Lattice Potential Research Articles

Spectroscopy of heavy exotic mesons using lattice QCD static potentials and the Born-Oppenheimer approximation

I discuss the investigation of heavy exotic mesons using lattice QCD static potentials and the Born-Oppenheimer approximation. I summarize selected recent results for b¯b¯qq tetraquarks, for I = 0 bottomonium and for I = 1 bottomonium.

Transmission and control of band gap vortex solitons in fractional-order diffraction honeycomb lattices

In this paper, the existence and transmission characteristics of gap vortex optical solitons in a honeycomb lattice are investigated based on the fractional nonlinear Schrödinger equation. Firstly, the band-gap structure of honeycomb lattice is obtained by the plane wave expansion method. Then the gap vortex soliton modes and their transmission properties in the fractional nonlinear Schrödinger equation with the honeycomb lattice potential are investigated by the modified squared-operator method, the split-step Fourier method and the Fourier collocation method, respectively. The results show that the transmission of gap vortex solitons is influenced by the <inline-formula><tex-math id="M3">\begin{document}$ {\mathrm{L}}\acute{{\mathrm{e}}}{\mathrm{v}}{\mathrm{y}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M3.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M3.png"/></alternatives></inline-formula> index and the propagation constant. The stable transmission region of gap vortex soliton can be obtained through power graphs. In the stable region, the gap vortex soliton can transmit stably without being disturbed. However, in the unstable region, the gap vortex soliton will gradually lose ring structure and evolves into a fundamental soliton with the transmission distance increasing. And the larger the <inline-formula><tex-math id="M4">\begin{document}$ {\mathrm{L}}\acute{{\mathrm{e}}}{\mathrm{v}}{\mathrm{y}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M4.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M4.png"/></alternatives></inline-formula> index, the longer the stable transmission distance and the lower the power of the bandgap vortex soliton. When multiple vortex solitons transmit in the lattice, the interaction between them is influenced by the lattice position and phase. Two vortex solitons that are in phase and located at adjacent lattices, are superimposed with sidelobe energy, while two vortex solitonsthat are out of phase are cancelled with sidelobe energy. These vortex solitons will gradually lose ring structure and evolve into dipole modes in the transmission process. And they are periodic rotation under the azimuth angle modulating. When two vortex solitons located at non-adjacent lattice, vortex solitons can maintain a ring-shaped structure due to the small influence of sidelobes. When three gap vortex solitons are located at non-adjacent lattices, the solitons can also maintain their ring-like structures. However, when there are more than three gap vortex solitons, the intensity distribution of vortex solitons are uneven due to the sidelobe energy superimposed. These vortex solitons will form dipole modes and rotate under the azimuthal angle modulating in the transmission process. These results can offer theoretical guidance for transmitting and controlling the gap vortex solitons in the lattice.

A quantum ruler for orbital magnetism in moiré quantum matter.

For almost a century, magnetic oscillations have been a powerful "quantum ruler" for measuring Fermi surface topology. In this study, we used Landau-level spectroscopy to unravel the energy-resolved valley-contrasting orbital magnetism and large orbital magnetic susceptibility that contribute to the energies of Landau levels of twisted double-bilayer graphene. These orbital magnetism effects led to substantial deviations from the standard Onsager relation, which manifested as a breakdown in scaling of Landau-level orbits. These substantial magnetic responses emerged from the nontrivial quantum geometry of the electronic structure and the large length scale of the moiré lattice potential. Going beyond traditional measurements, Landau-level spectroscopy performed with a scanning tunneling microscope offers a complete quantum ruler that resolves the full energy dependence of orbital magnetic properties in moiré quantum matter.

Energy bands in a three dimension simple cubic lattice of contact potential

In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald’s summation method. In comparison with single point potential, the presence of lattice potential changes the existence condition of negative energy states near zero energy. It is found that the system always has negative energy states for an arbitrarily weak periodic potential. In addition, we prove that if an irreducible unitary representation is not a trivial representation of group of wave vector, the corresponding wave functions at lattice sites would be zero. With this theorem, the degeneracy of energy bands is explained with group theory. Furthermore, we find that there exists some energy bands which are not affected by the lattice potential. We call their corresponding eigenstates as dark states. The physical mechanism of the dark states is explained by explicitly constructing the standing wave-type Bloch wave functions.

The fracture toughness of demi-regular lattices

The properties of lattices are strongly influenced by their nodal connectivity; yet, previous studies have focused mainly on topologies with a single vertex configuration. This work investigates the potential of demi-regular lattices, with two vertex configurations, to outperform existing topologies, such as triangular and kagome lattices. We used finite element simulations to predict the fracture toughness of three elastic-brittle demi-regular lattices under modes I, II, and mixed-mode loading. The fracture toughness of two demi-regular lattices scales linearly with relative density ρ¯, and outperforms a triangular lattice by 15% under mode I and 30% under mode II. The third demi-regular lattice has a fracture toughness KIc that scales with ρ¯ and matches the remarkable toughness of a kagome lattice. Finally, a kinematic matrix analysis revealed that topologies with KIc∝ρ¯ have periodic mechanisms and this may be a key feature explaining their high fracture toughness.

