Session W28: Superlattices and Nanostructures: Electronic Properties II

Tunnel spectroscopy in an ac-driven triple dot quantum shuttle

Within the framework of a fully quantum mechanical approach we use the density matrix master equation formalism to study the electronic transport in a triple dot quantum shuttle in the presence of an ac-field. We show that the ac-field induces photo-assisted tunneling which manifests itself as sidebands in the electronic current. We also show that these new tunneling sidebands can be explained in terms of simple sum rules involving the number of absorbed and emitted photons and the oscillator states participating in the process. Finally, we demonstrate that the tunneling channels can be controlled by manipulating the frequency and intensity of the ac-field, giving rise in particular to coherent destruction of tunneling (CDT).   

Fabrication and Characterization of a CMOS-Based Quantum Dot Device

Silicon-based single electron devices are particularly attractive for implementing quantum information processing due to the extremely long electron spin lifetimes. We report here the demonstration of a stack-gated CMOS structure that can define a quantum dot in the few-electron regime and can be integrated with a sensitive, high bandwidth field effect transistor. Multiple lower layer side gates, as small as 50nm, on an ion-implanted Si/SiO2 wafer electrostatically define the quantum dot. A top gate that controls the electron population in the quantum dot is then fabricated on top of an isolating Al2O3 layer made by atomic layer deposition (ALD). The low-temperature ALD process provides excellent device stability while preserving the integrity of the side gates. We found that the devices can be operated effectively both in the accumulation mode and in the depletion mode. Transport through the quantum dots in the few-electron regime for currents less than 100fA can be reliably studied with a good reproducibility. We will detail our fabrication and characterization processes in this presentation.   

Transport through a triple quantum-dot ring in high-spin state

Using the numerical renormalization group (NRG), we study transport through a triple quantum-dot ring in high-spin state, connected to two noninteracting leads symmetrically. The transport is determined by two phase shifts for quasi-particles with even and odd parities. An isolated triple quantum-dot ring has a high-spin ground state of $S = 1$ caused by a Nagaoka ferromagnetism, when it has one extra electron introduced into a half-filling. The results show that the conduction electrons screen the local moment via two separate stages with different energy scales. The half of the $S = 1$ is screened first by one of the channel degrees, and then at very low temperature the remaining half is fully screened to form a Kondo singlet. A two-terminal conductance in the series configuration is suppressed similar or equal to 0, while plateau of a four-terminal parallel conductance reaches a unitary limit value similar or equal to $4e2/h$ of two conducting modes. We also present the relation between electronic states and thermodynamic quantities calculated using NRG eigen energies.   

Valley Splitting in Different Landau Levels of a Si/SiGe Quantum Point Contact

Si/SiGe is an interesting platform for spin physics and quantum information due to the weak spin-orbit coupling in Si and the presence of nuclear spin zero isotopes. However, silicon has a near degeneracy of orbital states in the conduction band arising from multiple valley minima, which could enhance decoherence rates and complicate qubit operation. Recent measurements in a quantum point contact have shown that the valley splitting is large, of order 0.5 - 2 meV$^{1}$. Here, we investigate fundamental mechanisms of valley splitting by taking into account the valley couplings between Landau levels. We also account for the dependence of valley splitting on materials parameters such as miscut angle and device orientation. From our data, we are able to extract distinct valley splittings from the lowest two Landau levels, which vary similarly as a function of gate voltage (i.e., channel width). We are further able to place bounds on local variations of the tilt angle of the quantum well interface. Work supported by ARO, NSA, and NSF. 1 S. Goswami et al., Nature Physics 3 (1): 41-45 JAN 2007.   

