Nontrivial Ground State Research Articles

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.

On the Excitations of a Balian–Werthamer Superconductor

My contribution to this collection of articles in honor of David Lee and John Reppy on their 90th birthdays is a reflection on the remarkable phenomenology of the excitation spectra of superfluid $^3$He, in particular the B-phase which was identified by NMR and acoustic spectroscopy as Balian-Werthamer state shown in 1963 to be the ground state of a spin-triplet, p-wave superconductor within weak-coupling BCS theory. The superfluid phases of $^3$He provide paradigms for electronic superconductors with broken space-time symmetries and non-trivial ground-state topology. Indeed broken spin- and orbital rotation symmetries lead to a rich spectrum of collective modes of the order parameter that can be detected using NMR, acoustic and microwave spectroscopies. The topology of the BW state implies its low-temperature, low-energy transport properties are dominated by gapless Majorana modes confined on boundaries or interfaces. Given the central role the BW state played I discuss the acoustic and electromagnetic signatures of the BW state, the latter being relevant if an electronic analog of superfluid $^3$He-B is realized.

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.

Search for stable skyrmion lattices at the ground state in a multiferroic nanofilm using artificial neural networks

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. However, to study a large parametric space significant computational resources are required. To solve this problem, we propose the use 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 the 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.

Centre vortex structure of QCD-vacuum fields and confinement

The non-trivial ground-state vacuum fields of QCD form the foundation of matter. Using modern visualisation techniques, this presentation examines the microscopic structure of these fields. Of particular interest are the centre vortices identified within the ground-state fields of lattice QCD. Our current focus is on understanding the manner in which dynamical fermions in the QCD vacuum alter the centre-vortex structure. The impact of dynamical fermions is significant and provides new insights into the role of centre vortices in underpinning both confinement and dynamical chiral symmetry breaking in QCD.

Ground State Solutions for a Nonlocal System in Fractional Orlicz-Sobolev Spaces

We consider an elliptic system driven by the fractional a . -Laplacian operator, with Dirichlet boundary conditions type. By using the Nehari manifold approach, we get a nontrivial ground state solution on fractional Orlicz–Sobolev spaces.

Ground states for Schrödinger–Kirchhoff equations of fractional [formula omitted]-Laplacian involving logarithmic and critical nonlinearity

For 0<s<1<p<N/s and a parameter λ>0, we consider a class of Schrödinger–Kirchhoff equations of fractional p-Laplacian involving logarithmic nonlinearity and critical exponential growth: mup−Δpsu+Vxup−2u=λhxuθp−2ulnu+σups∗−2uinRNwith u=∫R2Nux−uypx−yN+spdxdy+∫RNVxupdx1/p,where ps∗=Np/N−sp, 1≤θ<ps∗/p, σ∈0,1, m(⋅) is a Kirchhoff function, V is a Rabinowitz potential, and h is a positive bounded perturbation. By using concentration-compactness principle and minimax argument, we prove the existence of a non-trivial ground state solution for λ sufficiently small.

Multiplicity, probabilities, and canonical sectors for cold QCD matter

At sufficiently low temperature, without requiring any numerical data at finite real chemical potential, we can clarify the canonical partition function with fixed quark number via the imaginary chemical potential region with few ansatzs. The canonical partition function relates to the multiplicity distribution which can be observed in collider experiments and thus we may access important information of the properties of the QCD matter based on the canonical method. In this paper, we estimate the multiplicity entropy, the configuration entropy, and the pointwise information which can be calculable with the canonical partition function to understand the properties of the cold QCD matter at finite density. With the large $N_\mathrm{c}$ limit where $N_\mathrm{c}$ is the number of colors, we can simply estimate the tendency of them, and then the relation to the quarkyonic phase is clarified. In addition, we discuss the nontrivial ground state degeneracy from the viewpoint of the canonical sectors.

Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity

We consider gravitational perturbation around maximally symmetric background of a theory of gravity involving quadratic curvature correction. This leads to a decoupled model of the standard transverse, traceless graviton mode and an additional scalar degree of freedom. Evolution of the latter is governed by a Lagrangian, which depends on higher derivative terms, inherited from the quadratic curvature correction in the action. It turns out that stability of the gravitational theory allows the scalar sector to choose between possible lowest energy states (or, ground states), that can sustain periodic form of inhomogeneity, either in space or in time. The latter, with a restricted form of invariance in time translation, is possibly a variant form of the time crystal. Existence of this novel ground state, depicting a time crystal, is solely related to the presence of higher curvature terms in the action. In particular, this non-trivial condensate-like ground state describe the spacetime fabric itself by introducing fundamental scales in the theory. Possible implications are also discussed.

