We consider the energy spectrum and the spin-parity structure of the eigenstates for a quantum dot made of a strong topological insulator. Using the effective low-energy theory in a finite-length cylinder geometry, numerical calculations show that even at the lowest energy scales, the spin direction in a topologically protected surface mode is not locked to the surface. We find "zero-momentum" modes, and subgap states localized near the "caps" of the dot. Both the energy spectrum and the spin texture of the eigenstates are basically reproduced from an analytical surface Dirac fermion description. Our results are compared to microscopic calculations using a tight-binding model for a strong topological insulator in a finite-length nanowire geometry.
We investigate electron localization and dynamical spin locking induced by ac magnetic fields in double quantum dots. We demonstrate that by tuning the ac magnetic fields parameters, i.e., the field intensity, frequency, and the phase difference between the fields within each dot, coherent destruction of tunneling (and thus charge localization) can be achieved. We show that in contrast with ac electric fields, ac magnetic fields are able to induce spin locking, i.e., to freeze the electronic spin, at certain field parameters. We show how the symmetry of the Hamiltonian determines the quasiener…
We study the influence of nuclei-induced frequency focusing on the mode locking of spin coherence in quantum dots subjected to a periodic train of optical pulses. In particular, we address the question whether or not nuclei-induced frequency focusing always enhances the effect of spin mode locking. We combine two advanced semiclassical approaches and extend the resulting model by including the full dynamics of the optically excited trion state. In order to reduce the discrepancy to a full quantum model, we establish a nondeterministic pulse description by interpreting each pump pulse as a meas…
The coherent spin dynamics of resident carriers, electrons and holes, in semiconductor quantum structures is studied by periodical optical excitation using short laser pulses and in an external magnetic field. The generation and dephasing of spin polarization in an ensemble of carrier spins, for which the relaxation time of individual spins exceeds the repetition period of the laser pulses, are analyzed theoretically. Spin polarization accumulation is manifested either as resonant spin amplification or as mode-locking of carrier spin coherences. It is shown that both regimes have the same orig…
The temperature dependence of the coherence time of hole spins confined in self-assembled (In,Ga)As/GaAs quantum dots is studied by spin mode-locking and spin echo techniques. Coherence times limited to about a μs are measured for temperatures below 8 K. For higher temperatures a fast drop occurs down to a few ns over a 10 K range. The hole-nuclear hyperfine interaction appears too weak to account for these limitations. We suggest that spin-orbit related interactions are the decisive sources for hole spin decoherence.
Quantum dots in GaAs/InGaAs structures have been proposed as a candidate system for realizing quantum computing. The short coherence time of the electronic quantum state that arises from coupling to the nuclei of the substrate is dramatically increased if the system is subjected to a magnetic field and to repeated optical pulsing. This enhancement is due to mode locking: Oscillation frequencies resonant with the pulsing frequencies are enhanced, while off-resonant oscillations eventually die out. Because the resonant frequencies are determined by the pulsing frequency only, the system becomes …
We measure the strength and the sign of hyperfine interaction of a heavy-hole with nuclear spins in single self-assembled quantum dots. Our experiments utilize the locking of a quantum dot resonance to an incident laser frequency to generate nuclear spin polarization. By monitoring the resulting Overhauser shift of optical transitions that are split either by electron or exciton Zeeman energy with respect to the locked transition using resonance fluorescence, we find that the ratio of the heavy-hole and electron hyperfine interactions is -0.09 +/- 0.02 in two QDs. Since hyperfine interactions …
Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree-Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave functions. The broken symmetry states with semi-classical charge density constructed from superpositions of the ED solutions are compared to the UHF results. UHF overlooks the dependence of the few-electron wave function on the actual relative positions of electrons localized in different charge puddles and partially compensates for this neglect by an exaggerated s…
The coherence of the electron spin in a semiconductor quantum dot is strongly enhanced by mode locking through nuclear focusing, where the synchronization of the electron spin to periodic pulsing is slowly transferred to the nuclear spins of the semiconductor material, mediated by the hyperfine interaction between these. The external magnetic field that drives the Larmor oscillations of the electron spin also subjects the nuclear spins to a Zeeman-like coupling, albeit a much weaker one. For typical magnetic fields used in experiments, the energy scale of the nuclear Zeeman effect is comparabl…
