Quantum Antidot (AD) structures have remarkable properties in the integer quantum Hall regime, exhibiting Coulomb-blockade charging and the Kondo effect despite their open geometry. In some regimes a simple single-particle (SP) model suffices to describe experimental observations while in others interaction effects are clearly important, although exactly how and why interactions emerge is unclear. We present a combination of experimental data and the results of new calculations concerning SP orbital states which show how the observed suppression of the energy spacing between states can be explained through a full consideration of the AD potential, without requiring any effects due to electron interactions such as the formation of compressible regions composed of multiple states, which may occur at higher magnetic fields. A full understanding of the regimes in which these effects occur is important for the design of devices to coherently manipulate electrons in edge states using AD resonances.
We report experiments on the energy structure of antidot-bound states. By measuring resonant tunneling line widths as function of temperature, we determine the coupling to the remote global gate voltage and find that the effects of interelectron interaction dominate. Within a simple model, we also determine the energy spacing of the antidot bound states, self consistent edge electric field, and edge excitation drift velocity.
We fabricated and measured antidot lattices in single layer graphene with lattice periods down to 90 nm. In large-period lattices, a well-defined quantum Hall effect is observed. Going to smaller antidot spacings the quantum Hall effect gradually disappears, following a geometric size effect. Lattices with narrow constrictions between the antidots behave as networks of nanoribbons, showing a high-resistance state and a transport gap of a few mV around the Dirac point. We observe pronounced weak localization in the magnetoresistance, indicating strong intervalley scattering at the antidot edges…
We derive a general capacitive interaction model for an antidot-based interferometer in the integer quantum Hall regime, and study Aharonov-Bohm resonances in a single antidot with multiple bound modes, as a function of the external magnetic field or the gate voltage applied to the antidot. The pattern of Aharonov-Bohm resonances is significantly different from the case of noninteracting electrons. The origin of the difference includes charging effects of excess charges, charge relaxation between the bound modes, the capacitive interaction between the bound modes and the extended edge channels…
An Andreev billiard was realized in an array of niobium filled antidots in a high-mobility InAs/AlGaSb heterostructure. Below the critical temperature T_C of the Nb dots we observe a strong reduction of the resistance around B=0 and a suppression of the commensurability peaks, which are usually found in antidot lattices. Both effects can be explained in a classical Kubo approach by considering the trajectories of charge carriers in the semiconductor, when Andreev reflection at the semiconductor-superconductor interface is included. For perfect Andreev reflection, we expect a complete suppressi…
We study the remanent domain configurations of rectangular permalloy antidot lattices over a range of lattice parameters. The influence of antidot diameter, antidot spacing, and the aspect ratio of the lattice on the remanent domain configuration are investigated by magnetic force microscopy and supported by micromagnetic simulations. In the remanent state, areas of cells with the same orientation of average magnetization form magnetic super domains separated by super domain walls (SDWs). Two types of SDWs are identified. The first type is characterized by low stray field energy, is linear, an…
Entropy of Non-Abelian Anyons from Slow Quasiparticle Dynamics in Quantum Hall Interferometers
Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University（特拉维夫大学雷蒙德和贝弗利·萨克勒物理与天文学学院）；Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Center for Quantum Science and Engineering (QSE Center), École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院量子科学与工程中心）
Scanning gate microscopy of quantum point contacts (QPC) in the integer quantum Hall regime is considered in terms of the scattering wave functions with a finite-difference implementation of the quantum transmitting boundary approach. Conductance ($G$) maps for a clean QPC as well as for a system including an antidot within the constriction are evaluated. The step-like locally flat $G$ maps for clean QPCs turn into circular resonances that are reentrant in external magnetic field when the antidot is introduced to the constriction. The current circulation around the antidot and the spacing of t…
We study the low frequency current correlations of an individual single-walled carbon nanotube at liquid He temperature. We have distinguished two physical regimes -- zero dimensional quantum dot and one dimensional quantum wire -- in terms of an energy spacing from the finite tube length in both differential conductance and shot noise measurements. In a one dimensional wire regime, we observed a highly suppressed shot noise from all measured tube devices, suggesting that electron-electron interactions play an important role.
