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Ciardi M, Cinti F, Pellicane G, Prestipino S. Supersolid Phases of Bosonic Particles in a Bubble Trap. PHYSICAL REVIEW LETTERS 2024; 132:026001. [PMID: 38277582 DOI: 10.1103/physrevlett.132.026001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Revised: 06/06/2023] [Accepted: 12/04/2023] [Indexed: 01/28/2024]
Abstract
Confinement can have a considerable effect on the behavior of particle systems and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field mimicking an isotropic bubble trap, which constrains the particles to a portion of space close to a spherical surface. Using path integral Monte Carlo simulations, we examine the spatial structure and superfluid fraction in two emblematic cases. First, we look at soft-core bosons, finding the existence of supersolid cluster arrangements with polyhedral symmetry; we show how different numbers of clusters are stabilized depending on the trap radius and the particle mass, and we characterize the temperature behavior of the cluster phases. A detailed comparison with the behavior of classical soft-core particles is provided too. Then, we examine the case, of more immediate experimental interest, of a dipolar condensate on the sphere, demonstrating how a quasi-one-dimensional supersolid of clusters is formed on a great circle for realistic values of density and interaction parameters. Crucially, this supersolid phase is only slightly disturbed by gravity. We argue that the predicted phases can be revealed in magnetic traps with spherical-shell geometry, possibly even in a lab on Earth. Our results pave the way for future simulation studies of correlated quantum systems in curved geometries.
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Affiliation(s)
- Matteo Ciardi
- Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019 Sesto Fiorentino (FI), Italy
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
- INFN, Sezione di Firenze, I-50019 Sesto Fiorentino (FI), Italy
| | - Fabio Cinti
- Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019 Sesto Fiorentino (FI), Italy
- INFN, Sezione di Firenze, I-50019 Sesto Fiorentino (FI), Italy
- Department of Physics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
| | - Giuseppe Pellicane
- Dipartimento di Scienze Biomediche, Odontoiatriche e delle Immagini Morfologiche e Funzionali, Università degli Studi di Messina, I-98125 Messina, Italy
- CNR-IPCF, Viale F. Stagno d'Alcontres, 37-98158, Messina, Italy
- School of Chemistry and Physics, University of Kwazulu-Natal, 3209 Pietermaritzburg, South Africa
- National Institute of Theoretical and Computational Sciences (NIThECS), 3209 Pietermaritzburg, South Africa
| | - Santi Prestipino
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, viale F. Stagno d'Alcontres 31, I-98166 Messina, Italy
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Li N, Li J, Qing L, Ma S, Li Y, Li B. Self-assembly of colloids with competing interactions confined in spheres. SOFT MATTER 2024; 20:304-314. [PMID: 38050746 DOI: 10.1039/d3sm01227a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/06/2023]
Abstract
At low temperatures, colloidal particles with short-range attractive and long-range repulsive interactions can form various periodic microphases in bulk. In this paper, we investigate the self-assembly behaviour of colloids with competing interactions under spherical confinement by conducting molecular dynamics simulations. We find that the cluster, mixture, cylindrical, perforated lamellar and lamellar structures can be obtained, but the details of the ordered structures are different from those in bulk systems. Interestingly, the system tends to form more perforated structures when confined in smaller spheres. The mechanism behind this phenomenon is driven by the relationship between the energy of the ordered structures and the bending of the confinement wall, which is different from the mechanism in copolymer systems.
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Affiliation(s)
- Ningyi Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Junhong Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Lijingting Qing
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Shicheng Ma
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Yao Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Baohui Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
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Franzini S, Reatto L, Pini D. Phase diagram of SALR fluids on spherical surfaces. SOFT MATTER 2021; 18:186-197. [PMID: 34859802 DOI: 10.1039/d1sm01257f] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We investigate the phase diagram of a fluid of hard-core disks confined to the surface of a sphere and whose interaction potential contains a short-range attraction followed by a long-range repulsive tail (SALR). Based on previous work in the bulk we derive a stability criterion for the homogeneous phase of the fluid, and locate a region of instability linked to the presence of a negative minimum in the spherical harmonics expansion of the interaction potential. The inhomogeneous phases contained within this region are characterized using a mean-field density functional theory. We find several inhomogeneous patterns that can be separated into three broad classes: cluster crystals, stripes, and bubble crystals, each containing topological defects. Interestingly, while the periodicity of inhomogeneous phases at large densities is mainly determined by the position of the negative minimum of the potential expansion, the finite size of the system induces a richer behavior at smaller densities.
