Density functional theory calculations are performed on phosphorene quantum dots having different shapes and edge terminations to investigate their structure stability, electronic properties, and gas sensing ability. All the selected phosphorene dots, namely hexagonal and triangular flakes with armchair and zigzag terminations, have positive binding energies which insure their stability even though the bond lengths are much longer than those in the infinite phosphorene layer. It is found that all the selected hydrogen passivated quantum dots have a wide energy gap. In contrast, the partial passivation with sulfur decreases the gap. Moreover, it transforms the system from antiferromagnetic to ferromagnetic state. The energy gap of hexagonal zigzag cluster can be additionally tuned by electric field: narrowed by about 1.7 eV for hydrogenated or broadened by 0.25 eV for partially sulfurated edges. It is shown that phosphorene quantum dots successfully adsorb H2S, CH4, CO, NH3 gas molecules either on their edge or surface. The highest adsorption energy is obtained for NH3 molecule, when it is placed over the surface. This adsorption is alleviated by in-plane electric field and hindered by perpendicular field.
We study electronic and optical properties of single layer phosphorene quantum dots with various shapes, sizes, and edge types (including disordered edges) subjected to an external electric field normal to the structure plane. Compared to graphene quantum dots, in phosphorene clusters of similar shape and size there is a set of edge states with energies dispersed at around the Fermi level. These states make the majority of phosphorene quantum dots metallic and enrich the phosphorene absorption gap with low-energy absorption peaks tunable by the electric field. The presence of the edge states d…
Dielectric screening is greatly important to an accurate calculation of the exciton binding energies in two-dimensional materials. In this work, we calculate the dielectric function and 2D polarizability of multilayer (up to three) phosphorene sheets using Density Functional Theory. The 2D polarizabilities are then used in the dielectric screening of the excitonic interaction in multilayer phosphorene quantum dots. In the limit of large quantum dots, excitonic gaps are shown to exhibit very good agreement with state-of-the-art measurements of the optical gaps of multilayer phosphorene sheets d…
We study the addition energy spectra of phosphorene quantum dots focusing on the role of dot size, edges passivation, number of layers and dielectric constant of the substrate where the dots are deposited. We show that for sufficiently low dielectric constants ($\varepsilon_{sub} < 4$), Coulomb blockade can be observed in dot sizes larger than 10 nm, for both passivated and unpassivated edges. For higher dielectric constants (up to $\varepsilon_{sub} = 30$), Coulomb blockade demands smaller dot sizes, but this depends whether the edges are passivated or not. This dramatic role played by the su…
We theoretically investigate phosphorene zigzag nanorribons as a platform for constriction engineering. In the presence of a constriction at the upper edge, quantum confinement of edge protected states reveals resonant tunnelling Breit-Wigner transmission peaks, if the upper edge is uncoupled to the lower edge. Coupling between edges in thin constrictions gives rise to Fano-like and anti-resonances in the transmission spectrum of the system.
