Extrinsic Symmetry Research Articles

Symmetry-engineered nodal lines and hourglass fermions in patterned two-dimensional electron gas

In most cases, the formation of topological quantum states requires intrinsic crystalline symmetry to protect either discrete or continuous degeneracies in real materials, which greatly hinders their realization in practice. Patterned two-dimensional electron gas (2DEG), on the other hand, has become a very effective external means to manipulate the symmetry to whatever we want. Here, taking nonsymmorphic symmetries as the focus of attention, based on patterned 2DEG decoration, we reveal rich band-crossing features in two-dimensional systems. It is demonstrated that in the presence of intrinsic spin-orbital coupling (SOC), wallpaper groups $p2mg,p2gg$, and $p4mg$ possess fourfold-degenerate Dirac nodal lines, and if Rashba SOC is further considered, the fourfold-degenerate nodal lines disappear and hourglass Weyl fermions then emerge. Our results not only afford an attractive route for designing robust nodal-line and hourglass Weyl semimetals in reality, but also pave the way for designing ideal macroscale materials through rational extrinsic symmetry engineering.

Exploring partial intrinsic and extrinsic symmetry in 3D medical imaging.

We present a novel methodology to detect imperfect bilateral symmetry in CT of human anatomy. In this paper, the structurally symmetric nature of the pelvic bone is explored and is used to provide interventional image augmentation for treatment of unilateral fractures in patients with traumatic injuries. The mathematical basis of our solution is based on the incorporation of attributes and characteristics that satisfy the properties of intrinsic and extrinsic symmetry and are robust to outliers. In the first step, feature points that satisfy intrinsic symmetry are automatically detected in the Möbius space defined on the CT data. These features are then pruned via a two-stage RANSAC to attain correspondences that satisfy also the extrinsic symmetry. Then, a disparity function based on Tukey's biweight robust estimator is introduced and minimized to identify a symmetry plane parametrization that yields maximum contralateral similarity. Finally, a novel regularization term is introduced to enhance similarity between bone density histograms across the partial symmetry plane, relying on the important biological observation that, even if injured, the dislocated bone segments remain within the body. Our extensive evaluations on various cases of common fracture types demonstrate the validity of the novel concepts and the accuracy of the proposed method.

Origins of size effects in initially dislocation-free single-crystal silver micro- and nanocubes

We report phenomenal yield strengths—up to one-fourth of the theoretical strength of silver—recorded in microcompression testing of initially dislocation-free silver micro- and nanocubes synthesized from a multistep seed-growth process. These high strengths and the massive strain bursts that occur upon yield are results of the initially dislocation-free single-crystal structure of the pristine samples that yield through spontaneous nucleation of dislocations. When the pristine samples are exposed to a focused ion-beam to fabricate pillars and then compressed, the dramatic strain burst does not occur, and they yield at a quarter of the strength compared to the pristine counterparts. Regardless of the defect-state of the samples prior to testing, a size effect is apparent—where the yield strength increases as the sample size decreases. Since dislocation starvation and the single-arm-source mechanisms cannot explain a size effect on yield strength in dislocation-free samples, we investigate the dislocation nucleation mechanisms controlling the size effect through careful experimental observations and molecular statics simulations. We find that intrinsic or extrinsic symmetry breakers such as surface defects, edge roundness, external sample shape, or a high vacancy concentration can influence dislocation nucleation, and thus contribute to the size effect on yield strength in initially dislocation-free samples.

Homogenization of layered media: Intrinsic and extrinsic symmetry breaking

A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and reflection are obtained even in cases where classical effective medium theory breaks down. Magnetoelectric coupling accounts for symmetry breaking in reflection and transmission when a non-symmetric structure is illuminated from two opposite sides.

Creation of the Dirac Nodal Line by Extrinsic Symmetry Engineering.

The formation of the Dirac nodal line (DNL) requires intrinsic symmetry that can protect the degeneracy of continuous Dirac points in momentum space. Here, as an alternative approach, we propose an extrinsic symmetry protected DNL. On the basis of symmetry analysis and numerical calculations, we establish a general principle to design the nonsymmorphic symmetry protected 4-fold degenerate DNL against spin-orbit coupling in the nanopatterned 2D electron gas. Furthermore, on the basis of experimental measurements, we demonstrate the approximate realization of our proposal in the Bi/Cu(111) system, in which a highly dispersive DNL is observed at the boundary of the Brillouin zone. We envision that the extrinsic symmetry engineering will greatly enhance the ability for artificially constructing the exotic topological bands in the future.

Intrinsic valley Hall transport in atomically thin MoS2

Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom in addition to charge and spin. In the absence of inversion symmetry, these systems were predicted to exhibit opposite Hall effects for electrons from different valleys. Such valley Hall effects have been achieved only by extrinsic means, such as substrate coupling, dual gating, and light illuminating. Here we report the first observation of intrinsic valley Hall transport without any extrinsic symmetry breaking in the non-centrosymmetric monolayer and trilayer MoS2, evidenced by considerable nonlocal resistance that scales cubically with local resistance. Such a hallmark survives even at room temperature with a valley diffusion length at micron scale. By contrast, no valley Hall signal is observed in the centrosymmetric bilayer MoS2. Our work elucidates the topological origin of valley Hall effects and marks a significant step towards the purely electrical control of valley degree of freedom in topological valleytronics.

What is natural in writing?

