Signatures of spin pairing in chaotic quantum dots

Coulomb blockade resonances are measured in a GaAs quantum dot in which both shape deformations and interactions are small. The parametric evolution of the Coulomb blockade peaks shows a pronounced pair correlation in both position and amplitude, which is interpreted as spin pairing. As a consequence, the nearest-neighbor distribution of peak spacings can be well approximated by a modified bimodal Wigner surmise, in which interactions are taken into account beyond the constant interaction model.     

Towards an explanation of the mesoscopic double-slit experiment: A new model for charging of a quantum Dot

For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels, and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD.     

石墨烯纳米带量子点中的量子混沌现象

在20 mK的极低温下测量了石墨烯纳米带量子点的电子输运性质,观测到清晰的库仑阻塞菱形块和对应量子点激发态的电导峰.对库仑阻塞近邻电导峰间距和峰值进行了统计分析,发现其统计分布分别满足无规矩阵理论描述的Wigner-Dyson分布和Porter-Thomas分布,说明石墨烯纳米带量子点在低温下出现了量子混沌现象.还讨论了这种长方形量子点中量子混沌的可能成因. 关键词： 石墨烯纳米带 量子点 库仑阻塞 量子混沌     

Correlations of conductance peaks and transmission phases in deformed quantum dots

We investigate the Coulomb blockade resonances and the phase of the transmission amplitude of a deformed ballistic quantum dot weakly coupled to leads. We show that preferred single-particle levels exist which stay close to the Fermi energy for a wide range of values of the gate voltage. These states give rise to sequences of Coulomb blockade resonances with correlated peak heights and transmission phases. The correlation of the peak heights becomes stronger with increasing temperature. The phase of the transmission amplitude shows lapses by between the resonances. Implications for recent experiments on ballistic quantum dots are discussed. Received 17 July 1998     

Correlation-induced resonances and population switching in a quantum-dot coulomb valley

Strong correlation effects on electron transport through a spinless quantum dot are considered. When two single-particle levels in the quantum dot are degenerate, a conserved pseudospin degree of freedom appears for generic tunneling matrix elements between the quantum dot and leads. Local fluctuations of the pseudospin in the quantum dot give rise to a pair of asymmetric conductance peaks near the center of a Coulomb valley. An exact relation to the population switching is provided.     

Quantum dot in the pseudogap Kondo state

We investigate the transport properties of a (small) quantum dot connected to Fermi liquid leads with a power-law density of states (DOS). Such a system, if experimentally realizable, will have interesting physical properties including: (i) non-saturating Coulomb blockade peak widths; (ii) a non-unitary Kondo peak symmetrically placed between Coulomb blockade peaks; (iii) an absence of conductance away from particle-hole symmetry at sufficiently low temperatures; and (iv) evidence of a quantum critical point as a function of dot-lead hopping. These properties are compared and contrasted with one dimensional Luttinger systems exhibiting a power-law “tunneling-DOS”.     

Spin filters with Fano dots

We compute the zero bias conductance of electrons through a single ballistic channel weakly coupled to a side quantum dot with Coulomb interaction. In contrast to the standard setup which is designed to measure the transport through the dot, the channel conductance reveals Coulomb blockade dips rather then peaks due to the Fano-like backscattering. At zero temperature the Kondo effect leads to the formation of broad valleys of small conductance corresponding to an odd number of electrons on the dot. By applying a magnetic field in the dot region we find two dips corresponding to a total suppression in the conductance of spins up and down separated by an energy of the order of the Coulomb interaction. This provides a possibility of a perfect spin filter.Received: 6 November 2003, Published online: 2 April 2004PACS: 72.15.Qm Scattering mechanisms and Kondo effect - 73.23.Ad Ballistic transport - 72.25.-b Spin polarized transport     

Dynamic localization and the Coulomb blockade in quantum dots under ac pumping

We study conductance through a quantum dot under Coulomb blockade conditions in the presence of an external periodic perturbation. The stationary state is determined by the balance between the heating of the dot electrons by the perturbation and cooling by electron exchange with the cold contacts. We show that the Coulomb blockade peak can have a peculiar shape if heating is affected by dynamic localization, which can be an experimental signature of this effect.     

Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states

We consider a quantum dot in the regime of the quantum Hall effect, particularly in Laughlin states and non-Abelian Read-Rezayi states. We find the location of the Coulomb blockade peaks in the conductance as a function of the area of the dot and the magnetic field. When the magnetic field is fixed and the area of the dot is varied, the peaks are equally spaced for the Laughlin states. In contrast, non-Abelian statistics is reflected in modulations of the spacing which depend on the magnetic field.     

Co-tunneling of the charge through a 2-D electron island

A double barrier Single Electron Transistor is realized in two dimensions by confining the 2-D electron gas of a GaAs/GaAlAs heterojunction to a small island by means of Schottky gates. Two gates provide adjustable tunnel barriers and a central gate controls the electron number in the island. The island has small single-particle energy level spacing and forms a metallic island. Periodic conductance oscillations characteristic of Coulomb blockade are observed when the central gate voltage is varied. The ability to vary the tunnel conductance allows us to study the basic physics of the Coulomb blockade: our results show that the quantum charge fluctuation mechanism which limits the tunneling blockade at low temperature is of second order in tunnel barrier transparencies in agreement with the charge Macroscopic Quantum Tunneling (q-MQT) or co-tunneling model.     

Coulomb blockade without potential barriers

We study transport through a strongly correlated quantum dot and show that Coulomb blockade can appear even in the presence of perfect contacts. This conclusion arises from numerical calculations of the conductance for a microscopic model of spinless fermions in an interacting chain connected to each lead via a completely open channel. The dependence of the conductance on the gate voltage shows well defined Coulomb blockade peaks which are sharpened as the interaction strength is increased. Our numerics is based on the embedding method and the DMRG algorithm. We explain the emergence of Coulomb blockade with perfect contacts by a reduction of the effective coupling matrix elements between many-body states corresponding to successive particle numbers in the interacting region. A perturbative approach, valid in the strong interaction limit, yields an analytic expression for the interaction-induced suppression of the conductance in the Coulomb blockade regime.     

Transport properties of quantum dots

Linear and nonlinear transport through a quantum dot that is weakly coupled to ideal quantum leads is investigated in the parameter regime where charging and geometrical quantization effects coexist. The exact eigenstates and spins of a finite number of correlated electrons confined within the dot are combined with a rate equation. The current is calculated in the regime of sequential tunneling. The analytic solution for an Anderson impurity is given. The phenomenological charging model is compared with the quantum mechanical model for interacting electrons. The current-voltage characteristics show Coulomb blockade. The excited states lead to additional fine-structure in the current voltage characteristics. Asymmetry in the coupling between the quantum dot and the leads causes asymmetry in the conductance peaks which is reversed with the bias voltage. The spin selection rules can cause a ‘spin blockade’ which decreases the current when certain excited states become involved in the transport. In two-dimensional dots, peaks in the linear conductance can be suppressed at low temperatures, when the total spins of the corresponding ground states differ by more than 1/2. In a magnetic field, an electron number parity effect due to the different spins of the many-electron ground states is predicted in addition to the vanishing of the spin blockade effect. All of the predicted features are consistent with recent experiments.     

Single-electron charging of triangular quantum dots in a ring interferometer

Small-size semiconductor ring interferometers operating in the Coulomb blockade regime have been experimentally and theoretically studied. The conductance as a function of the gate voltage exhibits narrow quasiperiodic peaks, which are further split into doublets. Based on the experimental structural data, a three-dimensional electrostatic potential, the energy spectrum, and the single-electron transport in the interferometer were modeled. The electron system can be divided into two triangular quantum dots connected by single-mode microcontacts to each other and to the reservoirs. A model of quantum dot charging in this system is proposed that explains the appearance of doublets in the conductance-gate voltage characteristics.     

