Two-dimensional Quantum Research Articles

Strategies for the alignment of electronic states in quantum-dot tunnel-injection lasers

In quantum-dot tunnel-injection lasers, the excited charge carriers are efficiently captured from the bulk states via an injector quantum well and then transferred into the quantum dots via a tunnel barrier. The alignment of the electronic levels is crucial for the high efficiency of these processes and especially for the fast modulation dynamics of these lasers. In particular, the quantum mechanical nature of the tunneling process must be taken into account in the transition from two-dimensional quantum well states to zero-dimensional quantum-dot states. This results in hybrid states, from which the scattering into the quantum-dot ground states takes place. We combine electronic state calculations of the tunnel-injection structures with many-body calculations of the scattering processes and insert this into a complete laser simulator. This allows us to study the influence of the structural design and the resulting electronic states as well as limitations due to inhomogeneous quantum-dot distributions. We find that the optimal electronic state alignment deviates from a simple picture in which the quantum-dot ground state energies are one LO-phonon energy below the injector quantum well ground state.

All-optical quality control of indenene intercalation into graphene/SiC

Intercalating two-dimensional quantum materials beneath a sheet of graphene provides effective environmental protection and facilitates ex situ device fabrication. However, developing a functional device requires rapid, large-scale screening methods to evaluate the quality of the intercalant, which to date can be monitored only by slow, ultra-high vacuum-based surface science techniques. In this study, we utilize ex situ Raman micro-spectroscopy to optically and nondestructively identify the quantum spin Hall insulator indenene, a monolayer of indium sandwiched between a SiC(0001) substrate and a single sheet of graphene. Color modulation combined with indenene's distinctive low-frequency Raman fingerprint enables rapid assessment of its homogeneity and crystalline quality. Density functional perturbation theory indicates that this Raman signature originates mainly from indenene's shear and breathing modes, while additional higher order modes are tentatively attributed to defect-assisted and two-phonon Raman processes.

Thermodynamic Properties of an Electron Gas in a Two-Dimensional Quantum Dot: An Approach Using Density of States

Potential applications of quantum dots in the nanotechnology industry make these systems an important field of study in various areas of physics. In particular, thermodynamics has a significant role in technological innovations. With this in mind, we studied some thermodynamic properties in quantum dots, such as entropy and heat capacity, as a function of the magnetic field over a wide range of temperatures. The density of states plays an important role in our analyses. At low temperatures, the variation in the magnetic field induces an oscillatory behavior in all thermodynamic properties. The depopulation of subbands is the trigger for the appearance of the oscillations.

Observation of Robust One-Dimensional Edge Channels in a Three-Dimensional Quantum Spin Hall Insulator

Topologically protected edge channels show prospects for quantum devices. They have been found experimentally in two-dimensional quantum spin Hall insulators (QSHIs), weak topological insulators, and higher-order topological insulators, but the number of materials realizing these topologies is still quite limited. Here, we provide evidence for topological edge states within a novel topology named three-dimensional QSHIs. Its topology originates solely from a nonzero Sz spin Chern number for each kz plane of the crystal and is realized in bulk α−Bi4I4 with trivial symmetry indicators, as we show by density-functional-theory calculations. We experimentally observe the related edge states at each type of monolayer and bilayer step of this material by scanning tunneling microscopy. Consistently, the edge states are neither interrupted nor backscattered by defects at the step edges corroborating their helical character as expected from the nontrivial topology. Furthermore, two individual edge channels are directly observed at bilayer steps without visible interaction gap opening, demonstrating the robustness of these edge modes against vertical stacking. Our results establish α−Bi4I4 as the first material realization of a 3D QSHI whose definition goes beyond the scope of topological symmetry indicators, and provide a pathway for realizing nearly quantized spin Hall conductivity per unit cell in a bulk crystal. Published by the American Physical Society 2024

On Krichever tau-function and Verlinde formula

We remind the definition and main properties of the Krichever quasiclassical tau-function, and turn to the application of these formulas for recent studies of two-dimensional quantum gravity. We show, that in the case of minimal gravity it turns to be directly related with the Verlinde formula for minimal models, giving in particular case its one more direct proof. Generalizations for continuous “complex Liouville” theory are also briefly discussed.

