Nontrivial Ground Research Articles

Crystalline electric field excitations and their nonlinear splitting under magnetic fields in YbOCl

Recently reported van der Waals layered honeycomb rare-earth chalcohalides REChX (RE = rare earth, Ch = chalcogen, and X = halogen) are considered to be promising Kitaev spin liquid (KSL) candidates. The high-quality single crystals of YbOCl, a representative member of the family with an effective spin of 1/2, are available now. The crystalline electric field (CEF) excitations in a rare-earth spin system are fundamentally important for understanding both finite-temperature and ground-state magnetism but remain unexplored in YbOCl so far. In this paper, we conduct a comprehensive Raman scattering study to unambiguously identify the CEF excitations in YbOCl and determine the CEF parameters and wave functions. Our Raman experiments further reveal the anomalous nonlinear CEF splitting under magnetic fields. We have grown single crystals of YbOCl, the nonmagnetic LuOCl, and the diluted magnetic Lu0.86Yb0.14OCl to make a completely comparative investigation. Polarized Raman spectra on the samples at 1.8 K allow us to clearly assign all the Raman-active phonon modes and explicitly identify the CEF excitations in YbOCl. The CEF excitations are further examined using temperature-dependent Raman measurements and careful symmetry analysis based on Raman tensors related to CEF excitations. By applying the CEF Hamiltonian to the experimentally determined CEF excitations, we extract the CEF parameters and eventually determine the CEF wave functions. The study experimentally pins down the CEF excitations in the Kitaev compound YbOCl and sets a foundation for understanding its finite-temperature magnetism and exploring the possible nontrivial spin ground state. Published by the American Physical Society 2024

Spin-orbit entanglement driven by the Jahn-Teller effect

Spin-orbit entanglement in 4d and 5d transition metal systems can enhance electronic correlations, leading to nontrivial ground states and the emergence of exotic excitations. There is also an interest to investigate spin-orbit entanglement in 3d compounds, though this is challenging due to their smaller spin-orbit coupling. Here we demonstrate that the Jahn-Teller effect in Mn3+ reduces the energy gap between high- and low- spin-orbital states that lead to enhanced spin-orbit entanglement. Our results show a rare example of synergistic effects of Jahn-Teller and spin-orbit interactions and provide a way to entangle different degrees of freedom in d-metal oxides, which may allow paths to explore the interplay of orbital, lattice and spins in 3d correlated systems.

Supersymmetric Quantum Mechanics on a noncommutative plane through the lens of deformation quantization

A gauge invariant mathematical formalism based on deformation quantization is outlined to model an N=2 supersymmetric system of a spin 1/2 charged particle placed in a nocommutative plane under the influence of a vertical uniform magnetic field. The noncommutative involutive algebra (C∞(R2)[[ϑ]],∗r) of formal power series in ϑ with coefficients in the commutative ring C∞(R2) was employed to construct the relevant observables, viz., SUSY Hamiltonian H, supercharge operator Q and its adjoint Q† all belonging to the 2 × 2 matrix algebra M2(C∞(R2)[[ϑ]],∗r) with the help of a family of gauge-equivalent star products ∗r. The energy eigenvalues of the SUSY Hamiltonian all turned out to be independent of not only the gauge parameter r but also the noncommutativity parameter ϑ. The nontrivial Fermionic ground state was subsequently computed associated with the zero energy which indicates that supersymmetry remains unbroken in all orders of ϑ. The Witten index for the noncommutative SUSY Landau problem turns out to be −1 corroborating the fact that there is no broken supersymmetry for the model we are considering.

Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral

This article examines a new family of (p,q)‐Laplacian type nonlinear fractional impulsive differential coupled equations involving both the ‐Caputo fractional derivative and –Riemann–Liouville fractional integral. With the help of Nehari manifold in critical point theory and fractional calculus properties, we obtain the existence of at least one nontrivial ground state solution for the coupled system with some natural and easily verifiable superlinear conditions on the nonlinearity.

Valence-Ordered Thin-Film Nickelate with Tri-component Nickel Coordination Prepared by Topochemical Reduction.

