Hopfions in Condensed Matter
A special issue of Condensed Matter (ISSN 2410-3896).
Deadline for manuscript submissions: closed (16 February 2024) | Viewed by 216
Special Issue Editor
Special Issue Information
Dear Colleagues,
The more complex topological cousin of a skyrmion (a noncollinear spin configuration), called a hopfion, is now beginning to be observed experimentally in many materials such as ferromagnets, ferroelectrics, liquid crystals, and even in the context of Bose‒Einstein condensates (BEC) and photonics. Micron-sized hopfions have been observed using fluorescence polarizing microscopy in a chiral ferromagnetic fluid (liquid crystal colloids in a nematic host) by way of twisting and linking the magnetization. The growing ubiquity of topological defects in materials, ranging from domain walls, vortices, and skyrmions to effective magnetic monopoles (such as in artificial spin ice) and now hopfions, points to an emerging new frontier of “topological engineering” just like band engineering in order to achieve unprecedented material properties.
A certain field configuration defines these topological defects. The field could be magnetization (for magnetic materials), polarization (for ferroelectrics), director (for liquid crystals), or local spin rotation (for BEC). A vortex is a mapping of the field from the surface of a 2D sphere (i.e., circle, S1) to another circle. This S1-to-S1 mapping defines a vortex. For skyrmions, the field can be viewed as residing on the surface of a 3D sphere (S2). It can be mapped uniquely to the surface of a physical 3D sphere. This S2-to-S2 mapping defines a (baby) skyrmion. The field for a hopfion lives on the surface of a 4D sphere (S3). It can also be mapped uniquely to the surface of a physical 3D sphere. This S3-to-S2 mapping characterizes a hopfion. Thus, two points on the physical sphere (P,Q) correspond to (what are called preimages) great circles on S3 and they are linked. This linking is a salient feature of the hopfion. Essentially, the hopfion is a stable three-dimensional, knotted or linked topological soliton. In a hopfion, any two field lines (e.g., of magnetization, polarization, director, etc.) are linked exactly once, which is the characteristic topological attribute of a hopfion. The S3-to-S3 mapping corresponds to the usual skyrmion.
Just as we have seen the fields of spintronics, valleytronics, skyrmionics, and twistronics during the past two decades, a new frontier of materials science is on the horizon: hopfionics. Once we fully understand the properties of a hopfion with a given Hopf index and how it interacts with other hopfions, it will likely usher in a new method of information processing and storage among other unconceived attributes as well as computing paradigms. This book purports to present the latest experimental and theoretical advances in the emerging field of hopfions in condensed matter, also including BEC and photonics.
Dr. Avadh Saxena
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Condensed Matter is an international peer-reviewed open access quarterly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