We calculate the nonlinear cotunneling conductance through interacting quantum dot systems in the deep Coulomb blockade regime using a rate equation approach based on the T-matrix formalism, which shows in the concerned regions very good agreement with a generalized master equation approach. Our focus is on inelastic cotunneling in systems with weakly broken degeneracies, such as complex quantum dots or molecules. We find for these systems a characteristic gate dependence of the non-equilibrium cotunneling conductance. While on one side of a Coulomb diamond the conductance decreases after the …
The Generalized Kohn Theorem in arrays of parabolic quantum dots with Coulomb interaction between the dots is violated, if there are different dot species involved. We solve the Schrödinger equation for cubic lattices with two different dots per unit cell: i) two different circular dots and ii) two elliptical dots, which are rotated by $90^o$ relative to each other. The interaction between the dots is considered in dipole approximation and long-- wavelength excitation spectra including FIR intensities are calculated. The energy spectrum of the first case can be expressed as a superposition of …
When treating interactions in quantum dots within a RPA-like approach, time-reversal symmetry plays an important role as higher-order terms -- the Cooper series -- need to be included when this symmetry is present. Here we consider model quantum dots in a magnetic field weak enough to leave the dynamics of the dot chaotic, but strong enough to break time-reversal symmetry. The ground state spin and addition energy for dots containing 120 to 200 electrons are found using local spin density functional theory, and we compare the corresponding distributions with those derived from an RPA-like trea…
Time-dependent electron transport through a quantum dot and double quantum dot systems in the presence of polychromatic external periodic quantum dot energy-level modulations is studied within the time evolution operator method for a tight-binding Hamiltonian. Analytical relations for the dc-current flowing through the system and the charge accumulated on a quantum dot are obtained for the zero-temperature limit. It is shown that in the presence of periodic perturbations the sideband peaks of the transmission are related to combination frequencies of the applied modulations. For a double quant…
Quantum dots in magnetic fields are studied within the current spin density functional formalism avoiding any spatial symmetry restrictions of the solutions. We find that the maximum density droplet reconstructs into states with broken internal symmetry: The Chamon-Wen edge co-exists with a modulation of the charge density along the edge. The phase boundaries between the polarization transition, the maximum density droplet and its reconstruction are in agreement with recent experimental results.
We investigate theoretically the electron states in HgTe quantum dots (QDs) with inverted band structures. In sharp contrast to conventional semiconductor quantum dots, the quantum states in the gap of HgTe quantum dot with an inverted band structure are fully spin-polarized, and show ring-like density distributions near the boundary of the QD and spin-angular momentum locking. The persistent charge currents and magnetic moments, i.e., the Aharonov-Bohm effect, can be observed in such QD structure and oscillate with increasing magnetic fields. This feature offers us a practical way to detect t…
We present measurements of transport through two tunnel-coupled quantum dots of different sizes connected in series in a strong, variable, perpendicular magnetic field. Double dot conductance was measured both as a function of magnetic field, which was varied across the filling factor nu = 4 quantum Hall plateau, and as a function of charge induced evenly on the two dots. The conductance peaks undergo position shifts and height modulations as the magnetic field is varied. These shifts and modulations form a pattern that repeats over large ranges of magnetic field and with the addition of doubl…
Generating and detecting radiation in the technologically relevant range of the so-called terahertz gap ($0.1 - 10$ THz) is challenging because of a lack of efficient sources and detectors. Quantum dots in carbon nanotubes have shown great potential to build sensitive terahertz detectors usually based on photon-assisted tunnelling. A recently reported mechanism combining resonant quantum dot transitions and tunnelling barriers asymmetries results in a narrow linewidth photocurrent response with a large signal-to-noise ratio under weak THz radiation. That device was sensitive to one frequency, …
