Orbital Quantization Research Articles

Minimal Quantization Model in Pilot-Wave Hydrodynamics.

Investigating how classical systems may manifest dynamics analogous to those of quantum systems is a broad subject of fundamental interest. Walking droplets, which self-propel through a resonant interaction with their own wave field, provide a unique macroscopic realization of wave-particle duality that exhibits behaviors previously thought exclusive to quantum particles. Despite significant efforts, elucidating the precise origin and form of the wave-mediated forces responsible for the walker's quantumlike behavior remained elusive. Here, we demonstrate that, owing to wave interference, the force responsible for orbital quantization originates from waves excited near stationary points on the walker's past trajectory. Moreover, we derive a minimal model with the essential ingredients to capture quantized orbital dynamics, including quasiperiodic and chaotic orbits. Notably, this minimal model provides an explicit distinction between local forces, which account for the walker's preferred speed and wave-induced added mass, and spatiotemporal nonlocal forces responsible for quantization. The quantization mechanism revealed here is generic, and will thus play a role in other hydrodynamic quantum analogs.

Electric field-tuneable crossing of hole Zeeman splitting and orbital gaps in compressively strained germanium semiconductor on silicon

With the emergence of the quantum computing era, the spin physics of engineered semiconductor materials with large and tuneable effective g*-factor, which is a measure of the interaction between the magnetic field and the spin of the particle, has become of great interest because it offers new physics and engineering tools for spin’s manipulation and its addressable control. Here we suggest a semi-empirical method to determine out of plane effective g*-factor in high mobility 2D hole heterostructures. We experimentally study the electric-field tuneablity of effective g*-factor of holes in a strained germanium quantum well heterostructure. As a result of the material’s engineering, the g*-factor can be tuned in a large range from 13 to 24 that corresponds to the tuneable Zeeman spin splitting of heavy holes in the range from smaller, to equal, and to larger than the orbital Landau level quantization gap.

Quantum geometry, flat Chern bands, and Wannier orbital quantization

Flat bands provide a natural platform for emergent electronic states beyond Landau paradigm. Among those of particular importance are flat Chern bands, including bands of higher Chern numbers ($C$$>$$1$). We introduce a new framework for band flatness through wave functions, and classify the existing isolated flat bands in a "periodic table" according to tight binding features and wave function properties. Our flat band categorization encompasses seemingly different classes of flat bands ranging from atomic insulators to perfectly flat Chern bands and Landau Levels. The perfectly flat Chern bands satisfy Berry curvature condition $F_{xy} = \text{Tr} \, \mathcal G_{ij}$ which on the tight-binding level is fulfilled only for infinite-range models. Most of the natural Chern bands fall into category of $C=1$; the complexity of creating higher-$C$ flat bands is beyond the current technology. This is due to the breakdown of the microscopic stability for higher-$C$ flatness, seen atomistically e.g. in the increase of the hopping range bound as $\propto$$\sqrt{C} a$. Within our new formalism, we indicate strategies for bypassing higher-$C$ constraints and thus dramatically decreasing the implementation complexity.

Probing hole spin transport of disorder quantum dots via Pauli spin-blockade in standard silicon transistors

Single hole transport and spin detection is achievable in standard p-type silicon transistors owing to the strong orbital quantization of disorder based quantum dots. Through the use of the well acting as a pseudo-gate, we discover the formation of a double-quantum dot system exhibiting Pauli spin-blockade and investigate the magnetic field dependence of the leakage current. This enables attributes that are key to hole spin state control to be determined, where we calculate a tunnel coupling t c of 57 μeV and a short spin−orbit length l SO of 250 nm. The demonstrated strong spin−orbit interaction at the interface when using disorder based quantum dots supports electric-field mediated control. These results provide further motivation that a readily scalable platform such as industry standard silicon technology can be used to investigate interactions which are useful for quantum information processing.

