Curvature-induced geometric potential in strain-driven nanostructures
TL;DR: In this article, a general framework of the thin-wall quantization procedure is provided, and it is shown that the separability of the equation of motions is not endangered by the particular choice of the constraint imposed on the transversal fluctuations of the wavefunction.
Abstract: The experimental progress in synthesizing low-dimensional nanostructures where carriers are confined to bent surfaces has boosted the interest in the theory of quantum mechanics on curved two-dimensional manifolds. It was recently asserted that constrained electrically charged particles couple to a term linear in A_3 M, where A_3 is the transversal component of the electromagnetic vector potential and M the surface mean curvature, thereby making a dimensional reduction procedure impracticable in the presence of fields. Here we resolve this apparent paradox by providing a consistent general framework of the thin-wall quantization procedure. We also show that the separability of the equation of motions is not endangered by the particular choice of the constraint imposed on the transversal fluctuations of the wavefunction, which renders the thin-wall quantization procedure well-founded. It can be applied without restrictions.
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TL;DR: Streubel et al. as mentioned in this paper presented a review of the application potential of three-dimensional-shaped objects as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices.
Abstract: Author(s): Streubel, R; Fischer, P; Kronast, F; Kravchuk, VP; Sheka, DD; Gaididei, Y; Schmidt, OG; Makarov, D | Abstract: Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
280 citations
TL;DR: The flexoelectricity describes the contribution of the linear couplings between the electric polarization and strain gradient and between polarization gradient and strain to the thermodynamics of a solid as discussed by the authors.
210 citations
TL;DR: In this paper, a consistent derivation of an effective model Hamiltonian to describe spin transport along a helical pathway and in the presence of spin-orbit interaction, the latter being induced by an external field with helical symmetry, is presented.
Abstract: This study is devoted to a consistent derivation of an effective model Hamiltonian to describe spin transport along a helical pathway and in the presence of spin–orbit interaction, the latter being induced by an external field with helical symmetry. It is found that a sizable spin polarization of an unpolarized incoming state can be obtained without introducing phase breaking processes. For this, at least two energy levels per lattice site in the tight-binding representation are needed. Additionally, asymmetries in the effective electronic-coupling parameters as well as in the spin–orbit interaction strength must be present to achieve net polarization. For a fully symmetric system—in terms of electronic and spin–orbit couplings—no spin polarization is found. The model presented is quite general and is expected to be of interest for the treatment of spin-dependent effects in molecular scale systems with helical symmetry.
103 citations
TL;DR: The power of this approach is demonstrated by deriving, in full generality, the surface contributions to the flexoelectric response of a finite object, a topic that has recently been a matter of controversy.
Abstract: A mechanical deformation of a continuum can be expressed as a generalized coordinate transformation of space. Consequently, the equations of electrostatics in deformable media must satisfy covariance requirements with respect to such transformations, a problem that has long been addressed in the context of general relativity. Here we show how these ideas can be incorporated into the framework of density-functional perturbation theory, providing access to the microscopic charge density and electrostatic potential response to an arbitrary deformation field. We demonstrate the power of our approach by deriving, in full generality, the surface contributions to the flexoelectric response of a finite object, a topic that has recently been a matter of controversy. The breakdown of translational periodicity produces consequences that might seem highly paradoxical at first sight: for example, the macroscopic bulk polarization does not always correspond to the physical surface charge. The electrostatic response of materials to macroscopic deformations is crucial for the operation of sensors and actuators. Here, the author combines ideas from transformation optics and density-functional perturbation theory to achieve a general description of surface flexoelectric effects.
60 citations
Cites background from "Curvature-induced geometric potenti..."
...) It is equally easy to show that Equation (13) and Equation (14) still hold, provided that one replaces the frozenion charge density and polarization response functions with their relaxed-ion counterparts....
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TL;DR: In this article, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetic, antiferromagnetism, and superconductivity are outlined.
Abstract: Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.
49 citations
References
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Book•
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01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
20,724 citations
Book•
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01 Jan 1951
TL;DR: The equilibrium of rods and plates Elastic waves Dislocations Thermal conduction and viscosity in solids Mechanics of liquid crystals Index as discussed by the authors The equilibrium of rod and plate elastic waves Elastic waves
Abstract: Fundamental equations The equilibrium of rods and plates Elastic waves Dislocations Thermal conduction and viscosity in solids Mechanics of liquid crystals Index.
6,229 citations