Layer codes

Quantum computers require memories that are capable of storing quantum information reliably for long periods of time. The surface code is a two-dimensional quantum memory with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet optimal code was not previously known. Here we present a family of three dimensional topological codes with optimal scaling code parameters and a polynomial energy barrier. Our codes are based on a construction that takes in a stabilizer code and outputs a three-dimensional topological code with related code parameters. The output codes are topological defect networks formed by layers of surface code joined along one-dimensional junctions, with a maximum stabilizer check weight of six. When the input is a family of good quantum low-density parity-check codes the output codes have optimal scaling. Our results uncover strongly-correlated states of quantum matter that are capable of storing quantum information with the strongest possible protection from errors that is achievable in three dimensions.

Controlled synthesis of branched 2D polytypic CdS quantum nanostructures

Colloidal two-dimensional (2D) semiconductor quantum nanostructures have attracted substantial interest owing to their atomically uniform thickness and spectrally sharp luminescence, exhibiting potential for optoelectronic and electronic device applications. Despite recent advancements in chemical synthesis enabling better control over lateral shapes and heterostructures, achieving morphological complexity in 2D semiconductor nanocrystals remains challenging. In this study, we report the controlled synthesis of branched 2D CdS quantum nanostructures, facilitating the realization of polytypism by growing zinc blende nano-domains within wurtzite-structured quantum nanoplates. The synthesized structures comprise multi-branched 2D quantum nanoplate arms with a precisely controlled thickness of ∼1.8 nm, joined at the zinc blende nano-domain junctions. The reaction conditions enable controlled variation in the length and complexity of these structures, while maintaining their sharp excitonic features of quantum-confined 2D semiconductor nanocrystals. In-situ small- and wide-angle X-ray scattering analysis, combined with spectroscopic and microscopic analyses, reveals that a discontinuous increase in thickness beyond a certain threshold is necessary to form zinc blende crystals within wurtzite nanoplates, upon which additional 2D quantum nanoplates subsequently grow. This study advances our understanding of 2D nanocrystal synthesis mechanisms and provides pathways for designing and fabricating branched 2D nanostructures with tailored properties.

Modified Martin-Puplett interferometer for magneto-optical Kerr effect measurements at sub-THz frequencies.

We present a magneto-optical Kerr effect (MOKE) spectrometer based on a modified Martin-Puplett interferometer, utilizing continuous wave sub-THz low-power radiation in a broad frequency range. This spectrometer is capable of measuring the frequency dependence of the MOKE response function, both the Kerr rotation and ellipticity, simultaneously, with accuracy limited by a sub-milliradian threshold, without the need for a reference measurement. The instrument's versatility allows it to be coupled to a cryostat with optical windows, enabling studies of a variety of quantum materials such as unconventional superconductors, two-dimensional electron gas systems, quantum magnets, and other systems showing optical Hall response at sub-Kelvin temperatures and in high magnetic fields. We demonstrate the functionality of the MOKE spectrometer using an undoped InSb wafer as a test sample.

Influence of pH on the Formation of Benzyl Ester Bonds Between Dehydrogenation Polymers and Konjac Glucomannan.

A thorough understanding of the lignin-carbohydrate complex (LCC) structure has a significant meaning in the high-value utilization of lignocellulose. In this work, the complex (DHPKGC) was obtained by an addition reaction between konjac glucomannan (KGM) and quinone methides generated in the synthesis of dehydrogenation polymers (DHPs) to simulate the formation of LCCs. The effect of pH on the prepared DHPKGC was investigated. The structure of the DHPKGC was characterized by Fourier Transform Infrared (FTIR), 13C-Nuclear Magnetic Resonance (13C-NMR), and two-dimensional Heteronuclear Single Quantum Coherence Nuclear Magnetic Resonance (2D HSQC NMR) analyses. The results indicated the pH of 4.0 was conducive to the polymerization reaction between DHPs and oxidized KGM by the TEMPO/NaClO/NaBr system. In addition, the resultant DHPKGC was connected by benzyl ester linkages. Overall, this study aims to gain greater insight into the process of LCC formation in plants.