Resonance breakdown of a Coulomb blockade due to the mechanical vibrations of a quantum dot

The effect of forced mechanical vibrations of a suspended single-electron transistor on Coulomb-blockade limited electron tunneling through a quantum dot has been studied. The mechanical vibrations of the quantum dot have been shown to result in the Coulomb blockade breakdown, which is manifested by narrow resonance peaks of the transistor conductance as a function of the excitation frequency at the frequencies corresponding to the eigenmodes of the mechanical vibrations. The mechanism of the observed effect presumably associated with the oscillations of the mutual electrical capacitances between the quantum dot and the surrounding electrodes is discussed.     

Capacitance fluctuations in quantum dots

We discuss fluctuations of the charging energy E_C and gate voltage spacings between Coulomb oscillation conductance peaks, as computed within spin density functional theory for a realistic GaAs–AlGaAs dot. We explicitly exhibit the fluctuations in the portion of the total free energy which incorporate the interaction between the dot and its surroundings. These variations in the dot capacitance show a dispersion which is typically greater than the dispersion of the total dot charging energy.     

The effect of confinement on the electron thermal conductance of a nanocrystal

Coulomb blockade oscillations are found in the electron thermal conductance of a quantum dot (nanocrystal) in the regime of weak coupling with two electrode leads that is calculated within a linear response theory. An analytical expression is obtained in the quantum limit where electron level spacing is non-negligible. The effect of confinement on the electron thermal conductance is thereby explicitly shown. It is shown that in the quantum limit the periodicity of the Coulomb-blockade oscillations of the electron thermal conductance is the same as of the conductance. The shape and the magnitude of the electron thermal conductance depend explicitly on the temperature and the energy level spacing. It is found that the electron thermal conductance decreases nearly exponentially with increasing confinement and decreasing temperature.     

Coulomb blockade in an open quantum dot

We report the observation of Coulomb blockade in a quantum dot contacted by two quantum point contacts each with a single fully transmitting mode, a system thought to be well described without invoking Coulomb interactions. Below 50 mK we observe a periodic oscillation in the conductance of the dot with gate voltage, corresponding to a residual quantization of charge. From the temperature and magnetic field dependence, we infer the oscillations are mesoscopic Coulomb blockade, a type of Coulomb blockade caused by electron interference in an otherwise open system.     

Conductance peak splitting in charge polarized coupled quantum dots

We report a measurement of linear conductance through a series double dot as a function of the total double dot charge and the charge difference for interdot tunnel conductances between zero and one mode. The dots are defined by ten independently tunable electrostatic gates on the surface of a GaAs/AlGaAs heterostructure to allow separate adjustment of dot charge and interdot conductance. For weak interdot tunneling the measured double dot conductance agrees with a transport model in which each dot is individually governed by Coulomb blockade theory. As interdot tunnel conductance increases toward one mode, the measured conductance peak positions and shapes indicate both a relaxation of the charge quantization condition for individual dots and quantum mechanical charge sharing between dots. The results are in quantitative agreement with many body charge fluctuation theory.     

Heat transport through a quantum dot with one-dimensional interacting leads under Coulomb blockade regime

The peculiarities of a low temperature heat transfer through a ballistic quantum dot (a double potential barrier) with interacting leads due to a long-range Coulomb interaction (in the geometrical capacitance approach) are considered. It is found that the thermal conductance K shows periodic peaks as a function of the electrostatic potential of a dot at low temperatures. At the peak maximum it is whereas near the minimum it is . Near the peak maximum the dependence K(T) is essentially nonmonotonic at the temperatures correspondent to the level spacing in the quantum dot. Received 20 October 1999 and Received in final form 20 January 2000     

Electronic transport in graphene nanostructures on SiO2

We report two experiments on graphene nanostructures. The first was performed on a graphene nanoribbon, where the nature of electronic transport was investigated in detail. Electrons or holes are found to localize in pockets of the potential along the ribbon. Transport is governed by the joint action of localization and Coulomb interaction. The temperature-dependence of the conductance shows activated behavior at temperatures above a few Kelvin. The activation energy retraces the edges of Coulomb blockade diamonds found in nonlinear transport. In the second experiment the metallic tip of a low-temperature scanning force microscope was scanned above a graphene quantum dot. In addition to the familiar Coulomb blockade fringes, localized states are detected forming in the constrictions connecting the dot to source and drain.