The metal-hydride-based "topochemical reduction" process has produced several thermodynamically unstable phases across various transition metal oxide series with unusual crystal structures and nontrivial ground states. Here, by such an oxygen (de-)intercalation method we synthesis a samarium nickelate with ordered nickel valences associated with tri-component coordination configurations. This structure, with a formula of Sm9Ni9O22 as revealed by four-dimensional scanning transmission electron microscopy (4D-STEM), emerges from the intricate planes of {303}pc ordered apical oxygen vacancies. X-ray spectroscopy measurements and ab initio calculations show the coexistence of square planar, pyramidal, and octahedral Ni sites with mono-, bi-, and tri-valences. It leads to an intense orbital polarization, charge-ordering, and a ground state with a strong electron localization marked by the disappearance of ligand-hole configuration at low temperature. This nickelate compound provides another example of previously inaccessible materials enabled by topotactic transformations and presents an interesting platform where mixed Ni valence can give rise to exotic phenomena.

Non-trivial ground and excited state photophysics of a substituted phenol.

5-(tert-Butyl)-2-hydroxy-1,3-isophthalaldehyde (5-tBHI) shows solvent dependent single or dual emission. The photophysics of 5-tBHI has been studied in a variety of solvents and the results were compared with that of the methyl derivative of the probe as well as the 5-tBHI anion. It has been found that the intramolecular H-bonded conformer of 5-tBHI predominantly exists in non-polar solvents, and undergoes facile excited state intramolecular proton transfer (ESIPT). On the other hand, a dynamic equilibrium can be found in polar, protic solvents, even in the ground state, except in water. NMR analyses confirm the loss of aromaticity of the probe in the ground state via anion formation, in equilibrium with the solvent mediated intermolecularly H-bonded state, in neat polar protic solvents like methanol. The proton transfer process, either intramolecularly or intermolecularly, was found to be of the order of 1 ps, and even faster than the instrumental resolution in the case of water. The current finding provides important insights on the photophysics of this small, substituted phenol.

Emergence of exotic electronic and magnetic phases upon electron filling in Na2BO3 (B = Ta, Ir, Pt, and Tl): a first-principles study.

Competition between spin-orbit interaction and electron correlations can stabilize a variety of non-trivial electronic and magnetic ground states. Using density functional theory calculations, here we show that different exotic electronic and magnetic ground states can be obtained by electron filling of the B-site cation in the Na2BO3 family of compounds (B = Ta, Ir, Pt and Tl). Electron filling leads to a Peierls insulator state with a direct band gap to j = 1/2 spin-orbit assisted Mott-insulator to band insulator and then to negative charge-transfer half-metal transition. The magnetic ground state also undergoes a transition from a non-magnetic state to a zigzag antiferromagnetic state, a re-entrant non-magnetic state and finally to a ferromagnetic state. The electron localization function shows a ladder type dimerization or Peierls instability in Na2TaO3. Maximally localized Wannier function calculations reveal delocalization of electrons through the eg orbitals, which form a π bond, and localization of electrons through the t2g orbitals, which form a σ bond, between the neighbouring tantalum ions. Na2TlO3 shows Stoner or band ferromagnetism due to the localized moments with up-spin on oxygen ligands created by the negative charge-transfer character, interacting via the down-spin itinerant electrons of the Tl 5d-O 2p hybridized band. These findings are significant for practical applications; for instance the direct band gap insulator Na2TaO3 shows potential for utilisation in solar cells, while Na2TlO3, which exhibits ferromagnetic half metallicity, holds promise for spintronic device applications.

Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model

We examine the condensation and confinement mechanisms exhibited by a deformed toric code model proposed in [Castelnovo and Chamon, Phys. Rev. B 77, 054433 (2008)]. The model describes both sides of a phase transition from a topological phase to a trivial phase. Our findings reveal an unconventional confinement mechanism that governs the behavior of the toric code excitations within the trivial phase. Specifically, the confined magnetic charge can still be displaced without any energy cost, albeit only via the application of non-unitary operators that reduce the norm of the state. This peculiar phenomenon can be attributed to a previously known feature of the model: It maintains the non-trivial ground state degeneracy of the toric code throughout the transition. We describe how this degeneracy arises in both phases in terms of spontaneous symmetry breaking of a generalized (1-form) symmetry and explain why such symmetry breaking is compatible with the trivial phase. The present study implies the existence of subtle considerations that must be addressed in the context of recently posited connections between topological phases and broken higher-form symmetries.