Realizing multiband states with ultracold dipolar quantum simulators

The manipulation of dipolar interactions within ultracold molecular ensembles represents a pivotal advancement in experimental physics, aiming at the emulation of quantum phenomena unattainable through mere contact interactions. Our study uncovers regimes of multiband occupation which allow to probe more realistic, complex long-range interacting lattice models with ultracold dipolar simulators. By mapping out experimentally relevant ranges of potential depths, interaction strengths, particle fillings, and geometric configurations, we calculate the agreement between the state prepared in the quantum simulator and a target lattice state. We do so by separately calculating numerically exact many-body wave functions in the continuous space and single- or multiband lattice representations, and building their many-body state overlaps. Our findings reveal that for shallow lattices and stronger interactions above half filling, multiband population increases, resulting in fundamentally different ground states than the ones observed in simple lowest-band descriptions, e.g., striped vs checkerboard states. A wide range of probed parameter regimes in its turn provides a systematic and quantitative blueprint for realizing multiband states with two-dimensional quantum simulators employing ultracold dipolar molecules. Published by the American Physical Society 2024

Cornertronics in Two-Dimensional Second-Order Topological Insulators.

Traditional electronic devices rely on the electron's intrinsic degrees of freedom (d.o.f.) to process information. However, additional d.o.f., like the valley, can emerge in the low-energy states of certain systems. Here, we show that the quantum dots constructed from two-dimensional second-order topological insulators posses a new kind of d.o.f., namely corner freedom, related to the topological corner states that reside at different corners of the systems. Since the corner states are well separated in real space, they can be individually and intuitively manipulated, giving rise to the concept of cornertronics. Via symmetry analysis and material search, we identify the TiSiCO-family monolayers as the first prototype of cornertronics materials, where the corner states can be controlled by both electric and optical fields due to novel corner-layer coupling effect and corner-contrasted linear dichroism. Furthermore, we find that the band gap of the TiSiCO nanodisk lies in the terahertz region and is robust to size reduction. These results indicate that the TiSiCO nanodisks can be used to design terahertz devices with ultrasmall size and electric-field tunable band gap. Besides, the TiSiCO nanodisks are simultaneously sensitive to both the strength and polarization of the terahertz waves. Our findings not only pave the way for cornertronics, but also open a new direction for research in two-dimensional second-order topological insulators, quantum dots, and terahertz electronics.

Model and Energy Bounds for a Two-Dimensional System of Electrons Localized in Concentric Rings.

We study a two-dimensional system of interacting electrons confined in equidistant planar circular rings. The electrons are considered spinless and each of them is localized in one ring. While confined to such ring orbits, each electron interacts with the remaining ones by means of a standard Coulomb interaction potential. The classical version of this two-dimensional quantum model can be viewed as representing a system of electrons orbiting planar equidistant concentric rings where the kinetic energy may be discarded when one is searching for the lowest possible energy. Within this framework, the lowest possible energy of the system is the one that minimizes the total Coulomb interaction energy. This is the equilibrium energy that is numerically determined with high accuracy by using the simulated annealing method. This process allows us to obtain both the equilibrium energy and position configuration for different system sizes. The adopted semi-classical approach allows us to provide reliable approximations for the quantum ground state energy of the corresponding quantum system. The model considered in this work represents an interesting problem for studies of low-dimensional systems, with echoes that resonate with developments in nanoscience and nanomaterials.

Tensor-Network Decoding Beyond 2D

Decoding algorithms based on approximate tensor-network (TN) contraction have proven tremendously successful in decoding two-dimensional (2D) local quantum codes such as toric or surface codes and color codes, effectively achieving optimal decoding accuracy. In this work, we introduce several techniques to generalize TN decoding to higher dimensions so that it can be applied to three-dimensional (3D) codes as well as 2D codes with noisy syndrome measurements (phenomenological noise or circuit-level noise). The 3D case is significantly more challenging than 2D, as the involved approximate tensor contraction is dramatically less well behaved than its 2D counterpart. Nonetheless, we numerically demonstrate that the decoding accuracy of our approach outperforms state-of-the-art decoders on the 3D surface code, both in the point and loop sectors, as well as for depolarizing noise. Our techniques could prove useful in near-term experimental demonstrations of quantum error correction, when decoding is to be performed off line and accuracy is of the utmost importance. To this end, we show how TN decoding can be applied to circuit-level noise and demonstrate that it outperforms the matching decoder on the rotated surface code. Published by the American Physical Society 2024