We study theoretically the electron states in a system of two vertically stacked quantum dots. We investigate the influence of the geometrical symmetry breaking (caused by the displacement as well as the ellipticity of the dots) on the electron states. Our modeling is based on the 8-band kp method. We show that the absence of axial symmetry of the system leads to a coupling of the s state from one dot with the p and d states from the other. Our findings indicate, that this coupling can produce a strong energy splitting at resonance (on the order of several meV) in the case of closely spaced qu…
The main obstacle to coherent control of two-level quantum systems is their coupling to an uncontrolled environment. For electron spins in III-V quantum dots, the random environment is mostly given by the nuclear spins in the quantum dot host material; they collectively act on the electron spin through the hyperfine interaction, much like a random magnetic field. Here we show that the same hyperfine interaction can be harnessed such that partial control of the normally uncontrolled environment becomes possible. In particular, we observe that the electron spin resonance frequency remains locked…
Electrostatically defined quantum dots (QDs) in Bernal stacked bilayer graphene (BLG) are a promising quantum information platform because of their long spin decoherence times, high sample quality, and tunability. Importantly, the shape of QD states determines the electron energy spectrum, the interactions between electrons, and the coupling of electrons to their environment, all of which are relevant for quantum information processing. Despite its importance, the shape of BLG QD states remains experimentally unexamined. Here we report direct visualization of BLG QD states by using a scanning …
We present a tight-binding theory of triangular graphene quantum dots (TGQD) with zigzag edge and broken sublattice symmetry in external magnetic field. The lateral size quantization opens an energy gap and broken sublattice symmetry results in a shell of degenerate states at the Fermi level. We derive a semi-analytical form for zero-energy states in a magnetic field and show that the shell remains degenerate in a magnetic field, in analogy to the 0th Landau level of bulk graphene. The magnetic field closes the energy gap and leads to the crossing of valence and conduction states with the zero…
The optically induced polarization of localized electron spins in an ensemble of quantum dots (QDs) dephases due to the interaction with the surrounding nuclear spins. Despite this dephasing, the spins in the QDs can be controlled to respond coherently by applying periodic laser pulses, leading to a revival of the spin polarization before each pulse. This effect, known as spin mode locking, strongly depends on an emerging selection of certain polarizations of the nuclear spin bath which is driven to a steady state far from equilibrium. We investigate the influence of the nuclear composition in…
We develop a microscopic and atomistic theory of electron spin-based qubits in gated quantum dots in a single layer of transition metal dichalcogenides. The qubits are identified with two degenerate locked spin and valley states in a gated quantum dot. The two-qubit states are accurately described using a multi-million atom tight-binding model solved in wavevector space. The spin-valley locking and strong spin-orbit coupling result in two degenerate states, one of the qubit states being spin-down located at the $+K$ valley of the Brillouin zone, and the other state located at the $-K$ valley w…
Full distributions of conductance through quantum dots with single-mode leads are reported for both broken and unbroken time-reversal symmetry. Distributions are nongaussian and agree well with random matrix theory calculations that account for a finite dephasing time, $τ_ϕ$, once broadening due to finite temperature $T$ is also included. Full distributions of the derivatives of conductance with respect to gate voltage $P(dg/dV_g)$ are also investigated.
We study coherent oscillations in double quantum dots tunnel-coupled to metallic leads by means of full counting statistics of electron transport. If two such systems are coupled by Coulomb interaction, there are in total six (instead of only two) oscillation modes of the entangled system with interaction-dependent oscillation frequencies. By tuning the bias voltage, one can engineer decoherence such that only one of the six modes, in which the charge oscillations in both double quantum dots become synchronized in antiphase, is singled out. We suggest to use waiting-time distributions and the …
We study the effect of electron-electron interaction on the conductance of open quantum dots. We find that Coulomb interactions (i) do not affect the ensemble averaged conductance <G> if time-reversal symmetry has been broken by a magnetic field, (ii) enhance weak localization and weak anti-localization corrections to <G> in the absence of a magnetic field, (iii) increase conductance fluctuations, and (iv) enhance the effect of short trajectories on the conductivity of quantum dot.