We consider states localized by electrostatic potentials in phosphorene using an atomistic tight binding approach. From the results of the tight-binding calculations of the confined states we extract effective masses for the conduction band electrons in the armchair and zigzag directions. The masses derived in this way are used for a simple single-band effective mass model which, as we find, reproduces very well the tight-binding energy spectrum in external magnetic field, the probability densities and the interaction effects. Both methods produce Wigner crystallization for the ground-state of…
We theoretically investigate the electronic and magneto-optical properties of rectangular, hexangular, and triangular monolayer phosphorene quantum dots (MPQDs) utilizing the tight-binding method. The electronic states, density of states, electronic density distribution, and Laudau levels as well as the optical absorption spectrum are calculated numerically. Our calculations show that: (1) edge states appear in the band gap in all kinds of MPQDs regardless of their shapes and edge configurations due to the anisotropic electron hopping in monolayer phosphorene (MLP). Electrons in any edge state…
Recently, black phosphorus quantum dots were fabricated experimentally. Motivated by these experiments, we theoretically investigate the electronic and optical properties of rectangular phosphorene quantum dots (RPQDs) in the presence of an in-plane electric field and a perpendicular magnetic field. The energy spectra and wave functions of RPQDs are obtained numerically using the tight-binding (TB) approach. We find edge states within the band gap of the RPQD which are well separated from the bulk states. In an undoped RPQD and for in-plane polarized light, due to the presence of well-defined …
Using the tight-binding approach, we investigate the electronic properties of bilayer phosphorene (BLP) quantum dots (QDs) in the presence of perpendicular electric and magnetic fields. Since BLP consists of two coupled phosphorene layers, it is of interest to examine the layer-dependent electronic properties of BLP QDs, such as the electronic distributions over the two layers and the so-produced layer-polarization features, and to see how these properties are affected by the magnetic field and the bias potential. We find that in the absence of a bias potential only edge states are layer-polar…
We study Wigner crystallization of electron systems in phosphorene quantum dots with confinement of an electrostatic origin with both circular and elongated geometry. The anisotropy of the effective mass allows for the formation of Wigner molecules in the laboratory frame with a confined charge density that has lower symmetry than the confinement potential. We find that in circular quantum dots separate single-electron islands are formed for two and four confined electrons but not for three trapped carriers. The spectral signatures of the Wigner crystallization to be resolved by transport spec…
We report on the theoretical electronic spectra of twisted phosphorene bilayers exhibiting moiré patterns, as computed by means of a continuous approximation to the moiré superlattice Hamiltonian. Our model is constructed by interpolating between effective $Γ$-point conduction- and valence-band Hamiltonians for the different stacking configurations approximately realized across the moiré supercell, formulated on symmetry grounds. We predict the realization of three distinct regimes for $Γ$-point electrons and holes at different twist angle ranges: a Hubbard regime for small twist angles $θ< 2^…
The adsorption behaviour of hazardous gas molecules, namely nitrogen dioxide (NO$_2$) and ammonia (NH$_3$), on phosphorene nanosheet (PNS) was explored by means of ab initio technique. To improve the structural solidity of pristine PNS, we have introduced the passivation of hydrogen and fluorine at the terminated edge. The structural solidity of both hydrogen and fluorine passivated PNS is verified in terms of formation energy. The main objective of this research work is to probe NO$_2$ and NH$_3$ gases using PNS as a base sensing material. The adsorption of various preferential adsorption sit…
The central question in the field of 2D materials is how a material behaves when it is patterned at nanometer scale with different edge geometries. Due to the anisotropy inherent in the puckered structure, black phosphorene nanostructures may have more varieties of edge geometries. Here, we present a comprehensive 2D planar crystallographic characterization of phosphorene uniformly by a chiral vector (angle), from which a new type of edge atomic configuration, the slope edge geometry is discovered. The phosphorene nanoribbons (PNRs) with slope edges, like previously noticed zigzag and skewed-a…