Counting statistics and conditional evolution in a quantum electromechanical system

We present a theoretical study of full counting statistics (FCS) and conditional evolution of a quantum point contact (QPC) coupled to a mechanical oscillator. Such a system has recently been studied in several experiments. Starting from a microscopic model, we derive a master equation for the reduced density matrix that contains several important differences from the usual equation used to describe conditional position evolution ({\it i.e.} the dynamics of the oscillator inferred from a particular measurement outcome of current through the QPC). The master equation may then be solved analytically to obtain the FCS and conditional evolution. We find that the oscillator can significantly affect the FCS, leading to a highly non-Gaussian distribution characterized by an enhanced third moment even for very weak coupling. In the conditional evolution we find clear evidence that the back-action of the QPC on the oscillator cannot simply be described as coupling to an effective thermal bath.   

Thermo-electric effects in nanoscale systems out of equilibrium

As technology advances into the nanoscale regime, probing the electronic properties of nanoscale circuits has become a major challenge. Specifically, it has been suggested that thermo-electric effects may serve as a tool to study electronic properties of nanoscale systems, and experiments on thermo-power in quantum point contacts (QPCs) and molecular circuits have been performed. On the theoretical side, however, linear-response theory is inadequate to determine the dynamical formation of the thermo-electric effect. Here, we propose a novel scheme to calculate dynamical thermo-electric effects in nanostructures arbitrarily far from equilibrium using a local generalization of the Lindblad master equation. We demonstrate the method by calculating the charge imbalance of a QPC in the presence of Coulomb interactions and a temperature gradients, and obtain the long-time energy distribution in the QPC out of equilibrium. Our suggested scheme can be implemented into stochastic time-dependent current-density functional theory [PRL, 98, 226403 (2007)], thus providing a valuable tool in studying the interplay of charge and energy currents for arbitrary many-body systems.   

Universality and the thermal dependence of the conductance of nanodevices

The conductance of a quantum wire side-coupled to a quantum dot will be discussed. In this device, plots of the conductance $G$ vs.\ the gate voltage $V_g$ applied to the dot display Fano antiresonances due to the interference between the current traversing the~wire and the flux of electrons that hop to the dot to bypass the adjacent section of the wire; at fixed $V_g$'s, the interference accounts for a variety of thermal dependences $G(T)$. Analytical renormalization-group arguments will be presented that map $G(T)$ to the universal curve $g(T/T_K)$ for the conductance of the spin-degenerate Anderson impurity Hamiltonian, with temperatures normalized by the Kondo temperature $T_K$. This linear, universal mapping will be shown to (i) generate curves in excellent agreement with the measurements of Sato~et al.~[Phys.\ Rev.\ Lett.\ {\bf 95}, 066801 (2005)] and justify those authors' phenomenological description of their data; (ii) fit novel numerical renormalization-group data for the conductance of the side-coupled device; and (iii) link $G(T)$ to the conductance of the single-electron transistor.   

Electronic Properties of Quantum Point Contacts in a Quantum Ring

We investigate the electronic properties of a narrow constriction (quantum point contact) in a quantum ring using variational and diffusion Monte Carlo methods. Quantum point contacts are basic building blocks of nanoscale devices. The experimental control over their width allowed the observation of conductance quantization in integer steps of $G_0 =2e^2/h$. However, a puzzling additional structure is also observed around $0.7G_0$ in some devices. One possible explanation is the formation of a local quasi-bound state. Here, we present a first quantum Monte Carlo calculation showing that electrons can be strongly localized in the constriction, with a well quantized electron number $N$ that varies abruptly as the width of the point contact decreases. We also study the low-lying excited states and investigate the possibility of a spin texture as a function of applied gate voltage.   

Piezoelectric models for semiconductor quantum dots

The importance of fully-coupled and semi-coupled piezoelectric models for quantum dots will be presented and compared to corresponding results for one-dimensional heterostructures. Electron energies differences of up to around 30 meV were found possible for GaN/AlN quantum dots.   