Flat band separation and robust spin Berry curvature in bilayer kagome metals

AbstractKagome materials have emerged as a setting for emergent electronic phenomena that encompass different aspects of symmetry and topology. It is debated whether the XV6Sn6 kagome family (where X is a rare-earth element), a recently discovered family of bilayer kagome metals, hosts a topologically non-trivial ground state resulting from the opening of spin–orbit coupling gaps. These states would carry a finite spin Berry curvature, and topological surface states. Here we investigate the spin and electronic structure of the XV6Sn6 kagome family. We obtain evidence for a finite spin Berry curvature contribution at the centre of the Brillouin zone, where the nearly flat band detaches from the dispersing Dirac band because of spin–orbit coupling. In addition, the spin Berry curvature is further investigated in the charge density wave regime of ScV6Sn6 and it is found to be robust against the onset of the temperature-driven ordered phase. Utilizing the sensitivity of angle-resolved photoemission spectroscopy to the spin and orbital angular momentum, our work unveils the spin Berry curvature of topological kagome metals and helps to define its spectroscopic fingerprint.

Z_{2} Spin Liquids in the Higher Spin-S Kitaev Honeycomb Model: An Exact Deconfined Z_{2} Gauge Structure in a Nonintegrable Model.

The higher spin Kitaev model prominently features the extensive locally conserved quantities the same as the spin-1/2 Kitaev honeycomb model, although it is not exactly solvable. It remains an open question regarding the physical meaning of these conserved quantities in the higher spin model. In this Letter, by introducing a Majorana parton construction for a general spin-S we uncover that these conserved quantities are exactly the Z_{2} gauge fluxes in the general spin-S model, including the case of spin-1/2. Particularly, we find an even-odd effect that the Z_{2} gauge charges are fermions in the half integer spin model, but are bosons in the integer spin model. We further prove that the fermionic Z_{2} gauge charges are always deconfined; hence, the half integer spin Kitaev model would have nontrivial spin liquid ground states regardless of interaction strengths in the Hamiltonian. The bosonic Z_{2} gauge charges of the integer spin model, on the other hand, could condense, leading to a trivial product state, and this is indeed the case at the anisotropic limit of the model.

Метод нейронных сетей для моделирования скирмионной решетки в композитном мультиферроике

Magnetoelectric nanofilms are of great interest as functional elements of ultra-dense memory cells. In the ground state they may contain various topological magnetic vortex structures of several nanometers in size. The qualitative and quantitative properties of such structures strongly depend on a set of physical parameters. To calculate the ground state configuration with given parameters, we use the steepest descent method; to study a large parametric space, however, significant computational resources are required. To solve this problem, we propose the use of artificial neural networks (ANN), which can help us uncover the relationship between combinations of parameters and the corresponding ground state configurations, using a relatively small number of pre-computed configurations as training data. The application of the ANN allows one to avoid excessive computational costs in the study of the parametric space and narrow down the parametric area in which the existence of stable non-trivial ground state configurations in the form of a stable skyrmion crystal is possible.

Configurational entropy of black hole quantum cores

Two types of information entropy are studied for the quantum states of a model for the matter core inside a black hole geometry. A detailed description is first given of the quantum mechanical picture leading to a spectrum of bound states for a collapsing ball of dust in general relativity with a non-trivial ground state. Information entropies are then computed, shedding new light on the stability of the ground state and the spectrum of higher excited states.

The ground states of Hénon equations for [formula omitted]-Laplacian in [formula omitted] involving upper weighted critical exponents

In this paper, we investigate the existence of nontrivial ground state solutions of the Hénon equations with p-Laplacian in RN involving weighted upper critical exponents including Sobolev, Hardy–Sobolev and Hénon–Sobolev critical exponents. The Nehari manifold method and the mountain pass theorem are applied to get the nontrivial ground states for the problems under a subcritical weighted perturbation. Regularity and non-existence of the nontrivial solutions are also discussed.