Measuring single-electron charge is one of the most fundamental quantum technologies. Charge sensing, which is an ingredient for the measurement of single spins or single photons, has been already developed for semiconductor gate-defined quantum dots, leading to intensive studies on the physics and the applications of single-electron charge, single-electron spin and photon-electron quantum interface. However, the technology has not yet been realized for self-assembled quantum dots despite their fascinating quantum transport phenomena and outstanding optical functionalities. In this paper, we r…
We demonstrate dispersive readout of individual charge states in a gate-defined few-electron quantum dot in bilayer graphene. We employ a radio frequency reflectometry circuit, where an LC resonator with a resonance frequency close to 280 MHz is directly coupled to an ohmic contact of the quantum dot device. The detection scheme based on changes in the quantum capacitance operates over a wide gate-voltage range and allows to probe excited states down to the single-electron regime. Crucially, the presented sensing technique avoids the use of an additional, capacitively coupled quantum device su…
Quantum dot arrays are a versatile platform for the implementation of spin qubits, as high-bandwidth sensor dots can be integrated with single-, double- and triple-dot qubits yielding fast and high-fidelity qubit readout. However, for undoped silicon devices, reflectometry off sensor ohmics suffers from the finite resistivity of the two-dimensional electron gas (2DEG), and alternative readout methods are limited to measuring qubit capacitance, rather than qubit charge. By coupling a surface-mount resonant circuit to the plunger gate of a high-impedance sensor, we realized a fast charge sensing…
Holes in silicon quantum dots are receiving significant attention due to their potential as fast, tunable, and scalable qubits in semiconductor quantum circuits. Despite this, challenges remain in this material system including difficulties using charge sensing to determine the number of holes in a quantum dot, and in controlling the coupling between adjacent quantum dots. In this work, we address these problems by fabricating an ambipolar complementary metal-oxide-semiconductor (CMOS) device using multilayer palladium gates. The device consists of an electron charge sensor adjacent to a hole …
We investigate gate-defined quantum dots in silicon on insulator nanowire field-effect transistors fabricated using a foundry-compatible fully-depleted silicon-on-insulator (FD-SOI) process. A series of split gates wrapped over the silicon nanowire naturally produces a $2\times n$ bilinear array of quantum dots along a single nanowire. We begin by studying the capacitive coupling of quantum dots within such a 2$\times$2 array, and then show how such couplings can be extended across two parallel silicon nanowires coupled together by shared, electrically isolated, 'floating' electrodes. With one…
The advanced nanoscale integration available in silicon complementary metal-oxide-semiconductor (CMOS) technology provides a key motivation for its use in spin-based quantum computing applications. Initial demonstrations of quantum dot formation and spin blockade in CMOS foundry-compatible devices are encouraging, but results are yet to match the control of individual electrons demonstrated in university-fabricated multi-gate designs. We show here that the charge state of quantum dots formed in a CMOS nanowire device can be sensed by using floating gates to electrostatically couple it to a rem…
We demonstrate fast readout of a double quantum dot (DQD) that is coupled to a superconducting resonator. Utilizing parametric amplification in a nonlinear operational mode, we improve the signal-to-noise ratio (SNR) by a factor of 2000 compared to the situation with the parametric amplifier turned off. With an integration time of 400 ns we achieve a SNR of 76. By studying SNR as a function of the integration time we extract an equivalent charge sensitivity of 8 x 10^{-5} e/root(Hz). The high SNR allows us to acquire a DQD charge stability diagram in just 20 ms. At such a high data rate, it is…
In Si quantum dots, valley degree of freedom, in particular the generally small valley splitting and the dot-dependent valley-orbit phase, adds complexities to the low-energy electron dynamics and the associated spin qubit manipulation. Here we propose a four-level model to extract tunnel coupling information for a Si double quantum dot (DQD). This scheme is based on a charge sensing measurement on the ground state as proposed in the widely used protocol for a GaAs double dot [DiCarlo et. al., PRL 92. 226801]. Our theory can help determine both intra- and inter-valley tunnel coupling with high…
We report direct detection of charge-tunneling between a quantum dot and a superconducting island through radio-frequency gate sensing. We are able to resolve spin-dependent quasiparticle tunneling as well as two-particle tunneling involving Cooper pairs. The quantum dot can act as an RF-only sensor to characterize the superconductor addition spectrum, enabling us to access subgap states without transport. Our results provide guidance for future dispersive parity measurements of Majorana modes, which can be realized by detecting the parity-dependent tunneling between dots and islands.