The dynamics of the coupled electron-nuclear spin system is studied in an ensemble of singly-charged (In,Ga)As/GaAs quantum dots (QDs) using periodic optical excitation at 1 GHz repetition rate. In combination with the electron-nuclei interaction, the highly repetitive excitation allows us to lock the electron spins into magnetic resonance in a transverse external magnetic field. Sweeping the field to higher values, the locking leads to an effective "diamagnetic" response of significant strength due to dynamic nuclear polarization, which shields the QD electrons at least partly from the extern…
Whereas the concept of topological band-structures was developed originally for insulators with a bulk bandgap, it has become increasingly clear that the prime consequences of a non-trivial topology -- spin-momentum locking of surface states -- can also be encountered in gapless systems. Concentrating on the paradigmatic example of mercury chalcogenides HgX (X = Te, Se, S), we show that the existence of helical semimetals, i.e. semimetals with topological surface states, critically depends on the presence of crystal inversion symmetry. An infinitesimally small broken inversion symmetry (BIS) r…
Realistic relaxed configurations of triaxially strained graphene quantum dots are obtained from unbiased atomistic mechanical simulations. The local electronic structure and quantum transport characteristics of y-junctions based on such dots are studied, revealing that the quasi-uniform pseudomagnetic field induced by strain restricts transport to Landau level- and edge state-assisted resonant tunneling. Valley degeneracy is broken in the presence of an external field, allowing the selective filtering of the valley and chirality of the states assisting in the resonant tunneling. Asymmetric str…
Solid-state qubits integrated on semiconductor substrates currently require at least one wire from every qubit to the control electronics, leading to a so-called wiring bottleneck for scaling. Demultiplexing via on-chip circuitry offers an effective strategy to overcome this bottleneck. In the case of gate-defined quantum dot arrays, specific static voltages need to be applied to many gates simultaneously to realize electron confinement. When a charge-locking structure is placed between the quantum device and the demultiplexer, the voltage can be maintained locally. In this study, we implement…
Understanding strongly interacting electrons enables the design of materials, nanostructures and devices. Developing this understanding relies on the ability to tune and control electron-electron interactions by, e.g., confining electrons to atomically thin layers of 2D crystals with reduced screening. The interplay of strong interactions on a hexagonal lattice with two nonequivalent valleys, topological moments, and the Ising-like spin-orbit interaction gives rise to a variety of phases of matter corresponding to valley and spin polarized broken symmetry states. In this work we describe a hig…
We present a microscopic theory of the nonequilibrium nuclear spin dynamics driven by the electron and/or hole under continuous wave pumping in a quantum dot. We show the correlated dynamics of the nuclear spin ensemble and the electron and/or hole under optical excitation as a quantum feedback loop and investigate the dynamics of the many nuclear spins as a nonlinear collective motion. This gives rise to three observable effects: (i) hysteresis, (ii) locking (avoidance) of the pump absorption strength to (from) the natural resonance, and (iii) suppression (amplification) of the fluctuation of…
Using spin-density-functional theory, we study the electronic states of a two-dimensional parabolic quantum dot with up to N=58 electrons. We observe a shell structure for the filling of the dot with electrons. Hund's rule determines the spin configuration of the ground state, but only up to 22 electrons. At specific N, the ground state is degenerate, and a small elliptical deformation of the external potential induces a rotational charge-density-wave (CDW) state. Previously identified spin-density-wave (SDW) states are shown to be artifacts of broken spin symmetry in density-functional theory…
We investigate the electronic and transport properties of topological and trivial InAs$_{1-x}$Bi$_x$ quantum dots (QDs). By considering the rapid band gap change within valence band anticrossing theory for InAs$_{1-x}$Bi$_x$, we predicted that Bi-alloyed quantum wells become $\sim 30$meV gapped 2D topological insulators for well widths $d>6.9$nm $(x = 0.15)$ and obtain the $\boldsymbol{k.p}$ parameters of the corresponding Bernevig-Hughes-Zhang (BHZ) model. We analytically solve this model for cylindrical confinement via modified Bessel functions. For non-topological dots we find "geometricall…