Ground state solutions of a fractional advection–dispersion equation

In this paper, a class of fractional Sturm–Liouville advection–dispersion equations with instantaneous and noninstantaneous impulsive boundary conditions is considered. At the beginning, the existence of at least one nontrivial ground state solution is proved by the method of Nehari manifold without the Ambrosetti–Rabinowitz condition. Then, the existence of infinitely many nontrivial weak solutions is obtained by using the genus properties. Finally, an example is given to illustrate the main results obtained in this paper.

Existence of solutions for a coupled Schrödinger equations with critical exponent

&lt;abstract&gt;&lt;p&gt;In this paper we study the existence of multiple nontrivial solutions of the coupled Schrödinger system with external sources terms as perturbations. This type of the system arises from Bose-Einstein condensate. As these external sources terms are nonlinear functions and small in some sense, we use fibre map to divide the Nehari manifold into threes parts, and then prove the existence of a nontrivial ground state solution and a bound state solution.&lt;/p&gt;&lt;/abstract&gt;

Dynamical fermions, centre vortices, and emergent phenomena

The non-trivial ground-state vacuum fields of QCD form the foundation of matter. Here we examine the centre vortices identified within the ground-state fields of lattice QCD. We aim to understand the manner in which dynamical fermions in the QCD vacuum alter the centre-vortex structure. Using modern visualisation techniques, the centre-vortex structure of pure-gauge and dynamical-fermion fields is quantified and compared. We then explore the impact this modified structure has on measures of confinement and dynamical mass generation. The string tension of the static quark potential, positivityviolation in the gluon propagator, and dynamical mass generation in the overlap quark propagator are of particular interest. The impact of dynamical fermions is significant and provides new insights into the role of centre vortices in underpinning both confinement and dynamical chiral symmetry breaking in QCD.

Coexisting ferromagnetic-antiferromagnetic state in twisted bilayer CrI3.

Moiré engineering1-3 of van der Waals magnetic materials4-9 can yield new magnetic ground states via competing interactions in moiré superlattices10-13. Theory predicts a suite of interesting phenomena, including multiflavour magnetic states10, non-collinear magnetic states10-13, moiré magnon bands and magnon networks14 in twisted bilayer magnetic crystals, but so far such non-trivial magnetic ground states have not emerged experimentally. Here, by utilizing the stacking-dependent interlayer exchange interactions in two-dimensional magnetic materials15-18, we demonstrate a coexisting ferromagnetic (FM) and antiferromagnetic (AF) ground state in small-twist-angle CrI3 bilayers. The FM-AF state transitions to a collinear FM ground state above a critical twist angle of about 3°. The coexisting FM and AF domains result from a competition between the interlayer AF coupling, which emerges in the monoclinic stacking regions of the moiré superlattice, and the energy cost for forming FM-AF domain walls. Our observations are consistent with the emergence of a non-collinear magnetic ground state with FM and AF domains on the moiré length scale10-13. We further employ the doping dependence of the interlayer AF interaction to control the FM-AF state by electrically gating a bilayer sample. These experiments highlight the potential to create complex magnetic ground states in twisted bilayer magnetic crystals, and may find application in future gate-voltage-controllable high-density magnetic memory storage.

Nontrivial Ground State Degeneracy of the Spin–Pseudospin Model of a Two-Dimensional Magnet Near the Frustration Point

The classical Monte Carlo method is used to study the properties of the ground state and phase transitions of the spin-pseudospin model, which describes a two-dimensional Ising magnet with competing charge and spin interactions. This competition leads to the ground state degeneracy and the frustration of the system. It is shown that the ground state degeneracy is observed in the frustration area with nonzero probabilities of the formation of two different ordered states. Based on the histogram analysis of the Monte Carlo data, the type of phase transitions is analyzed. It is found that, near the frustration point, first-order phase transitions are observed in the dependence on the ratio between the spin ($s = 1/2$) and pseudospin ($S = 1$) interactions.

Photoinduced anomalous Hall effect in the interacting Haldane model: Targeting topological states with pump pulses

We investigate the nonequilibrium dynamics of the spinless Haldane model with nearest-neighbor interactions on the honeycomb lattice by employing an unbiased numerical method. In this system, a first-order transition from the Chern insulator (CI) at weak coupling to the charge-density-wave (CDW) phase at strong coupling can be characterized by a level crossing of the lowest energy levels. Here we show that adiabatically following the eigenstates across this level crossing, their Chern numbers are preserved, leading to the identification of a topologically-nontrivial low-energy excited state in the CDW regime. By promoting a resonant energy excitation via an ultrafast circularly polarized pump pulse, we find that the system acquires a non-vanishing Hall response as a result of the large overlap enhancement between the time-dependent wave-function and the topologically non-trivial excited state. This is suggestive of a photoinduced topological phase transition via unitary dynamics, despite a proper definition of the Chern number remaining elusive for an out-of-equilibrium interacting system. We contrast these results with more common quench protocols, where such features are largely absent in the dynamics even if the post-quench Hamiltonian displays a topologically nontrivial ground state.