Formation of multi-peak gap solitons and stable excitations for double-Lévy-index and mixed fractional NLS equations with optical lattice potentials

In this paper, we investigate the new two-Lévy-index fractional nonlinear Schrödinger (FNLS) equations with optical lattices, where two fractional derivative terms are introduced to control the diffractions. Especially, we explore the linear Bloch bandgaps and existence of gap solitons for the two-Lévy-index mixed FNLS equations with optical lattices. We analyse the effects of different coefficients of normal and abnormal diffraction terms on bandgap structures. Families of single-, double-, triple-, as well as quadruple-peak solitons are found in the first gap with the defocusing nonlinearity while such solitons can be found in the semi-infinite gap when it turns to the focusing regime. Meanwhile, we find that the above-obtained gap solitons can be roughly divided into two types, one of which branches out from the band edge, and another one cannot branch out from the band edge. Moreover, the stability of gap solitons is discussed via the linear stability analysis, and then their dynamical behaviours are verified by means of direct simulations. And stable multi-peak solitons can be obtained via analysing the phase structure. Meanwhile, we find the stable excitations of gap solitons via excitations of system parameters. The stable gap solitons are also verified to appear in the two-Lévy-index FNLS equation. These results may pave the way for the study of linear and nonlinear phenomena of two-Lévy-index and mixed FNLS equations or other mixed fractional physical models in optical lattices and the related physical experimental designs.

Rationality of two-phase coexistence with no element segregation in a CuZr-based amorphous alloy composite

Here, the structure features of Cu62Zr34.4Al3Nb0.6 amorphous alloy composites (AACs) are studied by combining experimental characterization with first-principles calculation. Element segregation, which is common in conventional alloy materials, does not occur in two phases (crystalline and amorphous phase) of the AACs due to complex solid solution. The lattice parameters, electron distribution, charge transfer and electrical potential, which are directly related to atomic bonding and lattice parameters of different structures, are obtained by calculating the various types of structural models, including interstitial solid solution, substitutional solid solution, B2 and amorphous phase. Finally, the formation and stability of solid solution in crystalline phase and amorphous phase are elucidated by first-principles calculation. The work has important guiding significance for understanding the two-phase structure and solidification mechanism in AACs materials.

Ultrafast enhancement of electron-phonon coupling via dynamic quantum well states

The density of states at the Fermi surface controls many material properties by influencing the low-energy interactions of conductive electrons. Typically, external tuning knobs generate only small perturbations to the density of states in crystals, since their band structure depends strongly on the lattice potential. In contrast, quantum well states are contingent on a localized potential extrinsic to the crystal lattice and can be easily modified leading to changes in the density of states at the Fermi level. Here, we are able to control the quantum well potential on the surface of Bi2Se3 with light, driving a density of states singularity below EF at ultrafast timescales, thereby triggering a reversible Lifshitz transition. We reveal a substantial ultrafast enhancement of the electron-phonon coupling with repercussions on the relaxation dynamics in the system. We argue that the relaxation dynamics are governed largely by the interplay of the dynamic density of states of the quantum wells with c-axis scattering from the {A}_{{{{{{{{rm{1g}}}}}}}}}^{2} optical phonon mode. These results demonstrate a powerful way to enhance electron-boson interaction on ultrafast timescales providing new avenues for controlling material properties and driving novel quantum phases of matter.

Температурна залежність границі плинності в термінах двох компонент поля зсувних напружень в площині ковзання в сплаві CrCoNiFeMn

The temperature dependence of the yield strength in the multicomponent CrCoNiFeMn alloy was investigated, using computer modelling and taking into account the short-wave and long-wave components of the shear stress field in the glide plane. The yield strength of a multicomponent alloy in the form of a concentrated solid solution without taking into account grain boundary strengthening is determined by three factors: the periodic lattice potential, the short-wave and long-wave components of the field of stochastic shear stresses in the glide plane, which are created by dissolved atoms. The force barriers resulting from the short-wave component will dominate. Overcoming them by dislocation with the assistance of applied stress and thermal activation will be a critical event to start dislocation movement. Barriers resulting from the periodic lattice potential and the long-wave component will be insignificant against the background of the short-wave component. Their effect on the yield strength can be taken into account by terms that do not depend on temperature. Thermal activation analysis of overcoming barriers resulting from a short-wave component, taking into account the probability of direct and reverse jumps through the barrier, gives the opportunity to describe the temperature dependence of the yield strength of a multicomponent alloy in a wide range of temperatures, including in the region of the high-temperature “plateau”. The dependence of the yield strength calculated in this way for the CrCoNiFeMn alloy correlates well with the corresponding experimental data. Keywords: temperature dependence, multicomponent alloy, glide plane, dislocation.