Magnetic Field Effects in Optical Harmonics Generation by Excitons

Mechanisms that are responsible for the optical harmonics generation at exciton transitions are analyzed in several classes of materials. In the cubic GaAs semiconductor, the magneto-induced optical second-harmonic generation second optical harmonic is observed in the region of orbital quantization of the valence and conduction bands. An unusually strong amplitude of the optical third-harmonic generation in an external magnetic field in the region of 1s exciton due to exciton–polariton resonance is found. The optical second-harmonic generation due to 1s, 2s, and 2p exciton resonances in a magnetic field is revealed in a hexagonal wide band-gap ZnO semiconductor. Depending on the symmetry of the exciton states, the mechanisms of the optical second-harmonic generation involve the spin and orbital Zeeman effects, and the magneto-Stark effect. The magneto-induced contribution to second harmonic generation (SHG) in the region of exciton transitions in the Cr2O3 antiferromagnet placed in an external magnetic field is studied.

Эффекты магнитного поля в экситонной генерации оптических гармоник

Mechanisms responsible for the optical harmonics generation in several classes of materials at excitonic transitions are considered. In the cubic semiconductor GaAs, magnetically induced second harmonic generation (SHG) was observed in the region of orbital quantization for the valence and conduction bands. An unusually strong third harmonic generation was detected in the region of the 1s exciton in an external magnetic field due to the exciton-polariton resonance. Magnetic field induced SHG was revealed in the hexagonal wide bandgap semiconductor ZnO at exciton resonances 1s, 2s, and 2p. Depending on the symmetry of the exciton states, the SHG mechanisms are determined by the spin and orbital Zeeman effects, and the magneto-Stark effect. Magnetically induced contribution to SHG was studied in the antiferromagnet Cr2O3 at exciton transitions in an external magnetic field.

Landau quantization effects on hole-acoustic instability in semiconductor plasmas

The growth rate of the hole acoustic waves (HAWs) exciting in magnetized semiconductor quantum plasma pumped by the electron beam has been investigated. The instability of the waves contains quantum effects including the exchange and correlation potential, Bohm potential, Fermi-degenerate pressure, and the magnetic quantization of semiconductor plasma species. The effects of various plasma parameters, which include relative concentration of plasma particles, beam electron temperature, beam speed, plasma temperature (temperature of electrons/holes), and Landau electron orbital magnetic quantization parameter η, on the growth rate of HAWs, have been discussed. The numerical study of our model of acoustic waves has been applied, as an example, to the GaAs semiconductor exposed to electron beam in the magnetic field environment. An increment in either the concentration of the semiconductor electrons or the speed of beam electrons, in the presence of magnetic quantization of fermion orbital motion, enhances remarkably the growth rate of the HAWs. Although the growth rate of the waves reduces with a rise in the thermal temperature of plasma species, at a particular temperature, we receive a higher instability due to the contribution of magnetic quantization of fermions to it.

Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits.

We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an integro-differential trajectory equation, which is found to admit steady orbital solutions. Predictions for the dependence of the orbital radius and frequency on the strength of the radial harmonic force field agree favorably with experimental data. The orbital quantization is rationalized through an analysis of the orbital solutions. The predicted dependence of the orbital stability on system parameters is compared with experimental data and the limitations of the model are discussed.

Double-slit experiment with single wave-driven particles and its relation to quantum mechanics

In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

Current resonances and current platforms in a two-level InAs quantum dot with asymmetric terahertz irradiations

Both the charging and orbital quantization energies of InAs quantum dot (QD) typically correspond to the terahertz (THz) region. In this letter, under the asymmetric THz irradiations on two leads, electron transport through a two-level InAs QD is theoretically discussed. We demonstrate that when both the frequencies and amplitudes of THz irradiations on two leads are different with the higher asymmetry, the photon–electron pump effect vanishes, even a negative platform appears on the left of the Coulomb peak and a positive platform occurs on the right of the Coulomb interaction related energy level, respectively. This behavior is favorable for the design of THz optoelectronic device.

Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization

AbstractWe present the results of a theoretical investigation of droplets walking on a rotating vibrating fluid bath. The droplet’s trajectory is described in terms of an integro-differential equation that incorporates the influence of its propulsive wave force. Predictions for the dependence of the orbital radius on the bath’s rotation rate compare favourably with experimental data and capture the progression from continuous to quantized orbits as the vibrational acceleration is increased. The orbital quantization is rationalized by assessing the stability of the orbital solutions, and may be understood as resulting directly from the dynamic constraint imposed on the drop by its monochromatic guiding wave. The stability analysis also predicts the existence of wobbling orbital states reported in recent experiments, and the absence of stable orbits in the limit of large vibrational forcing.

Droplets walking in a rotating frame: from quantized orbits to multimodal statistics

AbstractWe present the results of an experimental investigation of a droplet walking on the surface of a vibrating rotating fluid bath. Particular attention is given to demonstrating that the stable quantized orbits reported by Fort et al. (Proc. Natl Acad. Sci., vol. 107, 2010, pp. 17515–17520) arise only for a finite range of vibrational forcing, above which complex trajectories with multimodal statistics arise. We first present a detailed characterization of the emergence of orbital quantization, and then examine the system behaviour at higher driving amplitudes. As the vibrational forcing is increased progressively, stable circular orbits are succeeded by wobbling orbits with, in turn, stationary and drifting orbital centres. Subsequently, there is a transition to wobble-and-leap dynamics, in which wobbling of increasing amplitude about a stationary centre is punctuated by the orbital centre leaping approximately half a Faraday wavelength. Finally, in the limit of high vibrational forcing, irregular trajectories emerge, characterized by a multimodal probability distribution that reflects the persistent dynamic influence of the unstable orbital states.

Terahertz Photon-Assisted Tunneling in InAs Quantum Dots

We have investigated electron transport in a single self-assembled InAs quantum dot (QD) coupled to nanogap metal electrodes under terahertz (THz) radiation. The fabricated QD samples operated as single electron transistors in a few electron regime, exhibiting clear shell structures. Under the THz radiation, in addition to the original Coulomb oscillation peaks, new side-peaks showed up. The dependence of the new side-peak current on the THz power follows the prediction of the photon-assisted tunneling (PAT) theory. Moreover, two types of PAT processes were observed in the THz range; the ground state resonance and the photon-induced excited state resonance, depending on the relative magnitude between the orbital quantization energy of the QDs and the THz photon energy. Furthermore, a very high coupling efficiency between the THz waves and the QDs was realized in our system and we observed multi-photon absorption up to the fourth-order during the tunneling process, resulting in almost complete lifting of the Coulomb blockade. This high coupling efficiency between THz wave and electrons in QDs opens a way to the manipulation of single electron charge/spin states in the THz frequency range.

Orbital quantization in a system of edge Dirac fermions in nanoperforated graphene

The dependence of the electric resistance R of nanoperforated graphene samples on the position of the Fermi level E F, which is varied by the gate voltage V g, has been studied. Nanoperforation has been performed by irradiating graphene samples on a Si/SiO2 substrate by heavy (xenon) or light (helium) ions. A series of regular peaks have been revealed on the R(V g) dependence at low temperatures in zero magnetic field. These peaks are attributed to the passage of E F through an equidistant set of levels formed by orbitally quantized states of edge Dirac fermions rotating around each nanohole. The results are in agreement with the theory of edge states for massless Dirac fermions.

Single electron transport through site-controlled InAs quantum dots

We have grown site- and size-controlled InAs quantum dots (QDs) in shallow nanoholes prepared using atomic force microscope-assisted anodic nano-oxidation and subsequent etching, and investigated their transport properties by depositing metal nanogap electrodes on a single QD. We have observed clear diamond-like patterns in Coulomb stability diagrams, indicating that the fabricated single QD transistors operate as single electron transistors and that the site-controlled QDs have a good crystalline quality. Furthermore, we show that the charging energies and the orbital quantization energies can be controlled over a wide range by controlling the size of the QDs.

Photon-Assisted Tunneling through Self-Assembled InAs Quantum Dots in the Terahertz Frequency Range

We have investigated terahertz (THz) photon-assisted tunneling in single self-assembled InAs quantum dots (QDs). Two types of photon-assisted tunneling processes have been observed in the THz range: ground state resonance and photon-induced excited state resonance, depending on the relative magnitude between the orbital quantization energy of the QDs and the THz photon energy. Furthermore, we could realize a very high coupling efficiency between THz waves and QDs and observed multiphoton absorption up to the fourth-order during the tunneling process, resulting in almost complete lifting of the Coulomb blockade.