We demonstrate the use of the magnetic-field-dependence of highly spatially confined, GHz-frequency ferromagnetic resonances in a ferromagnetic nanostructure for the detection of adsorbed magnetic nanoparticles. This is achieved in a large area magnonic crystal consisting of a thin ferromagnetic film containing a periodic array of closely spaced, nano-scale anti-dots. Stray fields from nanoparticles within the anti-dots modify resonant dynamic magnetisation modes in the surrounding magnonic crystal, generating easily measurable resonance peak shifts. The shifts are comparable to the resonance …
Measurement of charge configurations in few-electron quantum dots is a vital technique for spin-based quantum information processing. While fast and high-fidelity measurement is possible by using proximal quantum dot charge sensors, their operating range is limited and prone to electrical disturbances. Here we demonstrate realtime operation of a charge sensor in a feedback loop to maintain its sensitivity suitable for fast charge sensing in a Si/SiGe double quantum dot. Disturbances to the charge sensitivity, due to variation of gate voltages for operating the quantum dot and $1/f$ charge fluc…
We demonstrate the application of a fiber-coupled quantum-dot-in-a-tip as a probe for scanning electric field microscopy. We map the out-of-plane component of the electric field induced by a pair of electrodes by measurement of the quantum-confined Stark effect induced on a quantum dot spectral line. Our results are in agreement with finite element simulations of the experiment. Furthermore, we present results from analytic calculations and simulations which are relevant to any electric field sensor embedded in a dielectric tip. In particular, we highlight the impact of the tip geometry on bot…
Quantum sensing exploits fundamental features of quantum mechanics and quantum control to realise sensing devices with potential applications in a broad range of scientific fields ranging from basic science to applied technology. The ultimate goal are devices that combine unprecedented sensitivity with excellent spatial resolution. Here, we propose a new platform for all-electric nanoscale quantum sensing based on a carbon nanotube double quantum dot. Our analysis demonstrates that the platform can achieve sensitivities that allow for the implementation of single-molecule magnetic resonance sp…
We study the detection of electrons undergoing coherent transfer via adiabatic passage (CTAP) in a triple quantum-dot system with a quantum point-contact sensing the change of the middle dot. In the ideal scenario, the protocol amounts to perfect change transfer between the external dots with vanishing occupation of the central dot at all times, rendering the measurement and its backaction moot. Nevertheless, even with minor corrections to the protocol, a small population builds up in the central dot. We study the measurement backaction by a Bayesian formalism simulation of an instantaneous de…
Dispersive sensing is a powerful technique that enables scalable and high-fidelity readout of solid-state quantum bits. In particular, gate-based dispersive sensing has been proposed as the readout mechanism for future topological qubits, which can be measured by single electrons tunneling through zero-energy modes. The development of such a readout requires resolving the coherent charge tunneling amplitude from a quantum dot in a Majorana-zero-mode host system faithfully on short time scales. Here, we demonstrate rapid single-shot detection of a coherent single-electron tunneling amplitude be…
We study double quantum dots in a Ge/SiGe heterostructure and test their maturity towards singlet-triplet ($S-T_0$) qubits. We demonstrate a large range of tunability, from two single quantum dots to a double quantum dot. We measure Pauli spin blockade and study the anisotropy of the $g$-factor. We use an adjacent quantum dot for sensing charge transitions in the double quantum dot at interest. In conclusion, Ge/SiGe possesses all ingredients necessary for building a singlet-triplet qubit.
Spin qubits in silicon quantum dots offer a promising platform for a quantum computer as they have a long coherence time and scalability. The charge sensing technique plays an essential role in reading out the spin qubit as well as tuning the device parameters and therefore its performance in terms of measurement bandwidth and sensitivity is an important factor in spin qubit experiments. Here we demonstrate fast and sensitive charge sensing by a radio-frequency reflectometry of an undoped, accumulation-mode Si/SiGe double quantum dot. We show that the large parasitic capacitance in typical acc…
Top-down fabricated nanoantenna architectures of both metallic and dielectric materials demonstrated powerful functionalities for Raman and fluorescence enhancement with relevance to single molecule sensing, while inducing directionality of chromophore emission with implications for single photon sources. Herein, we synthesize the smallest bowtie nanoantenna by selective tip-to-tip fusion of two tetrahedral colloidal quantum dots (CQDs) forming a dimer. While the tetrahedral monomers emit non-polarized light, the bowtie architecture manifests nanoantenna functionality of enhanced emission pola…
The valence band edge in tiny angle twist bilayers of MoS$_2$ and phosphorene is shown to consist of highly localized energy levels created by a `moiré quantum well', i.e. trapped by the interlayer moiré potential. These approximately uniformly spaced energy levels exhibit a richly modulated charge density, becoming ultra-localized at the valence band maximum. The number and spacing of such levels is controllable by the twist angle and interlayer interaction strength, suggesting the possibility of `moiré engineering' ordered arrays of quantum dots in 2d twist semi-conductors.