Ab Initio Derivation of Lattice-Gauge-Theory Dynamics for Cold Gases in Optical Lattices

We introduce a method for quantum simulation of U$(1)$ lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices. The proposal enables the study of both gauge and fermionic-matter fields without integrating out one of them in one and two dimensions. We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species. Starting from an $ab\,initio$ modelling of the experimental setting, we systematically carry out a derivation of the target U$(1)$ gauge theory. This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that - while pivotal for a successful implementation - have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions, and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics. We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope $^{173}$Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one- and two-dimensional settings.

Generating soliton trains through Floquet engineering

We study a gas of interacting ultracold bosons held in a parabolic trap in the presence of an optical lattice potential. Treating the system as a discretized Gross-Pitaevskii model, we show how Floquet engineering, by rapidly ``shaking'' the lattice, allows the ground state of the system to be converted into a train of bright solitons by inverting the sign of the hopping energy. We study how the number of solitons produced depends on the system's nonlinearity and the curvature of the trap, show how the technique can be applied in both the high- and low-driving-frequency regimes, and demonstrate the phenomenon's stability against noise. We conclude that the Floquet approach is a useful and stable method of preparing solitons in cold-atom systems.

On the intrinsic pinning and shape of charge-density waves in 1D Peierls systems

Within the standard perturbative approach of Peierls, a charge-density wave is usually assumed to have a cosine shape of weak amplitude. In nonlinear physics, we know that waves can be deformed. What are the effects of the nonlinearities of the electron-lattice models in the physical properties of Peierls systems? We study in details a nonlinear discrete model, introduced by Brazovskii, Dzyaloshinskii and Krichever. First, we recall its exact analytical solution at integrable points. It is a cnoidal wave, with a continuous envelope, which may slide over the lattice potential at no energy cost, following Fröhlich’s argument. Second, we show numerically that integrability-breaking terms modify some important physical properties. The envelope function may become discontinuous: electrons form stronger chemical bonds which are local dimers or oligomers. We show that an Aubry transition from the sliding phase to an insulating pinned phase occurs when the model is no longer integrable.

Ultracold Feshbach molecules in an orbital optical lattice

Quantum gas systems provide a unique experimental platform to study the crossover between Bose–Einstein condensed molecular pairs and Bardeen–Cooper–Schrieffer superfluidity. The few studies in optical lattices have so far focused on the case when only the lowest Bloch band is populated, thus excluding orbital degrees of freedom. Here we demonstrate the preparation of ultracold Feshbach molecules of fermionic atoms in the second Bloch band of an optical square lattice. We cover a wide range of interaction strengths, including the regime of unitarity in the middle of the crossover. Binding energies and band relaxation dynamics are measured by means of a method resembling mass spectrometry. We find that the longest lifetimes arise for strongly interacting Feshbach molecules at the onset of unitarity. In the case of strong confinement in a deep lattice potential, we observe bound dimers also for negative values of the scattering length, extending previous findings for molecules in the lowest band.

Thermohydraulic performance comparison of 3D printed circuit heatsinks with conventional integral fin heatsinks

Additive manufacturing has enabled the fabrication of intricate geometries and structures of numerous sizes at high accuracy, which has attracted researchers towards its application as 3D-printed heatsinks. In this context, current work is focused on exploring the potential of periodic lattices of cellular materials as heat sinks and their comparison with conventional thermal management systems. Thermohydraulic characteristics of the heatsinks with channel designs of cellular structures, namely, simple cubic and body-centered cubic, are evaluated and compared with the performance of conventional heatsinks with integral fins. The heatsinks' conjugate heat transfer and flow are solved numerically, employing a validated model built on 3D Reynolds averaged Navier Stokes with the Shear Stress Turbulence model. Water and critical CO2 are used as coolants in this study. Results show that the SC design performs best compared to the classic finned design with an overall performance evaluation criterion of around 4.45 times higher at a flow rate of 1.5 L/min using water as a coolant. In addition, body-centered cubic lattice performs with a PEC of 4.33 at the same flow rate and working fluid. The computed results demonstrate that the performance of 3D-printed heatsinks geometries is significantly superior to the classic designs making them an ideal candidate for designing further compact and efficient heat removal systems for electronic devices.