The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges. We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite size systems with disk geometry, and found numerical evidence of edge reconstruction under rather general conditions. In the present work we have taken into account effects like layer thickness and Landau level mixing, which are found to be of quantitative importance in edge physics. Due to edge reconstruction, additional nonchiral edge modes ari…
We investigate the suppression of superconducting transition temperature in granular metallic systems due to (i) fluctuations of the order parameter (bosonic mechanism) and (ii) Coulomb repulsion (fermionic mechanism) assuming large tunneling conductance between the grains $g_{T}\gg 1$. We find the correction to the superconducting transition temperature for 3$d$ granular samples and films. We demonstrate that if the critical temperature $T_c > g_T δ$, where $δ$ is the mean level spacing in a single grain the bosonic mechanism is the dominant mechanism of the superconductivity suppression, whi…
Spin-orbit scattering suppresses Zeeman splitting of individual energy levels in small metal particles. This suppression becomes significant when the spin-orbit scattering rate τ_{so}^{-1} is comparable with the quantum level spacing δ. The g-factor exhibits mesoscopic fluctuations; at small δτ_{so} it is distributed according to the Maxwell distribution. At δτ_{so}\to 0 the average g-factor levels off at a small value g\sim(l/L)^{1/2} given by the ratio of the electron mean free path l to the particle size L. On the contrary, in 2D quantum dots the g-factor is strongly enhanced by spin-orbit …
The average height of the Coulomb-blockade conductance peaks for chaotic elastic scattering is known to increase by a factor of 4/3 upon breaking time-reversal symmetry. We calculate the temperature dependence of this factor in the regime that the inelastic scattering rate Gamma_in is greater than the mean tunneling rate Gamma_el, which itself is less than the mean level spacing Delta. Comparison with recent experimental data by Folk et al. (cond-mat/0008052) demonstrates that Gamma_in lies below Gamma_el and hence also below Delta, consistent with the low-energy suppression of inelastic elect…
Richardson model with complex level structure and spin-orbit coupling for hybrid superconducting islands: stepwise suppression of pairing and magnetic pinning
The effect of the surface curvature on the magnetic moment and persistent currents in two-dimensional (2D) quantum rings and dots is investigated. It is shown that the surface curvature decreases the spacing between neighboring maxima of de Haas -- van Alphen (dHvA) type oscillations of the magnetic moment of a ring and decreases the amplitude and period of Aharonov -- Bohm (AB) type oscillations. In the case of a quantum dot, the surface curvature reduces the level degeneracy at zero magnetic fields. This leads to a suppression of the magnetic moment at low magnetic fields. The relation betwe…
An interacting quantum dot inserted in a mesoscopic ring is investigated. A variational ansatz is employed to describe the ground state of the system in the presence of the Aharonov-Bohm flux. It is shown that, for even number of electrons with the energy level spacing smaller than the Kondo temperature, the persistent current has a value similar to that of a perfect ring with the same radius. On the other hand, for a ring with odd number electrons, the persistent current is found to be strongly suppressed compared to that of an ideal ring, which implies the suppression of the Kondo-resonant t…
How small superconductors can be? For isolated nanoparticles subject to quantum size effects, P.W. Anderson conjectured in 1959 that superconductivity could only exist when the electronic level spacing $δ$ is smaller than the superconducting gap energy $Δ$. Here, we report a scanning tunneling spectroscopy study of superconducting lead (Pb) nanocrystals grown on the (110) surface of InAs. We find that for nanocrystals of lateral size smaller than the Fermi wavelength of the 2D electron gas at the surface of InAs, the electronic transmission of the interface is weak; this leads to Coulomb block…
We show that, nonlinear optical processes of nanoparticles can be controlled by the presence of interactions with a molecule or a quantum dot. By choosing the appropriate level spacing for the quantum emitter, one can either suppress or enhance the nonlinear frequency conversion. We reveal the underlying mechanism for this effect, which is already observed in recent experiments: (i) Suppression occurs simply because transparency induced by Fano resonance does not allow an excitation at the converted frequency. (ii) Enhancement emerges since nonlinear process can be brought to resonance. Path i…
We review recent theoretical developments about the role of spins, electron-electron interactions, and spin-orbit coupling in metal nanoparticles and semiconductor quantum dots. For a closed system, in the absence of spin-orbit coupling or of an external magnetic field, electron-electron interactions make it possible to have ground states with spin $S > 1/2$. We review here a theoretical analysis which makes predictions for the probability of finding various values of spin $S$ for an irregular particle in the limit where the number of electron is large but finite. We also present results for t…
We consider arrays of Luttinger liquids, where each node is described by a unitary scattering matrix. In the limit of small electron-electron interaction, we study the evolution of these scattering matrices as the high-energy single particle states are gradually integrated out. Interestingly, we obtain the same renormalization group equations as those derived by Lal, Rao, and Sen, for a system composed of a single node coupled to several semi-infinite 1D wires. The main difference between the single node geometry and a regular lattice is that in the latter case, the single particle spectrum is…
The heat capacity (C) of a mesoscopic nonsuperconducting fermion system treated as a canonical ensemble of independent particles is studied in a wide range of particle numbers and temperatures which vary from values close to zero up to the Fermi energy. The temperature evolution of C is naturally divided into four stages. On the first one the heat capacity exponentially increases with temperature and at a resonance temperature reaches either a local maximum or an irregularity in its growth. This resonance temperature being measured can give information concerning the level spacings in the imme…