AbstractNaturalness Theory (NT)is founded on the notion of naturalness and claims that when a linguistic phenomenon can be processed by humans with little effort, both sensomotorically and cognitively, it is deemed more natural compared to other, more complex phenomena. Drawing on evidence such as language change, language acquisition, and language disorders, various parameters of naturalness (e.g., biuniqueness, constructional iconicity) have been postulated, which focus on the phonological and morphological subsystems of language. This paper offers an outline of how naturalness can be adapted to grapholinguistic phenomena.Comparative graphematics(cf.Weingarten 2011), extended tocomparative grapholinguistics, is assessed as a method that can be used to reveal naturalness parameters which apply to both material (graphetic) and linguistic (graphematic) aspects of writing. The reduction of extrinsic symmetry across various scripts will be discussed as an example. By integrating these preliminary theoretical ideas into the framework of NT, it is demonstrated that so-calledNatural Grapholinguisticscould offer promising new insights as well as atertium comparationismethod for future comparative analyses of scripts and writing systems.

Group Representation of Global Intrinsic Symmetries

AbstractGlobal intrinsic symmetry detection of 3D shapes has received considerable attentions in recent years. However, unlike extrinsic symmetry that can be represented compactly as a combination of an orthogonal matrix and a translation vector, representing the global intrinsic symmetry itself is still challenging. Most previous works based on point‐to‐point representations of global intrinsic symmetries can only find reflectional symmetries, and are inadequate for describing the structure of a global intrinsic symmetry group. In this paper, we propose a novel group representation of global intrinsic symmetries, which describes each global intrinsic symmetry as a linear transformation of functional space on shapes. If the eigenfunctions of the Laplace‐Beltrami operator on shapes are chosen as the basis of functional space, the group representation has a block diagonal structure. We thus prove that the group representation of each symmetry can be uniquely determined from a small number of symmetric pairs of points under certain conditions, where the number of pairs is equal to the maximum multiplicity of eigenvalues of the Laplace‐Beltrami operator. Based on solid theoretical analysis, we propose an efficient global intrinsic symmetry detection method, which is the first one able to detect all reflectional and rotational global intrinsic symmetries with a clear group structure description. Experimental results demonstrate the effectiveness of our approach.

Full and Partial Symmetries of Non-rigid Shapes

Symmetry and self-similarity are the cornerstone of Nature, exhibiting themselves through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones: extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we present a generalization of symmetries for non-rigid shapes and a numerical framework for their analysis, addressing the problems of full and partial exact and approximate symmetry detection and classification.

Do symmetrical letter pairs affect readability?

Our everyday experience shows that we have problems in recognizing objects which only differ in their symmetry properties (street signs with two arrows in different directions or mathematical signs such as 〈 and 〉). Perception is closely correlated with an inner comparison: the perceived object with its surrounding, the perceived object with former experience and so on. The brain has evolved different constancy abilities (e.g. colour constancy) and one of them is object constancy. This object constancy makes it possible to perceive an object regardless of its orientation in space. Symmetric letter pairs with different sound representations (such as 〈b〉 and 〈d〉) are, due to object constancy, typically identified as one object. This deficiency of distinctiveness should affect their readability. The above hypothesis was examined in many scripts. The result was that mature scripts (which usually developed for a long time) avoid these symmetric letter pairs (called extrinsic symmetry) by adding distinctive features such as serifs or different stroke thickness. On the other hand, if a writer is allowed to invent letter shapes freely, he makes use of extrinsic symmetrical letter pairs. This is supposed to have aesthetic reasons — letters are often perceived as a standing object or even as a “body” on a plane. It is therefore possible to statistically separate mature scripts which show up no extrinsic symmetry from invented scripts full of extrinsic symmetry. The runes are a writing system which does not quite fit in this widely proved distinction. They have developed from the Latin writing system (or a close relative of it) and have therefore inherited the avoidance of extrinsic symmetry. The reduction of the character set from 24 signs in the Old Futhark to 16 characters in the Younger Futhark is accompanied by a simplification of runic signs. During this period the runes develop a high degree of extrinsic symmetry. Moreover, the letter shapes are often related to different sound representations. These irregularities in usage may be caused by interference from the Latin writing system. The resulting lesser readability could have been one reason for the decline of the runes. This paper shows in many figures and graphs how symmetry emerges and under what circumstances it is used to create new letter shapes.

A liouville space formulation of wangsness-bloch-redfield theory of nuclear spin relaxation suitable for machine computation. I. fundamental aspects

This is the first of a projected series of papers whose ultimate aim is to construct a general computational framework for the analysis of relaxation effects in multispin systems. In the present paper we address ourselves to the fundamental aspects of the theory of nuclear spin relaxation developed by Wangsness, Bloch, and Redfield. It is shown that by starting from a consistent quantum-mechanical treatment of the combined system of spins and bath, thereby avoiding the ad hoc assumptions of the semiclassical approach, and by making systematic use of the Liouville representation of quantum mechanics, it is possible to arrive at a formulation which is simultaneously compact, coherent, and well adapted to computer implementation. The formalism presented covers the most general case, but is at the same time capable of accommodating the simplifications arising from the special situations commonly encountered in practice. The latter are subdivided into intrinsic symmetry properties inherent in the basic structure of the theory itself or attributable to special features of the spin system, such as nuclear permutation symmetry or the weak coupling approximation, and into extrinsic symmetry properties ensuing from special physical situations or associated with specific types of experiments. Each of these symmetries is subjected to a separate analysis by means of general operator techniques and group theory and it is demonstrated how the resulting invariance properties can be exploited in practice. In the final section we tie all this together and are thus led to the global symmetry groups that apply under particular sets of conditions.