Session W44: Focus Session: Nanoscale Transport - Mostly Quantum Dots

Spin-Lattice Relaxation Rate in Lateral Quantum Dots

Laterally gated quantum dots (QDs) fabricated on AlGaAs/GaAs heterostructures show promise for spin-based quantum computation. One limit to the coherence time in QDs, which sets the timescale on which quantum operations must be completed, comes from the spin-orbit interaction. In a magnetic field $B$ the spin states of a single electron in a QD are split by the Zeeman energy $g\mu_{B}B$; the spin-orbit interaction couples the spin states of a QD to its orbital degrees of freedom, which in turn can interact with piezoelectric phonons to relax the spin from the excited state to the ground spin state. The time scale over which this happens is the relaxation time $T_1$. We present measurements of the relaxation rate $W = T_1^{-1}$ of one electron in a single laterally gated QD at magnetic fields down to 1 T, much lower than previously measured. These measurements are possible because of the good stability of the AlGaAs/GaAs heterostructure we have used combined with an active feedback system that compensates for residual drift and switches of the dot energy levels. We find that $T_1$ is as long as 1s at 1 T. We compare our measurements to theoretical predictions of $W$ caused by spin-orbit coupling to phonons and extract the spin-orbit length, which describes the strength of the spin-orbit interaction. This demonstrates that spin-orbit coupling to phonons can account for $W$ down to fields as low as 1 T in laterally gated QDs and establishes an upper limit to the spin coherence time. This work is in collaboration with K. MacLean, D. M. Zumb\"{u}hl, I. P. Radu, M. A. Kastner, M. P. Hanson, and A. C. Gossard. This work has been supported by the ARO (W911NF-05-1-0062), the NSF (DMR-0353209), and in part by the NSEC Program of the NSF (PHY-0117795).   

Spin Blockade in electronic transport through quantum dots

Recently, Spin Blockade (SB) transport through quantum-dots has attracted attention owing to potential applications in quantum state control. In this talk, we identify the mechanism underlying current collapse (NDR), current leakage and bias dependent asymmetry in the I-V characteristics of quantum dot systems, which characterize spin blockade transport. As a specific example of this generic mechanism, we examine the conditions for SB to occur in transport through coupled quantum dots. This leads to a consistent interpretation of the non-trivial features in the experimental I-Vs of coupled quantum dots including multiple NDR, gate-able current collapse, and current rectification. Most importantly, our study elaborates on how a delicate interplay of orbital energy offset, delocalization, and Coulomb interaction between conduction electrons localized on either dot, strongly influences the aforementioned transport signatures.   

Resonant dephasing of the electronic Mach-Zehnder interferometer

We address the recently observed unexpected behavior of Aharonov-Bohm oscillations in the electronic Mach-Zehnder interferometer experimentally realized in a quantum Hall system [1]. We argue that the measured lobe-like structure in the visibility of oscillations and the phase rigidity result from a long-range {\em local} interaction between two adjacent counter-propagating edge states, which leads to a resonant scattering of bosonic charge excitations. The visibility and phase shift, expressed in terms of the transmission coefficient for bosons, provide the tool for investigating the nature of quantum Hall edge states. [1] I. Neder {\em et al}., Phys. Rev. Lett. {\bf 96}, 016804 (2006).   

Electron population control of an isolated quantum dot using surface-acoustic-wave pulses

In developing quantum information technology, isolation from the environment is a key for long coherence times. However, many quantum-dot (QD) experiments require a fair degree of coupling to electron reservoirs. The electron number becomes progressively difficult to control as the degree of isolation increases and the electron dwell time exceeds the timescale of experiments. In such a system, a means to transfer electrons on demand between a QD and another QD or reservoir is desirable. We report our recent experiments on sending surface acoustic waves (SAWs) past a QD that is isolated from the leads by strong barriers, such that electrons take hundreds of seconds to tunnel. A short pulse of SAWs is used to characterize the electronic structure of the QD, and to transport electrons in and out of the QD. The mechanism of electron transfer from dynamic QDs defined by the SAWs themselves into a gate-defined static QD is investigated. This has applications for quantum information transfer and processing.   

Coulomb-energy-dependent tunnelling from few-electron dynamic quantum dots defined by surface acoustic waves

Electrons confined in dynamic quantum dots (DQDs) have been proposed as an implementation for the control and manipulation of quantum information. In this scheme, entanglement is achieved at a tunnel barrier between neighbouring DQDs. In this presentation we investigate the escape rate from a DQD at a tunnel barrier. One or few electron DQDs were created by a surface acoustic wave travelling through a pinched-off channel, isolated from a reservoir by a narrow tunnel barrier. The tunneling rates across the barrier were determined using a rate-equation model, and found to increase with the electron occupation of the DQD. This effect can be explained in terms of Coulomb interactions between the confined electrons.   