Moiré Skyrmions and Chiral Magnetic Phases in Twisted CrX3 (X = I, Br, and Cl) Bilayers.

We present a comprehensive theory of the magnetic phases in twisted bilayer chromium trihalides through a combination of first-principles calculations and atomistic simulations. We show that the stacking-dependent interlayer exchange leads to an effective moiré field that is mostly ferromagnetic with antiferromagnetic patches. A wide range of noncollinear magnetic phases can be stabilized as a function of the twist angle and Dzyaloshinskii-Moriya interaction as a result of the competing interlayer antiferromagnetic coupling and the energy cost for forming domain walls. In particular, we demonstrate that for small twist angles various skyrmion crystal phases can be stabilized in both CrI3 and CrBr3. Our results provide an interpretation for the recent observation of noncollinear magnetic phases in twisted bilayer CrI3 and demonstrate the possibility of engineering further nontrivial magnetic ground states in twisted bilayer chromium trihalides.

Existence and multiplicity of solutions for the fractional p-Laplacian Choquard logarithmic equation involving a nonlinearity with exponential critical and subcritical growth

In the present work, we obtain the existence and multiplicity of nontrivial solutions for the Choquard logarithmic equation (−Δ)psu+a|u|p−2u+λ(ln|⋅|*|u|p)|u|p−2u=f(u)inRN, where N = sp, s ∈ (0, 1), p &amp;gt; 2, a &amp;gt; 0, λ &amp;gt; 0, and f:R→R is a continuous nonlinearity with exponential critical and subcritical growth. We guarantee the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution under critical and subcritical growth. Moreover, when f has subcritical growth, we prove the existence of infinitely many solutions via genus theory.

Epitaxial Stabilization of Metastable 3C BaRuO3 Thin Film with Ferromagnetic Non‐Fermi Liquid Phase

AbstractThin films of perovskite ruthenates of the general formula ARuO3 (A = Ca and Sr) are versatile electrical conductors for viable oxide electronics. They are also scientifically intriguing, as they exhibit nontrivial electromagnetic ground states depending on the A‐site element. Among them, realization of the cubic perovskite (3C) BaRuO3 in thin film form has been a challenge so far, because the 3C phase is metastable with the largest formation energy among the various polymorph phases of BaRuO3. In this study, 3C BaRuO3 thin films are successfully prepared employing epitaxial stabilization. The 3C BaRuO3 thin films show itinerant ferromagnetism with a transition temperature of ≈48 K and a non‐Fermi liquid phase. The epitaxial stabilization of the 3C BaRuO3 further enables to make a standard comparison of perovskite ruthenates, thereby establishing the importance of the RuO orbital hybridization in understanding the itinerant magnetic system.

Schrödinger equations in $\mathbb{R}^4$ involving the biharmonic operator with critical exponential growth

In this paper we prove the existence of at least one nontrivial ground state solution for fourth-order elliptic equations of the form Δ2u−Δu+u=K(x)[f(u)+g(u)],x∈ℝ4,u∈H2(ℝ4),(P) where Δ2:=Δ(Δ) is the biharmonic operator, f is a continuous nonnegative function with polynomial growth at infinity, g is a continuous nonnegative function with exponential growth and K is a positive bounded continuous function that can vanish at infinity. Our results complete the analysis made in F. Sani (Comm. Pure Appl. Anal. 12 (2013), 405–428), where the author studied Schrödinger equations involving the biharmonic operator with coercive potentials. Our approach is based on various techniques such as the mountain-pass theorem, Trundinger–Moser type inequalities and compactness results.

Coupled Spin States in Armchair Graphene Nanoribbons with Asymmetric Zigzag Edge Extensions.

Exact positioning of sublattice imbalanced nanostructures in graphene nanomaterials offers a route to control interactions between induced local magnetic moments and to obtain graphene nanomaterials with magnetically nontrivial ground states. Here, we show that such sublattice imbalanced nanostructures can be incorporated along a large band gap armchair graphene nanoribbon on the basis of asymmetric zigzag edge extensions, achieved by incorporating specifically designed precursor monomers. Scanning tunneling spectroscopy of an isolated and electronically decoupled zigzag edge extension reveals Hubbard-split states in accordance with theoretical predictions. Mean-field Hubbard-based modeling of pairs of such zigzag edge extensions reveals ferromagnetic, antiferromagnetic, or quenching of the magnetic interactions depending on the relative alignment of the asymmetric edge extensions. Moreover, a ferromagnetic spin chain is demonstrated for a periodic pattern of zigzag edge extensions along the nanoribbon axis. This work opens a route toward the fabrication of graphene nanoribbon-based spin chains with complex magnetic ground states.