Quantum metrology with Bloch oscillations in Floquet phase space

Quantum particles performing Bloch oscillations in a spatially periodic potential can be used as a very accurate detector of constant forces. We find that the similar oscillations that can appear in the Floquet phase space of a quantum particle subjected a periodic temporal driving, even in the absence of periodic lattice potential, can likewise be exploited as detectors. Compared with their spatial Bloch analog, however, the Floquet-Bloch oscillations provide significant added flexibility and open the way to a broad range of precision metrology applications. We illustrate this property on the examples of a tachometer and a magnetometer.

Dimensional cross-over in self-organised super-radiant phases of ultra-cold atoms inside a cavity

We consider a condensate of ultra-cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump makes different angles with the direction of the cavity axis. We show that such a configuration allows a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by the cavity–atom interaction. Using a Holstein–Primakoff transformation, we find the atomic density profile of such a self-organised ground state in the super-radiant phase as a function of the angular orientations of the pumps in such a dynamical quantum optical lattice, and also provide an analysis of their structures in coordinate and momentum space. In the later part of the paper, we show how the corresponding results can also be qualitatively understood in terms of an extended Bose–Hubbard model in such a quantum optical lattice potential.

Stable quantum droplets with higher-order vortex in radial lattices

The existence and stability of quantum droplets are studied in ultracold atoms in Bose–Einstein condensates with a radial period lattice under the Lee–Huang–Yang correction. Both stable bell-shaped and ring-shaped zero-vorticity quantum droplets are found in this radial lattice. It is found that the existence curves of the zero-vorticity quantum droplets could violate the V–K criterion, which is a necessary condition to form stable solitons. Under the effect of the radial lattice potential, vortex quantum droplets can be still stable when embedded vorticity S is up to S=10. The vortex quantum droplets can be trapped at the first as well as at the second circular trough of the radial lattice. The stability areas of the vortex quantum droplets with different embedded vorticity S are identified by the long time evolution. The chemical potential of the vortex quantum droplets also violates the V–K criterion. The peak value and effective area of the vortex quantum droplets are independent of the vorticity S, while it only depends on the total norm and the potential of the radial lattice. The double ring quantum droplets, with different embedded vorticity in their inner and outer ring, are also discussed.

Electric-field-induced metal-semiconductor transitions in twisted bilayers of WSe2

We have examined the electronic structure of twisted bilayers of ${\mathrm{WSe}}_{2}$ within ab initio electronic structure calculations. Flat bands are found to emerge above a set of dispersing bands at a twist angle of $3.48{}^{\ensuremath{\circ}}$, whereas they are absent at $19.03{}^{\ensuremath{\circ}}$ which has a similar-sized moir\'e cell. The presence of the flat bands at the valence-band maximum are traced to the strong perturbations from zone-boundary scattering found for small angles. This follows from the fact that the strongest Fourier components of the lattice potential are associated with the primitive cell vectors, justifying a description of the electronic structure as a perturbation to the unrotated limit. The layer polarization of the charge density associated with the valence-band maximum also allows for tuning the electronic structure with an electric field, thereby driving a semiconductor-metal-semiconductor transition.

Floquet topological insulators with hybrid edges

Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet topological insulators unidirectional edge states appear upon breakup of the effective time-reversal symmetry due to dynamical modulations of the underlying lattice potential. However, such states are usually reported for certain simple lattice terminations, for example, at zigzag or bearded edges in honeycomb lattices. Here we show that unconventional topological edge states may exist in Floquet insulators based on arrays of helical waveguides with hybrid edges involving alternating zigzag and armchair segments, even if the latter are long. Such edge states appear in the largest part of the first Brillouin zone and show topological protection upon passage through the defects. Topological states at hybrid edges persist in the presence of focusing nonlinearity of the material. Our results can be extended to other lattice types and physical systems, they lift some of the constraints connected with lattice terminations that may not support edge states in the absence of effects breaking time-reversal symmetry of the system and expand the variety of geometrical shapes in which topological insulators can be constructed.

Dual-density waves with neutral and charged dipolar excitons of GaAs bilayers.

Strongly correlated quantum particles in lattice potentials are the building blocks for a wide variety of quantum insulators-for instance, Mott phases and density waves breaking lattice symmetry1-3. Such collective states are accessible to bosonic and fermionic systems2,4-10,11,12. To expand further the spectrum of accessible quantum matter phases, mixing both species is theoretically appealing because density order then competes with phase separation13-16. Here we manipulate such a Bose-Fermi mixture by confining neutral (boson-like) and charged (fermion-like) dipolar excitons in an artificial square lattice of a GaAs bilayer. At unitary lattice filling, strong inter- and intraspecies interactions stabilize insulating phases when the fraction of charged excitons is around (1/3, 1/2, 2/3). We evidence that dual Bose-Fermi density waves are then realized, with species ordered in alternating stripes. Our observations highlight that dipolar excitons allow for controlled implementations of Bose-Fermi Hubbard models extended by off-site interactions.