Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0601217

Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity

Hidetsugu Sakaguchi·Boris A. Malomed
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce a dynamical model of a Bose-Einstein condensate based on the 2D Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative atomic scattering length, via the Feshbach resonance controlled by a properly shaped magnetic of optical field. We focus on the configuration with the nonlinear coefficient different from zero in a circle or annulus, including the case of a narrow ring. Two-dimensional axisymmetric solitons are found in a numerical form, and also by means of a variational approximation; for an infinitely narrow ring, the soliton is found in an exact form (in the latter case, exact solitons are also found in a two-component model). A stability region for the solitons is identified by means of numerical and analytical methods. In particular, if the nonlinearity is supported on the annulus, the upper stability border is determined by azimuthal perturbations; the stability region disappears if the ratio of the inner and outer radii of the annulus exceeds a critical value 0.47. The model gives rise to bistability, as the stationary solitons coexist with stable axisymmetric breathers, whose stability region extends to higher values of the norm than that of the static solitons. The collapse threshold strongly increases with the radius of the inner hole of the annulus. Vortex solitons are found too, but they are unstable.

Explore related subjects

cond-mat.supr-concond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hidetsugu Sakaguchi, Boris A. Malomed. 2006-01-11. Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity. https://doi.org/10.1103/physreve.73.026601

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Superconductivity in MgHCu3 perovskite revisited

We reexamine the crystal structure, electronic structure, lattice dynamics, phonon dispersion, electron-phonon coupling, and superconducting properties of MgHCu3 perovskite using the PBEsol and PBE functionals. This perovskite phase was recently proposed to exhibit superconductivity with the critical superconducting temperature, TC, of 42 K, which falls slightly over the classical 40 K limit for the phonon driven superconductivity. We show that although the crystal and electronic structure of this hypothetical compound are quite robust with respect to the k point mesh and functional used, yet the phonons and phonon related properties are extremely sensitive to the density of the grid chosen as well as functional used for calculations. Correspondingly, the values of the critical superconducting temperature calculated here for different Gaussian broadenings vary in a broad range of ca. 10 to 31 K and they do not exceed the classical limit. We suggest that the properties of this and many other high TC hydrides claimed should be thoroughly scrutinized using a variety of functionals, and benchmarked with experiment, to provide more reliable values of TC.

cond-mat.supr-con↗
arXiv2026

Multigap superconductivity in Ising superconductors: The case of (LaSe)1.14(NbSe2)m misfit layer compounds

Strong spin-orbit coupling and broken inversion symmetry in transition metal dichalcogenides give rise to Ising superconductivity, a spin-protected pairing state first identified in monolayer NbSe$_2$ through in-plane critical fields far exceeding the Pauli limit. More recently, Ising superconductivity has been proposed as a potential route to unconventional and even topological superconductivity in bulk misfit compounds. Here, we investigate the superconducting order parameter of layered misfit compounds composed of alternating transition metal dichalcogenide and rocksalt layers, which host extremely doped, electronically decoupled NbSe$_2$ sheets within a three-dimensional crystal. Using directional scanning tunneling spectroscopy on the misfit superconductors (LaSe)$_{1.14}$(NbSe$_2$) and (LaSe)$_{1.14}$(NbSe$_2$)$_2$, we uncover a strongly anisotropic multigap superconducting state: a fragile gap on the $Γ$-centered Fermi-surface pocket coexists with a robust, intrinsic gap on the K and K$'$ pockets. These features are in quantitative agreement with momentum-resolved gaps $Δ(\mathbf{k})$ obtained from anisotropic Migdal-Eliashberg calculations. The marked fragility of the $Γ$-centered gap, combined with the strong sensitivity of the critical temperature to non-magnetic disorder, points to pairing beyond conventional $s$-wave symmetry, potentially involving a topological order parameter. These results establish NbSe$_2$-based misfit compounds as a tunable bulk platform for multigap, unconventional superconductivity, with Ising protection offering a promising route toward topological pairing.

cond-mat.supr-con↗
arXiv2026

Different reconstruction pathways toward superconductivity in TaRhTe4 and TaIrTe4 Weyl semimetals

Pressure can drive Weyl semimetals toward superconductivity through qualitatively distinct reconstructions of their lattices and normal-state electronic structures. Here, we report the first observation of superconductivity in compressed TaRhTe4. This finding enables a direct comparison of the distinct reconstruction pathways leading to superconductivity in TaRhTe4 and the previously studied TaIrTe4, both of which belong to the TaXTe4 (X = Rh, Ir) family of type-II Weyl semimetals. For TaRhTe4, high-pressure electrical-resistance, Hall effect, and magnetoresistance measurements, together with synchrotron X-ray diffraction and first-principles calculations, reveal a superconducting transition that emerges near 20 GPa, with onset Tc increasing to approximately 2.6 K at 65.2 GPa and zero resistance achieved above 63 GPa. The onset of superconductivity coincides with a progressive lattice distortion, a strong suppression of the positive magnetoresistance, and a continuous decrease of the Hall coefficient toward zero. Calculations further show that additional electron-like bands cross the Fermi level (EF) and that N(EF) increases upon compression. This evolution contrasts with TaIrTe4, where the Hall coefficient initially increases before reversing its pressure dependence near the superconducting threshold, while the structural anomaly is confined to a narrower pressure interval. This comparison indicates that superconductivity in the TaXTe4 family is not tied to a unique critical pressure or a single Fermi-surface reconstruction, but can emerge through distinct material-specific pathways once pressure sufficiently reconstructs the low-carrier Weyl-semimetal-derived state into a multiband metallic regime.

cond-mat.supr-con↗