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Affiliation(s)
- Stefano Franzini
- Dipartimento di Fisica "A. Pontremoli", Università di Milano, Via Celoria 16, 20133 Milano, Italy.
| | - Luciano Reatto
- Dipartimento di Fisica "A. Pontremoli", Università di Milano, Via Celoria 16, 20133 Milano, Italy.
| | - Davide Pini
- Dipartimento di Fisica "A. Pontremoli", Università di Milano, Via Celoria 16, 20133 Milano, Italy.
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Zhu G, Gao L, Xu Z, Dai X, Zhang X, Yan LT. Entropy-Driven Unconventional Crystallization of Spherical Colloidal Nanocrystals Confined in Wide Cylinders. NANO LETTERS 2021; 21:8439-8446. [PMID: 34591482 DOI: 10.1021/acs.nanolett.1c03127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The densest packings of identical spherical colloidal nanocrystals in a thin cylinder generally give rise to confinement-induced chiral ordering. Here, we demonstrate that entropy can invalidate Pauling's packing rules for the nanocrystals confined in wide cylinders and novel ordered phases, where chiral ordering is broken, emerge. The nucleation and growth of spherical colloidal nanocrystals in the wide cylinders exhibit unique mechanisms which are distinctly different from that of thin ones. Furthermore, theoretical models which capture the essential physics of the ordering transitions are developed to reproduce the achiral ordering and reveal that the ordered phases are thermodynamically stable and stabilized through confinement-mediated entropic effect. These findings demonstrate that entropy arising from thermal motion can invalidate Pauling's packing rules of spherical colloidal nanocrystals confined in cylinders, which provides new insights into confinement physics of colloidal particles and might inspire nonintuitive design rules for the fabrication of novel ordered phases through confinement.
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Affiliation(s)
- Guolong Zhu
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Lijuan Gao
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Ziyang Xu
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Xiaobin Dai
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Xuanyu Zhang
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Li-Tang Yan
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
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Gnidovec A, Čopar S. Long-range order in quadrupolar systems on spherical surfaces. SOFT MATTER 2021; 17:4874-4883. [PMID: 33890591 DOI: 10.1039/d1sm00228g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The interplay between curvature, confinement and ordering on curved manifolds, with anisotropic interactions between building blocks, takes a central role in many fields of physics. In this paper, we investigate the effects of lattice symmetry and local positional order on orientational ordering in systems of long-range interacting point quadrupoles on a sphere in the zero temperature limit. Locally triangular spherical lattices show long-range ordered quadrupolar configurations only for specific symmetric lattices as strong geometric frustration prevents general global ordering. Conversely, the ground states on Caspar-Klug lattices are more diverse, with many different symmetries depending on the position of quadrupoles within the fundamental domain. We also show that by constraining the quadrupole tilts with respect to the surface normal, which models interactions with the substrate, and by considering general quadrupole tensors, we can manipulate the ground state configuration symmetry.
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Affiliation(s)
- AndraŽ Gnidovec
- University of Ljubljana, Faculty of Mathematics and Physics, SI-1000 Ljubljana, Slovenia.
| | - Simon Čopar
- University of Ljubljana, Faculty of Mathematics and Physics, SI-1000 Ljubljana, Slovenia.
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Prestipino S. Ultracold Bosons on a Regular Spherical Mesh. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1289. [PMID: 33287057 PMCID: PMC7712534 DOI: 10.3390/e22111289] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/22/2020] [Revised: 11/08/2020] [Accepted: 11/11/2020] [Indexed: 11/19/2022]
Abstract
Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh ("Platonic mesh") and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system.
