Session V11: Quantum Dots and Single Electron Structures: Optical, Electronic and Transport Properties

Precision Displacement Measurement Using a Shearing Interferometer

The emission spectra from semiconductor quantum dots consists of closely spaced spectral peaks, which cannot be resolved by a conventional grating spectrometer. An alternative solution is to use a scanning Fabry-Perot interferometer (FPI), which functions as a narrow bandwidth tunable filter, to enhance the resolution. This technique demands very precise control of the distance between the two FPI mirrors with a resolution of 1 nm. Direct optical feedback would be ideal, but would require an expensive frequency-tunable laser. We demonstrate an economic way to achieve the required precision by mechanically connecting the FPI cavity to a shearing interferometer where fluctuations in the mirror separation can be measured using the interference pattern formed by a relatively inexpensive single-frequency laser. We are able to stabilize the RMS displacement fluctuation between the two mirrors in the shearing interferometer to 0.11 nm. This precision was sufficient to keep the FPI stable for ~40 minutes.   

Spin-selective AC Stark shifts in a charged quantum dot

The energy levels of an optically active quantum system can be shifted via the AC Stark effect by applying a strong, far-detuned laser. We achieve an AC Stark shift of up to 20 GHz in a single negatively charged InGaAs quantum dot. In addition to the AC Stark shift we observe a small Overhauser shift of <1 GHz which we attribute to dynamic nuclear polarization via electron spin pumping induced by the high power, although far-detuned AC Stark laser. Both shifts are polarization selective, meaning polarization control of the applied laser provides control over the energy level structure of the system. Applying a circularly polarized laser therefore allows for a spin-selective modification to the energies, shifting one spin manifold and not the other. The reconfiguration of the energy levels is reversible and can be applied or removed rapidly on the timescale of a few nanoseconds. In principal this ability to rapidly and coherently reconfigure the energy structure and polarization selection rules may enable single-shot fluorescence readout in a small transverse magnetic field.   

Superconducting transport in InAs nanowire double quantum dots

Quantum dot arrays in narrow-gap semiconductors coupled to
superconducting reservoirs can serve as a platform for studying the
interaction between solitary spins and the Cooper pair condensate, which
can give rise to topologically protected Majorana modes.

We define double quantum dots (DQDs) in InAs nanowires with epitaxial
aluminum shell. We demonstrate that we can reach both the strongly and
weakly coupled regimes owing to the five wrap-around electrostatic gates
on the nanowire. We characterize the Josephson coupling via the DQD as a
function of the charge occupation of the islands, and find abrupt
changes which are possible experimental signatures of the change in the
ground state spin configuration of the device. Finite voltage bias
spectroscopy reveals Yu-Shiba-Rusinov states below the superconducting
gap exhibiting the weakly and strongly coupled behavior at different
gate configurations.   

Charging of a Single InAs QD with Electrically-Injected Holes using a Lateral Electric Field

InAs/GaAs quantum dot (QD) and quantum dot molecules (QDM) are self-assembled semiconductor nanostructures that can trap a single electron or hole in a 3-D potential-well. Grown by molecular beam epitaxy (MBE), they have excellent optical qualities that can be used in applications of quantum information processing and quantum computing. The property of a single QD can be tuned by external electric field, giving it great potential for scalable quantum photonic applications. Deterministically charging a QD with a single electron or hole has been demonstrated by embedding the QD in a diode structure and applying growth direction electric fields. Here, we report a new charging mechanism of a single QD using lateral electric field with a 3-electrode device. We designed a 3-electrode device that embeds a single QD in an unintentionally doped GaAs matrix. We fabricate the device with E-beam lithography and characterize a single QD’s photoluminescence under different bias configurations. We observe charging of a single hole through the lateral electric field, supported by device simulation using COMSOL. We will discuss the potential applications of a 2-D electric field on a single QD using a 3-electrode device.   