High sensitivity cantilevers for measuring persistent currents in normal metal rings

We propose a new approach to measuring persistent currents in normal metal rings. By integrating micron-scale metal rings into sensitive micromechanical cantilevers and using the cantilevers as torque magnetometers, it should be possible to measure the rings' persistent currents with greater sensitivity than the SQUID-based and microwave resonator-based detectors used in the past. In addition, cantilever-based detectors may allow for measurements in a cleaner electromagnetic environment. We have fabricated ultra sensitive cantilevers with integrated rings and measured their mechanical properties. We present an estimate of the persistent current sensitivity of these cantilever-based detectors, focusing on the limits set by the cantilever's Brownian motion and the shot noise in the laser interferometer that monitors the cantilever.   

Electron Pair Resonance in the Coulomb Blockade

Transport through a nanostructure in the regime of Coulomb blockade is dominated by {\em elastic} single-electron cotunneling. We study many-body corrections to the cotunneling current via a localized state with energy $\epsilon_d$ at large bias voltages $V$. We show that the transfer of electron pairs, enabled by the Coulomb repulsion in the localized level, results in ionization resonance peaks in the third derivative of the current with respect to $V$, centered at $eV = \pm 2\epsilon_d/3$. Our results predict the existence of previously unnoticed structure within Coulomb-blockade diamonds. Remarkably, this new structure emerges within the standard Anderson Hamiltonian conventionally used for description of transport through nanostructures.   

Quantum Dot Array for Simulating the Hubbard Model

As the simplest theory that incorporates strong onsite Coulomb repulsion, the Hubbard model is fundamental to the understanding of phenomena in strongly correlated systems, e.g. the metal-insulator transition in transition-metal oxides. It is further widely believed that the 2D square-lattice Hubbard model captures the puzzling physics of high-temperature superconductivity. Since an analytical solution of the model is not viable, we propose to study its properties through a ``quantum simulator'' made from quantum dot arrays (QDAs). In this talk, we first demonstrate the correspondence between the Hubbard Hamiltonian and the simplified model for the QDA. We then address the scaling of the crucial parameters for designing a practical simulator. Two systems for implementing the QDA are proposed -- the self-assembled nanocrystal arrays, and the lithographically defined 2D-electron-gas QDA. Preliminary experimental results derived from these systems will be presented.   

Correlation effects with low electron density along a potential barrier in quantum point contacts

We study correlated electrons effect in the conductance through Quantum Point Contacts (QPC). Conductance of a QPC is quantized in steps of $G_{0}=2e^{2}/h$ (e the charge of an electron and h Planck's constant). Experiments also reveal an additional shoulder near $0.7G_{0}$ referred to as the {\it 0.7 Anomaly}. Evidence supporting spin $1/2$ magnetic moment formation in the conductance channel has motivated scenarios such as the Kondo effect. We intend to address whether or not the $0.7$ anomaly is a many-body effect associated with the formation of a spin $1/2$ magnetic moment in the conductance channel. We employ the Quantum Monte Carlo (QMC) technique for electrons on a 1-D QPC lattice with an adiabatic potential barrier. The QPC lattice includes the Hubbard lattice in the QPC region and two leads modeled by semi-infinite chains and we calculate the conductance along the chain using the Kubo formula. The physics is determined by the competition between the many-body interaction and the small kinetic energy at the top of the potential barrier. Due to the singular nature of the density of states at low electron density along with the spatial inhomogeneity, the many-body effects are expected to differ from conventional wide-band limit physics.   

Persistent currents in normal metal rings

We have measured the magnetic response of more than 20 individual mesoscopic gold rings at low temperatures. The rings were characterized one by one using a scanning SQUID microscope, which also enabled in situ measurements of the sensor background. All measured rings show a paramagnetic linear susceptibility and a poorly understood anomaly around zero field, both of which we attribute to unpaired defect spins. The response of some sufficiently small rings also has a component that is periodic in the flux through the ring. Its period is close to $h/e$, and its sign and amplitude vary from ring to ring. Including rings without a detectable periodic response, the amplitude distribution is consistent with predictions for the typical $h/e$ persistent current in diffusive metal rings. The temperature dependence of the response, measured for two rings, is also consistent with theory.