Resonant optical excitation of lowest-energy excitonic transitions in self-assembled quantum dots lead to nuclear spin polarization that is qualitatively different from the well known optical orientation phenomena. By carrying out a comprehensive set of experiments, we demonstrate that nuclear spin polarization manifests itself in quantum dots subjected to finite external magnetic field as locking of the higher energy Zeeman transition to the driving laser field, as well as the avoidance of the resonance condition for the lower energy Zeeman branch. We interpret our findings on the basis of dy…
The quantum dot arrays (QDAs) embedded into inhomogeneous nanowires connected to metallic electrodes show an electron heat rectification effect, which is attributed to the thermal voltage arising from a temperature bias and the QDA with a broken spatial inversion symmetry. The staircase energy levels of QDAs can be controlled to the resonant and off resonant transports for electrons in the forward and backward temperature biases, respectively. The effect of electron Coulomb interactions on the rectification efficiency of heat diode is clarified by the case of double QDs. We find that it is imp…
Spin-momentum locking is essential to the spin-split Fermi surfaces of inversion-symmetry broken materials, which are caused by either Rashba-type or Zeeman-type spin-orbit coupling (SOC). While the effect of Zeeman-type SOC on superconductivity has experimentally been shown recently, that of Rashba-type SOC remains elusive. Here we report on convincing evidence for the critical role of the spin-momentum locking on crystalline atomic-layer superconductors on surfaces, for which the presence of the Rashba-type SOC is demonstrated. In-situ electron transport measurements reveal that in-plane upp…
Motivated by activities of several experimental groups we investigate electron transport through two coherent, strongly coupled quantum dots ("double quantum dots"), taking into account both intra- and inter-dot Coulomb interactions. The shot noise in this system is very sensitive to the internal electronic level structure of the coupled dot system and its specific coupling to the electrodes. Accordingly a comparison between experiments and our predictions should allow for a characterization of the relevant parameters. We discuss in detail the effect of asymmetries, either asymmetries in the c…
We investigate the statistical fluctuations of currents in chaotic quantum dots induced by pumping and rectification at finite temperature and in the presence of dephasing. In open quantum dots, dc currents can be generated by the action of two equal-frequency ac gate voltages. The adiabatic regime occurs when the driving frequency is smaller than the electron inverse dwell time. Using numerical simulations complemented by semiclassical calculations, we consider both limits of small and large number of propagating channels in the leads when time-reversal symmetry is fully broken. We find that …
We evaluate the spin density oscillations arising in quantum spin Hall quantum dots created via two localized magnetic barriers. The combined presence of magnetic barriers and spin-momentum locking, the hallmark of topological insulators, leads to peculiar phenomena: a half-integer charge is trapped in the dot for antiparallel magnetization of the barriers, and oscillations appear in the in-plane spin density, which are enhanced in the presence of electron interactions. Furthermore, we show that the number of these oscillations is determined by the number of particles inside the dot, so that t…
Magnetic semiconductor quantum dots with a few carriers represent an interesting model system where ferromagnetic interactions can be tuned by voltage. By designing the geometry of a doped quantum dot, one can tailor the anisotropic quantum states of magnetic polarons. The strong anisotropy of magnetic polaron states in disk-like quantum dots with holes comes from the spin splitting in the valence band. The binding energy and spontaneous magnetization of quantum dots oscillate with the number of particles and reflect the shell structure. Due to the Coulomb interaction, the maximum binding ener…
We study numerically the production of orbital and spin entangled states in chaotic quantum dots for non-interacting electrons. The introduction of spin-orbit coupling permit us to identify signatures of time-reversal symmetry correlations in the entanglement production previously unnoticed, resembling weak-(anti)localization quantum corrections to the conductance. We find the entanglement to be strongly dependent on spin-orbit coupling, showing universal features for broken time-reversal and spin-rotation symmetries.