Qunatum mechanics on a torus: Energy levels, Zeeman splitting and transport properties

Carrier confinement and transport in novel geometries have generated immense theoretical and experimental interest in recent years. Here we investigate the properties of an electron constrained to move on the surface of a torus. We derive the Schrodinger-Riccati equation on a torus using differential geometry. We construct the corresponding action and obtain the eigensolutions through a generalized varaional approach. We show that the dual circular symmetries related to the minor and major radii give rise to at most a 4-fold degeneracy. We obtain the level splitting pattern in the presence of a perpendicular magnetic field. We investigate the transport properties for an electron on a torus with two contacts attached. The torus being a multiply connected topology shows the Ahronov-Bohm effect in presence of a magnetic vector potential and manifests the interference occurring due to electron waves travelling through two different paths. Semiconductor quantum dots and carbon nanotori, for certain chirality, have bandgaps at K-points in the Brillouin zone. Hence they obey nonrelativistic equations, making our study relevant for experimentally amenable outcomes.   

Spectroscopy of Quantum-Dot Orbitals with In-Plane Magnetic Fields

While spins in quantum dots have received a lot of attention for the development as a qubit, the orbitals which are hosting the qubit have largely been ignored. However, important processes such as electric-dipole spin resonance and spin relaxation depend sensitively on the dot shape due to the anisotropic nature of the spin-orbit interaction.
Here, we present a method which allows quantifying the in-plane orientation angle and the strength of the hard confinement perpendicular to the 2D gas in which the gate-defined single-electron GaAs dot is formed. Using a piezo electric rotator, we control the direction of the magnetic field in the 2D plane and measure the in-plane orbital energies using pulse gate spectroscopy. Based on a model of the orbitals, we extract the orientation angle of the dot in the 2D plane, quantify the strong confinement and characterize deviations from a harmonic oscillator potential. Our measurements demonstrate a versatile tool for quantum dots with one dominant axis of strong confinement.   

Toward exploring multichannel charge Kondo effects for investigating quantum criticality

Recent proposals^[1,2] have demonstrated a non-Fermi liquid fixed point in superconducting and topological superconducting islands, analogous to the charge Kondo effect in normal metallic islands. The topological Kondo effect is predicted to be robust against channel detuning and to have a heightened crossover temperature when tuned to charge degeneracy, making this an especially attractive regime for investigating quantum criticality and for demonstrating nonlocal quantum phenomena through Majorana modes. I will talk about our efforts in experimentally realizing new multichannel charge Kondo devices on InAs 2DEG platforms.

[1] M. Pustilnik, et al., Phys. Rev. Lett. 119, 116802 (2017).
[2] K. Michaeli, et al., Phys. Rev. B 96, 205403 (2017).   

Transient dynamics of a quantum-dot: From Kondo regime to mixed valence and to empty orbital regimes

Based on the hierarchical equations of motion approach, we study the time-dependent transport properties of a strongly correlated quantum dot system in the Kondo regime (KR), mixed valence regime (MVR), and empty orbital regime (EOR). We find that the transient current in KR shows the strongest nonlinear response and the most distinct oscillation behaviors. Both behaviors become
weaker in MVR and diminish in EOR. To understand the physical insight, we examine also the corresponding dot occupancies and the spectral functions, with their dependence on the Coulomb interaction, temperature, and applied step bias voltage. The above nonlinear and oscillation behaviors could be understood as the interplay between dynamicalKondo resonance and single electron resonanttunneling.   

Fano and Fano-Kondo resonance in double quantum dot in parallel

It has been a controversial issue whether the Fano resonance is observed or not in the transport through a mesoscopic ring with an embedded quantum dot, so-called Aharonov-Bohm interferometer. To address this issue, we theoretically examine the nonequilibrium transport through a double quantum dot (DQD) in parallel: resonant tunneling at the Coulomb peak or Kondo effect in the Coulomb valley in quantum dot 1, with a broad linewidth in quantum dot 2. Our model is more tractable than a model for the AB interferometer [1]. We stress the importance of multiple channels in external leads to simulate the experimental systems, which was often neglected in previous studies. In the case of single channel in the leads, we find an asymmetric Fano resonance or Fano-Kondo resonance as a function of energy level in quantum dot 1. With an increase in the number of channels, these approach the symmetric Breit-Wigner resonance or Kondo plateau. This is because the coherence between the quantum dots is weakened, which can be characterized by the off-diagonal element normalized by the diagonal elements in a two-by-two matrix of the linewidth function.
[1] W. Hofstetter et al., Phys. Rev. Lett. 87, 156803 (2001).   