Quasiparton distributions in massive QED2: Toward quantum computation

We analyze the quasiparton distributions of the lightest η′ meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous η′ state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted η′ state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the η′ state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions. Published by the American Physical Society 2024

Data-driven two-dimensional stationary quantum droplets and wave propagations in the amended Gross–Pitaevskii equation with two potentials via deep neural networks learning

In this paper, we develop a systematic deep learning approach to solve two-dimensional stationary quantum droplets (QDs) and investigate their wave propagation in the two-dimensional amended Gross–Pitaevskii equation with Lee–Huang–Yang correction and two kinds of potentials. Firstly, we use the initial-value iterative neural network algorithm for two-dimensional stationary QDs of stationary equations. Then, the learned stationary QDs are used as the initial value conditions for physics-informed neural networks to explore their evolutions in the space-time region. Especially, we consider two types of potentials, one is the two-dimensional quadruple-well Gaussian potential and the other is the P T -symmetric harmonic-oscillator (HO)-Gaussian potential, which lead to spontaneous symmetry breaking and the generation of multi-component QDs. The used deep learning method can also be applied to study wave propagations of other nonlinear physical models.

Thermal transport of flexural phonons in a rectangular plate

The quantum thermal transport of elastic excitations through a two-dimensional elastic waveguide between two thermal reservoirs is studied. We solve the classical Kirchhoff–Love equation for rectangular plates and explore the dispersion relation for both the symmetric and antisymmetric solutions. Then, we study the phonon transport of these modes within the second quantization framework by analyzing the mean quadratic displacement, from which the energy density current, the temperature field, and conductance are determined. We identify the relevant modes contributing to thermal transport and explore the average temperature difference to reach the high-temperature limit. We expect our results to pave the way for understanding phonon-mediated thermal transport in two-dimensional mesoscopic quantum devices.

Remarks on 2D quantum cosmology

We consider two-dimensional quantum gravity endowed with a positive cosmological constant and coupled to a conformal field theory of large and positive central charge. We study cosmological properties at the classical and quantum level. We provide a complete ADM analysis of the classical phase space, revealing a family of either bouncing or big bang/crunch type cosmologies. At the quantum level, we solve the Wheeler-DeWitt equation exactly. In the semiclassical limit, we link the Wheeler-DeWitt state space to the classical phase space. Wavefunctionals of the Hartle-Hawking and Vilenkin type are identified, and we uncover a quantum version of the bouncing spacetime. We retrieve the Hartle-Hawking wavefunction from the disk path integral of timelike Liouville theory. To do so, we must select a particular contour in the space of complexified fields. The quantum information content of the big bang cosmology is discussed, and contrasted with the de Sitter horizon entropy as computed by a gravitational path integral over the two-sphere.

Dilaton shifts, probability measures, and decomposition

Abstract In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. Relative shifts between universes are fixed by locality and take a universal form, reflecting underlying (noninvertible, quantum) symmetries. The first part of this paper constructs a general formula for such dilaton shifts, and discusses related computations. In the second part of this paper, we comment on the relation between decomposition and ensembles.

First-principles computational methods for quantum defects in two-dimensional materials: A perspective

Quantum defects are atomic defects in materials that provide resources to construct quantum information devices such as single-photon emitters and spin qubits. Recently, two-dimensional (2D) materials gained prominence as a host of quantum defects with many attractive features derived from their atomically thin and layered material formfactor. In this Perspective, we discuss first-principles computational methods and challenges to predict the spin and electronic properties of quantum defects in 2D materials. We focus on the open quantum system nature of the defects and their interaction with external parameters such as electric field, magnetic field, and lattice strain. We also discuss how such prediction and understanding can be used to guide experimental studies, ranging from defect identification to tuning of their spin and optical properties. This Perspective provides significant insights into the interplay between the defect, the host material, and the environment, which will be essential in the pursuit of ideal two-dimensional quantum defect platforms.

Quantitative Hardy inequalities for magnetic Hamiltonians

In this paper we present a new method of proof of Hardy type inequalities for two-dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quantitative lower bound on the best constant in these inequalities both for Schrödinger and Pauli operators. Pauli operators with Aharonov-Bohm magnetic field are discussed as well.