Field-induced charge-density-wave transitions in the organic metal α-(BEDT-TTF)2KHg(SCN)4 under pressure

Successive magnetic-field-induced charge-density-wave transitions in the layered molecular conductor α-(BEDT-TTF)2KHg(SCN)4 are studied in a hydrostatic pressure regime in which the zero field charge-density- wave (CDW) state is completely suppressed. It is shown that the orbital effect of the magnetic field restores the density wave, while orbital quantization induces transitions between different CDW states as the field strength is varied. The latter show up as distinct anomalies in the magnetoresistance as a function of field. The interplay between the orbital and Pauli paramagnetic effects, which act, respectively, to enhance and to suppress the CDW instability, is particularly manifest in the angular dependence of the field-induced anomalies.

Quantization of Planetary Systems and its Dependency on Stellar Rotation

AbstractWith the discovery of now more than 500 exoplanets, we present a statistical analysis of the planetary orbital periods and their relationship to the rotation periods of their parent stars. We test whether the structural variables of planetary orbits, i.e. planetary angular momentum and orbital period, are ‘quantized’ in integer or half-integer multiples of the parent star's rotation period. The Solar System is first shown to exhibit quantized planetary orbits that correlate with the Sun's rotation period. The analysis is then expanded over 443 exoplanets to statistically validate this quantization and its association with stellar rotation. The results imply that the exoplanetary orbital periods are highly correlated with the parent star's rotation periods and follow a discrete half-integer relationship with orbital ranks n = 0.5, 1.0, 1.5, 2.0, 2.5, etc. The probability of obtaining these results by pure chance is p < 0.024. We discuss various mechanisms that could justify this planetary quantization, such as the hybrid gravitational instability models of planet formation, along with possible physical mechanisms such as the inner disc's magnetospheric truncation, tidal dissipation, and resonance trapping. In conclusion, we statistically demonstrate that a quantized orbital structure should emerge from the formation processes of planetary systems and that this orbital quantization is highly dependent on the parent star's rotation period.

Novel mechanisms of optical harmonics generation in semiconductors

AbstractSpectroscopic study of diamagnetic, diluted magnetic, and magnetically ordered semiconductors reveals several novel mechanisms of optical harmonics generation. It is found that Landau‐level orbital quantization of the band energy is a key mechanism for magnetic‐field‐induced second harmonic generation (MSHG) in diamagnetic semiconductors GaAs and CdTe. The giant Zeeman spin‐splitting of electronic states is essential for MSHG in diluted magnetic semiconductors (Cd,Mn)Te. Both mechanisms involving the optical nonlinearities of electric‐dipole type take place in noncentrosymmetric semiconductors. Spin‐induced second harmonic generation (SHG) is observed at the band gap in magnetic centrosymmetric semiconductors EuTe and EuSe. This mechanism involving the optical nonlinearities of magnetic‐dipole type is essential for centrosymmetric semiconductors. The magnetic field and temperature dependencies demonstrate that the nonlinear processes arise due to novel types of optical nonlinearities caused by the external magnetic field. The observed mechanisms of optical nonlinearities open access to a wide class of centrosymmetric and noncentrosymmetric systems by harmonics generation spectroscopy.

Control of tunnel coupling strength between InAs quantum dots and nanogap metallic electrodes through In-Ga intermixing

We have investigated the growth-temperature, T G, dependence of the electronic properties of single self-assembled InAs quantum dots (QDs) coupled to nanogap metallic electrodes. The orbital quantization energies of QDs and the tunnel resistances exhibited strong T G-dependence due to In-Ga intermixing during QD formation. It was found that the transparency of the tunnel junctions is controllable over a very wide range by simply changing the size and the growth temperature of QDs. By realizing strong QD-electrodes coupling, very high Kondo temperature T K∼80 K was observed in our InAs QD system.