Single-Electron Charging Effects in Sketched LaAlO3/SrTiO3 Single-Electron Transistors

Mesoscopic devices like the single-electron transistor (SET) exhibit quantum behavior by forcing electrical current through a point-like constriction with quantized energy levels. Such devices typically require extreme nanofabrication techniques. Complex-oxide heterostructures such as the LaAlO₃/SrTiO₃ system support conductive interfaces that can be controlled using a reversible conductive-AFM lithography technique. These interfaces have richer properties than III-V or silicon-based systems, and support intrinsic magnetic, superconducting and structural phases. Here we describe renewed efforts to explore the properties of “sketched” SETs at the LaAlO₃/SrTiO₃ interface, focusing on the temperature and magnetic-field dependence of transport. We observe non-equilibrium conductances that cleanly resolve addition energies in nanoscale quantum dots, and track interactions between electronic states vs. experimental parameters such as gate voltage, temperature and magnetic field. These results yield new insights into intrinsic interactions between electrons confined within the quantum dot.   

Ultra-stable atomically precise single electron transistors in Silicon

Single electron transistor devices (SETs) in solid-state quantum computing architecture serve as sensitive electrometers for realizing spin selective initialization & single shot readout during spin manipulation, & demand very stable operation. In this context, we demonstrate fully functional, ultra-stable atomically precise SETs fabricated using scanning tunneling microscope (STM) lithography on the Si (100) 2x1: H surface. Low-temperature transport measurement of SETs reveal highly stable Coulomb blockade oscillations. To better understand low-frequency time instabilities we have measured charge offset drift over a period of 4.5 days. SETs fabricated using STM lithography exhibit low charge offset drift magnitude (less than 0.02 e over 4 days, at both base temperature & 6 K) as compared to conventional metal & Silicon based SETs. The low charge offset drift magnitude likely results from the lack of a nearby interface & suggests low defect density in the STM fabrication process & low temperature epitaxial overgrowth. However, at elevated temperatures above 3 K a glassy relaxation is observed in response to gate voltage changes with a settling time that is strongly temperature- dependent.   

Tunnel Junction Design and Characterization in Si:P Single Electron Transistors

Atomically precise Si:P quantum devices are a promising architecture for scalable solid-state quantum computing. Quantification and control of the tunnel coupling between device components at the atomic scale is essential to successful donor-based quantum information processing (e.g. gate-tunable exchange coupling, electron spin readout, and ultrasensitive charge sensing all require precise control over tunnel coupling). We report on reproducibility of tunnel coupling as measured in atomically precise single electron transistors (SETs). We systematically vary gap separations on the nanometer scale, observing orders of magnitude changes in resistance. Combining low-temperature transport measurements with the orthodox theory of Coulomb blockade, we have extracted tunnel resistances in SETs and analyze to what degree resistances depend on applied voltages. We analyze the relationship between the tunnel conductance and physical barrier parameters and will discuss the limits of lithographically defining an atomically abrupt Si:P tunnel junction. We find the behavior of the tunnel junctions in these devices to be of exceptional quality and will discuss potential reasons for these improvements compared to previous devices fabricated in a similar manner.   

Fabrication and Measurement of Atomically Precise Single Electron Islands

Phosphorous donor devices fabricated in silicon with a scanning tunneling microscope (STM) are used as a discovery platform for everything ranging from quantum physics to ultra-efficient tunnel field effect transistors because the underlying hydrogen lithography step can be performed with atomic precision. Many of these devices designs rely on electrostatic gating to tune electrical tunneling through the device. It is expected that out-of-plane gates will be more efficient at gating than in-plane gates. We present on fabrication techniques for adding top gates to devices and the resulting low-temperature measurements on tunnel junctions and single electron islands.
  

The role of confinement and interaction in the emergence of aromatic features in nanoscale synthetic molecules

It has recently been demonstrated that the electronic structure of polyaromatic hydrocarbons can be qualitatively reproduced by quantum corrals made via atomic manipulation. This presents a quandary since the electronic structure of these molecules has been ascribed to a resonating valence bond like state requiring strong confinement to molecular orbitals and significant electron-electron interactions. However, quantum corrals fundamentally exhibit single-electron physics as evidenced by a short lifetime for an electron in a corral, resulting in the absence of Coulomb effects between electrons. We examine this problem from the experimental data obtained via scanning tunneling spectroscopy and topography, tight-binding modeling of hopping and interaction Hamiltonians, as well as density functional theory calculations to determine what aspects of the fully-interacting picture can be produced by the single-electron approach.