Phase diagrams and excitations of anisotropic S=1 quantum magnets on the triangular lattice

The $S=1$ bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner $\textit{et al.}$, Phys. Rev. B $\textbf{90}$, 144409 (2014)], including an extensive region of "supersolid" order. In this work, we amend the model by an XXZ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable $S=1$ generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the XXZ anisotropy parameter, ratio of bilinear and biquadratic interactions and single-ion anisotropy, and compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e. with $S^z=\pm1,0$) Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing non-trivial Ising-ordered ground states.

Schrödinger–Poisson system with zero mass and convolution nonlinearity in R 2

In this paper, we prove the existence of nontrivial solutions and ground state solutions for the following planar Schrödinger–Poisson system with zero mass − Δ u + ϕ u = ( I α ∗ F ( u ) ) f ( u ) , x ∈ R 2 , Δ ϕ = u 2 , x ∈ R 2 , where α ∈ ( 0 , 2 ), I α : R 2 → R is the Riesz potential, f ∈ C ( R , R ) is of subcritical exponential growth in the sense of Trudinger–Moser. In particular, some new ideas and analytic technique are used to overcome the double difficulties caused by the zero mass case and logarithmic convolution potential.

The Choquard logarithmic equation involving a nonlinearity with exponential growth

In the present work we are concerned with the Choquard Logarithmic equation $-\Delta u + au + \lambda (\ln|\cdot|\ast |u|^{2})u = f(u)$ in $\mathbb{R}^2$, for $ a>0 $, $ \lambda >0 $ and a nonlinearity $f$ with exponential critical growth. We prove the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution. Also, we provide these results under a symmetric setting, taking into account subgroups of $ O(2) $.

The ground states for Hartree–Fock systems with a general nonlinearity

We consider the least energy solutions of Hatree–Fock system with the coupling term in the two equations, and the nonlinearity are general subcritical with a small perturbation. By Nehari's manifold approach, the existence of nontrivial ground state solutions is obtained. The asymptotic behaviors with respect to parameters and are also studied.

Ground states of nonlinear Schrödinger systems with mixed couplings: the critical case

In this paper, we consider the following k-coupled nonlinear Schrödinger systems in the critical case: Here, is a smooth bounded domain, and for every , where is the first eigenvalue of with the Dirichlet boundary condition. Note that the nonlinearity and the coupling terms are both critical in dimension 4 (i.e. when ). We call the couplings are attractive if , while repulsive stands for . Under the assumption that all the couplings are purely attractive and large enough, we first show that this critical system has a fully nontrivial ground state solution, that is, a solution has all components nontrivial, under conditions providing additional , while ground state solution may be semitrivial ( has null components) without the above additional conditions. When the systems admit mixed couplings, i.e. there exist and such that and , we establish the existence of least energy positive solutions. The purpose of this paper is to solve some remaining open questions on Tavares and You (Calc. Var. Partial Differential Equations 59:26, 2020).

Synthesis of the Candidate Topological Compound Ni3Pb2.

Spin-orbit coupling enables the realization of topologically nontrivial ground states. As spin-orbit coupling increases with increasing atomic number, compounds featuring heavy elements, such as lead, offer a pathway toward creating new topologically nontrivial materials. By employing a high-pressure flux synthesis method, we synthesized single crystals of Ni3Pb2, the first structurally characterized bulk binary phase in the Ni-Pb system. Combining experimental and theoretical techniques, we examined structure and bonding in Ni3Pb2, revealing the impact of chemical substitutions on electronic structure features of importance for controlling topological behavior. From these results, we determined that Ni3Pb2 completes a series of structurally related transition-metal-heavy main group intermetallic materials that exhibit diverse electronic structures, opening a platform for synthetically tunable topologically nontrivial materials.

The ground states of quasilinear Hénon equation with double weighted critical exponents

We prove the existence of nontrivial ground state solutions of the critical quasilinear Hénon equation $\displaystyle -\Delta _p u=|x|^{\alpha _1}|u|^{p^{*}(\alpha _1)-2}u-|x|^{\alpha _2}|u|^{p^{*}(\alpha _2)-2}u\ \ {\rm in}\ \mathbb {R}^{N}.$ It is a new problem in the sense that the signs of the coefficients of critical terms are opposite.