Chiral light-matter interaction between photonic nanostructures with quantum emitters shows great potential to implement spin-photon interfaces for quantum information processing. Position-dependent spin momentum locking of the quantum emitter is important for these chiral coupled nanostructures. Here, we report the position-dependent chiral coupling between quantum dots (QDs) and cross waveguides both numerically and experimentally. Four quantum dots distributed at different positions in the cross section are selected to characterize the chiral properties of the device. Directional emission i…
We report growth and characterization of a coupled quantum dot structure that utilizes nanowire templates for selective epitaxy of radial heterostructures. The starting point is a zinc blende InAs nanowire with thin segments of wurtzite structure. These segments have dual roles: they act as tunnel barriers for electron transport in the InAs core, and they also locally suppress growth of a GaSb shell, resulting in coaxial InAs-GaSb quantum dots with integrated electrical probes. The parallel quantum dot structure hosts spatially separated electrons and holes that interact due to the type-II bro…
Transport through two quantum dots laterally embedded in Aharonov-Bohm interferometry with infinite intradot and arbitrary interdot Coulomb repulsion is analyzed in the weak coupling and Coulomb blockade regime. By employing the modified quantum rate equations and the slave-boson approach, we establish a general dc current formula at temperatures higher than the Kondo temperature for the case that the spin degenerate levels of two dots are close to each other. We examine two simple examples for identical dots - no doubly occupied states and no empty state. In the former, completely destructive…
We present a theory for the electronic and magneto-optical properties of spherical quantum dots consisting of an inner core surrounded by an outer shell. This core-shell quantum dot is doped by magnetic Mn impurities all of which are implanted at a preselected radius on a spherical surface within the dot. The spherical symmetry of the dot is broken by the application of an external magnetic field. The electronic states in the presence of a magnetic field are treated in an effective mass model which includes the s-d and p-d exchange interaction with localized Mn d electrons. The strain in the q…
Similar to atoms and nuclei, semiconductor quantum dots exhibit formation of shells. Predictions of magnetic behavior of the dots are often based on the shell occupancies. Thus, closed-shell quantum dots are assumed to be inherently nonmagnetic. Here, we propose a possibility of magnetism in such dots doped with magnetic impurities. On the example of the system of two interacting fermions, the simplest embodiment of the closed-shell structure, we demonstrate the emergence of a novel broken-symmetry ground state that is neither spin-singlet nor spin-triplet. We propose experimental tests of our…
A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or translational symmetry of the underlying jellium background. We study properties of a floating Wigner molecule in few-electron spin-polarized quantum dots, and show that the floating solid has the lower energy than the standard Wigner crystal with fixed lattice points. We also argue that internal rotational symmetry of individual dots can be broken in arrays …
The Josephson effect describes supercurrent flowing through a junction connecting two superconducting leads by a thin barrier [1]. This current is driven by a superconducting phase difference $ϕ$ between the leads. In the presence of chiral and time reversal symmetry of the Cooper pair tunneling process [2] the current is strictly zero when $ϕ$ vanishes. Only if these underlying symmetries are broken the supercurrent for $ϕ=0$ may be finite [3-5]. This corresponds to a ground state of the junction being offset by a phase $ϕ_{0}$, different from 0 or $π$. Here, we report such a Josephson $ϕ_{0}…
The exchange coupling between quantum dot spin qubits is isotropic, which restricts the types of quantum gates that can be formed. Here, we propose a method for controlling anisotropic interactions between spins arranged in a bus geometry. The symmetry is broken by an external magnetic field, resulting in XXZ-type interactions that can efficiently generate Greenberger-Horne-Zeilinger (GHZ) states or universal gate sets for exchange-only quantum computing. Analysis of the bus ground state provides a link between quantum critical phenomena and the communication capacity.
The magnetic field dependence of energy levels in gapped single- and bilayer graphene quantum dots (QDs) defined by electrostatic gates is studied analytically in terms of the Dirac equation. Due to the absence of sharp edges in these types of QDs, the valley degree of freedom is a good quantum number. We show that its degeneracy is efficiently and controllably broken by a magnetic field applied perpendicular to the graphene plane. This opens up a feasible route to create well-defined and well controlled spin- and valley-qubits in graphene QDs. We also point out the similarities and difference…
The dependence of mesoscopic conductance fluctuations on parallel magnetic field is used as a probe of spin degeneracy in open GaAs quantum dots. The variance of fluctuations at high parallel field is reduced from the low-field variance (with broken time-reversal symmetry) by factors ranging from roughly two in a 1 square-micron dot at low temperature, to four or greater in 8 square-micron dots. The factor of two is expected for simple Zeeman splitting of spin degenerate channels. A possible explanation for the unexpected larger factors in terms of field-dependent spin orbit scattering is prop…