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Affiliation(s)
- Santi Prestipino
- Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
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Prestipino S, Sergi A, Bruno E, Giaquinta PV. A variational mean-field study of clusterization in a zero-temperature system of soft-core bosons. EPJ WEB OF CONFERENCES 2020. [DOI: 10.1051/epjconf/202023000008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We work out the ground-state diagram of weakly-repulsive penetrable bosons, using mean-field theory with a Gaussian ansatz on the single-particle wave function. Upon compression, the fluid transforms into a cluster supersolid, whose structure is characterized for various choices of the embedding space. In Euclidean space, the stable crystals are those with the most compact structure, i.e., triangular and fcc in two and three dimensions, respectively. For particles confined in a spherical surface, as the sphere radius increases we observe a sequence of transitions between different cluster phases, all having a regular or semiregular polyhedron as supporting frame for the clusters. The present results are relevant for the behavior of ultracold bosons weakly coupled to a Rydberg state.
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Meyra AG, Zarragoicoechea GJ, Maltz AL, Lomba E, Torquato S. Hyperuniformity on spherical surfaces. Phys Rev E 2019; 100:022107. [PMID: 31574707 DOI: 10.1103/physreve.100.022107] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 11/07/2022]
Abstract
We study and characterize local density fluctuations of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the spatial distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focus on the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole, and charge-charge potentials. We show that the scaling of the local number variance as a function of the window size enables one to characterize hyperuniform and nonhyperuniform point patterns also on spherical surfaces.
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Affiliation(s)
- Ariel G Meyra
- IFLYSIB (UNLP, CONICET), 59 No. 789, B1900BTE La Plata, Argentina.,Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, E-28006 Madrid, Spain
| | - Guillermo J Zarragoicoechea
- IFLYSIB (UNLP, CONICET), 59 No. 789, B1900BTE La Plata, Argentina.,Comisión de Investigaciones Científicas de la Provincia de Buenos Aires, Argentina
| | - Alberto L Maltz
- Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CC 72 Correo Central 1900 La Plata, Argentina
| | - Enrique Lomba
- Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, E-28006 Madrid, Spain
| | - Salvatore Torquato
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.,Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
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Lošdorfer Božič A, Čopar S. Spherical structure factor and classification of hyperuniformity on the sphere. Phys Rev E 2019; 99:032601. [PMID: 30999521 DOI: 10.1103/physreve.99.032601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2018] [Indexed: 06/09/2023]
Abstract
Understanding how particles are arranged on the surface of a sphere is not only central to numerous physical, biological, soft matter, and materials systems but also finds applications in computational problems, approximation theory, and analysis of geophysical and meteorological measurements. Objects that lie on a sphere experience constraints that are not present in Euclidean (flat) space and that influence both how the particles can be arranged as well as their statistical properties. These constraints, coupled with the curved geometry, require a careful extension of quantities used for the analysis of particle distributions in Euclidean space to distributions confined to the surface of a sphere. Here, we introduce a framework designed to analyze and classify structural order and disorder in particle distributions constrained to the sphere. The classification is based on the concept of hyperuniformity, which was first introduced 15 years ago and since then studied extensively in Euclidean space, yet has only very recently been considered also for spherical surfaces. We employ a generalization of the structure factor on the sphere, related to the power spectrum of the corresponding multipole expansion of particle density distribution. The spherical structure factor is then shown to couple with cap number variance, a measure of density variations at different scales, allowing us to analytically derive different forms of the variance pertaining to different types of distributions. Based on these forms, we construct a classification of hyperuniformity for scale-free particle distributions on the sphere and show how it can be extended to include other distribution types as well. We demonstrate that hyperuniformity on the sphere can be defined either through a vanishing spherical structure factor at low multipole numbers or through a scaling of the cap number variance-in both cases extending the Euclidean definition, while at the same time pointing out crucial differences. Our work thus provides a comprehensive tool for detecting global, long-range order on spheres and for the analysis of spherical computational meshes, biological and synthetic spherical assemblies, and ordering phase transitions in spherically distributed particles.
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Affiliation(s)
- Anže Lošdorfer Božič
- Department of Theoretical Physics, Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Simon Čopar
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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