Conductance signatures of a quantum-critical transition and a Kondo filtered resonance in double quantum dots

We present conductance results for double quantum dot (DQD) systems containing one dot in the Kondo regime coupled to an effectively noninteracting dot. The system is mapped onto a single impurity Anderson model with a structured (nonconstant) density of states [1]. The linear conductance is obtained using the DQD's Green's function calculated from numerical renormalization-group calculations for both side-dot and parallel configurations. In the side dot case, the conductance shows signatures of the band filtering through the resonant dot. This mechanism can be interpreted as an interference between many-body and single-particle states, splitting the Kondo resonance while preserving the Kondo singlet ground-state. In the parallel configuration, interference between conducting channels through the dots create a pseudogapped effective density of states [1]. We discuss possible approaches for detecting the quantum-critical point separating Kondo and non-Kondo phases in conductance measurements. \newline \newline [1] L.G.G.V. Dias da Silva et al, PRL 97 096603 (2006)   

Kondo effect in a quantum dot via orbital population switching

Strong correlation effects in electron transport through a spinless quantum dot are considered. For general tunneling matrix elements between the quantum dot and leads, there exists a conserved pseudospin degree of freedom when two orbitals in the quantum dot are degenerate. The fluctuations of the pseudospin at the quantum dot give rise to the Kondo effect described by the anisotropic $s$-$d$ model. Interestingly the Kondo effect generates a pair of asymmetric conductance peaks near the center of a Coulomb valley, in clear contrast to the conductance behavior due to the spin Kondo effect. This explains the origin of the so-called correlation-induced resonances reported recently [V. Meden and F. Marquardt, Phys. Rev. Lett. 96, 146801 (2006)]. An exact relation to the phenomenon of the population switching is provided and differences from the conventional Kondo effects are clarified.   

Modeling of tunneling spectroscopy of a single quantum dot involving two levels

We have employed the two-level Anderson model to simulate the system of the tip/quantum dot (QD)/substrate double barrier junction. The tunneling current through the ground state and the first excited state in the cases of shell-tunneling and shell-filling is theoretically investigated in the framework of nonequilibrium Green's function technique by solving the two level Anderson model properly. We found that single-particle and two-particle occupation numbers significantly influence the probabilities of each resonant energies arising from the intralevel and interlevel Coulomb interactions. Compared with tunneling current spectra of CdSe QDs, we predict some resonant structures which can be observed in an isolated QD.   

Band filtering and quantum phase transition in an asymmetric double quantum dot

Double quantum dots (DQDs) are currently of great theoretical and experimental interest. A DQD device in which one of the dots is in the Kondo regime and the other is effectively a noninteracting resonant level has been shown [1] to reduce to an effective one-impurity Anderson problem with a structured (nonconstant) density of states. Depending on DQD parameters that can be controlled experimentally via gate voltages, such a device can exhibit zero-field splitting of the Kondo resonance on the interacting dot, or it can be tuned to access a quantum critical point separating Kondo-screened and local-moment phases. Using numerical renormalization-group techniques, we explore the robustness of these phenomena by increasing the Coulomb interaction on the resonant dot away from zero. We report the effects of the interaction on the device's magnetic susceptibility, spectral function, and linear conductance. [1] L. G. G. V. Dias da Silva, N. P. Sandler, K. Ingersent, and S. E. Ulloa, Phys. Rev. Lett. {\bf 97}, 096603 (2006).   

Imaging Electron Flow From a Quantum Point Contact

We image electron flow from a quantum point contact (QPC) into a high-mobility two-dimensional electron gas (2DEG) using scanning gate microscopy (SGM). We note two surprising phenomena, which we compare with results from simulations: 1. The beam of electrons immediately leaving the QPC is unexpectedly narrow and collimated. 2. Under certain conditions, the signal generally associated with current flow density (i.e. the change in differential conductance due to scattering from the scanning gate tip) can change sign from negative to positive.   

Imaging fringes in magnetic focusing of electron waves

Magnetic focusing of the electron flow between two quantum point contacts (QPCs) in a two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure occurs when the QPC spacing is an integer multiple of the diameter of a cyclotron orbit. Images of magnetic focusing taken with a cooled scanning probe microscope (SPM) exhibit fringes when multiple paths of electrons interfere, as well as branching of the electron paths caused by small angle scattering [1]. We use simulations to show that one could improve images of fringe structures by using devices smaller than the length required to form branches. The distance between QPCs can be made quite small ($\sim $~0.5 microns) without destroying the fringe structure. We plan to test our simulations using double QPC devices. \newline \newline [1] Kathy Aidala\textit{ et al.}~ to be published (2007).   

Phase-sensitive mapping of electronic wavefunctions in atomically precise nanostructures

We use a custom-built scanning tunneling microscope (STM) to assemble atomically precise nanostructures and to study the evolution of engineered electronic wavefunctions. We investigate resonant structures of different geometries constructed from individual atoms and molecules at 4 K. STM measurements directly probe wavefunction probability density but can indirectly provide information about quantum-mechanical phase. Through controlled quantum interference we thus use the STM as a phase-sensitive probe of single electron wavefunctions formed from the two-dimensional electron gas on the Cu(111) surface. By varying constraints imposed by symmetry, the boundary geometry, and relative or statistical phase (e.g. via magnetism or field effects), we can tune and elucidate energy and phase information of specific electronic quantum states. This level of detection and control is critical for new technologies based on few-electron devices.   

Quantum Isospectral Nanostructures

``Can one hear the shape of a drum?'' Recently, the answer to this long-standing puzzle in contemporary mathematics was proven to be ``no'': it is possible to construct two entirely different boundaries in which the wave equation possesses exactly the same eigenvalue spectrum. For the first time, we verify this result in the quantum mechanical realm by designing and studying isospectral electron resonators built one molecule at a time. We present scanning tunneling microscopy of pairs of nanostructures with dissimilar spatial structures yet identical electronic properties. We demonstrate that the wavefunctions of one structure can be transplanted onto those of its isospectral complement, but only if the electron phase -- which usually has no bearing on proximal probe measurements -- is taken into account.