs superlattices has been observed by varying the external d.c. bias. The chaotic current oscillations are observed for voltage ranges, which exhibit a large negative differential conductance in the time-averaged I–V characteristic. Since this system can be described by a spatially distributed, non-linear system with many degrees of freedom, the coupling between the degrees of freedom in the chaotic windows is repulsive, while in the periodic windows it is attractive.     

Trapping of quantum particles for a class of time-periodic potentials. A semi-classical approach

We study the time evolution for Schrödinger operators with time-periodic potentials when the classical equations of motion possess periodic orbits. We exhibit a class of time-periodic potentials such that for initial states suitably localized around these periodic orbits, then at the dominant order of the semi-classical approximation, the system is trapped forever at sufficiently large frequency. An estimation of the correction to the semi-classical approximation is given, which yields a minimum “trapping time” for these systems.     

Neutrino oscillations with three flavors in matter of varying density

In this paper, we discuss the evolution operator and the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter for three flavor neutrino oscillations in matter of varying density in the plane wave approximation. The applications of this to neutrino oscillations in a model of the earth's matter density profile, step function matter density profiles, constant matter density profiles, linear matter density profiles, and finally in a model of the sun's matter density profile are discussed. We show that for matter density profiles which do not fluctuate too much, the total evolution operator consisting of n operators can be replaced by one single evolution operator in the semi-classical approximation. Received: 23 March 2001 / Published online: 8 June 2001     

Dimensional crossover in quantum networks: from macroscopic to mesoscopic physics

We report on magnetoconductance measurements of metallic networks of various sizes ranging from 10 to 10(6) plaquettes, with an anisotropic aspect ratio. Both Altshuler-Aronov-Spivak h/2e periodic oscillations and Aharonov-Bohm h/e periodic oscillations are observed for all networks. For large samples, the amplitude of both oscillations results from the incoherent superposition of contributions of phase coherent regions. When the transverse size becomes smaller than the phase coherent length Lphi, one enters a new regime which is phase coherent (mesoscopic) along one direction and macroscopic along the other, leading to a new size dependence of the quantum oscillations.     

Combined effect of Aharonov-Bohm effect and uniaxial strain on quantum conductance oscillations of carbon nanotube resonators

Using the π orbital tight-binding model and the multi-channel Laudauer-Büttiker formula, the combined effect of Aharonov-Bohm effect (induced by an axial magnetic field) and uniaxial strain on quantum conductance oscillations of the electronic Fabry-Perot resonators composed of armchair and metallic zigzag single-walled carbon nanotubes (SWNTs) has been studied. It is found that, for the case of the armchair SWNT, conductance oscillations near the band gap are dominated by Aharonov-Bohm effect, while the conductance oscillations in other regions are dominated by the uniaxial strains. The combined effect of Aharonov-Bohm effect and uniaxial strains on quantum conductance oscillations is not obvious. But, for the case of the metallic zigzag SWNTs, obvious single-channel transport and one or two conductance oscillations existing in two different gate voltage ranges were found by the combined effect of uniaxial strain and axial magnetic field.     

Homoclinic orbits and mixed-mode oscillations in far-from-equilibrium systems

Nonlinear autonomous dynamical systems with ahomoclinic tangency to a periodic orbit are investigated. We study the bifurcation sequences of the mixed-mode oscillations generated by the homoclinicity, which are shown to belong to two different types, depending on the nature of the Liapunov numbers of the basic periodic orbit. A detailed numerical analysis is carried out to show how the existence of a tangent homoclinic orbit allows us to understand in a quantitative way a particular and regular sequence of cool flame-ignition oscillations observed in a thermokinetic model of hydrocarbon oxidation. Chaotic cool flame oscillations are also observed in the same model. When the control parameter crosses a critical value, this chaotic set of trajectories becomes globally unstable and forms a Cantor-like hyperbolic repellor, and the ignition mechanism generates ahomoclinic tangency to the Cantor set of trajectories. The complex bifurcation diagram may be globally reconstructed from a one-dimensional dynamical system, thanks to the strong contractivity of thermokinetics. It is found that a symbolic dynamics with three symbols is necessary to classify the periodic windows of the complex bifurcation sequence observed numerically in this system.     

Quantum interference of electrons in a ring: tuning of the geometrical phase

We calculate the oscillations of the dc conductance across a mesoscopic ring, simultaneously tuned by applied magnetic and electric fields orthogonal to the ring. The oscillations depend on the Aharonov-Bohm flux and of the spin-orbit coupling. They result from mixing of the dynamical phase, including the Zeeman spin splitting, and of geometric phases. By changing the applied fields, the geometric phase contribution to the conductance oscillations can be tuned from the adiabatic (Berry) to the nonadiabatic (Ahronov-Anandan) regime. To model a realistic device, we also include nonzero backscattering at the connection between ring and contacts, and a random phase for electron wave function, accounting for dephasing effects.     

Landauer conductance of tunnel junctions: strong impact from boundary conditions

We present model calculations for the Landauer conductance of tunnel junctions. The tunnelling of free electrons through a rectangular potential barrier is considered. The conductance of a finite number of barriers was calculated using a transfer matrix method. The periodic arrangement of the same barriers was described by a Kronig–Penney model to calculate the band structure and, from that, the conductance of a point contact in the ballistic limit. Comparison of the results showed the importance of the boundary conditions. Caused by resonant scattering in the superlattice, the conductance is overestimated by an order of 1/t, the transmission coefficient of the single barrier. In the case of metallic multilayers, these interferences are of minor importance. In conclusion, the application of the Landauer formula to periodic lattices to describe the tunnelling conductance of a single barrier is not appropriate.     

Thermal effect in phase-periodic electron transport in disordered mesoscopic normal metal/superconductor structures

We report measurements of the temperature dependence of the amplitude of phase-periodic conductance oscillations in disordered normal metal (Ag) structures, attached to a superconducting (Al) wire at two points. The amplitude of oscillations reaches its maximum at temperatureT ^*, when the Thouless energy is of the order ofk _B T. The results are in agreement with recent calculations by Nazarov and Stoof [Phys. Rev. Lett. 76 (1996) 823].     

Shell structure of a circular quantum dot in weak magnetic fields

The conductance of a circular quantum dot in a two-dimensional electron gas of a GaAlAs/GaAs heterostructure has been measured. Conductance oscillations as functions both of the magnetic field B and of the size of a dot confining about 1000 electrons are related to the formation of electronic shell structure. Modeling the dot by a circular billiard, we interpret the results semiclassically in terms of periodic orbit theory, providing a simple explanation of the B-periodic oscillations. A comparison to a harmonic confinement suitable for smaller quantum dots is given.