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Register a new userEmergent continuous symmetry in anisotropic flexible two-dimensional materials
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We develop the theory of anomalous elasticity in two-dimensional flexible materials with orthorhombic crystal symmetry. Remarkably, in the universal region, where characteristic length scales are larger than the rather small Ginzburg scale ${sim} 10, {rm nm}$, these materials possess an infinite set of flat phases which are connected by emergent continuous symmetry. This hidden symmetry leads to the formation of a stable line of fixed points corresponding to different phases. The same symmetry also enforces power law scaling with momentum of the anisotropic bending rigidity and Youngs modulus, controlled by a single universal exponent -- the very same along the whole line of fixed points. These anisotropic flat phases are uniquely labeled by the ratio of absolute Poissons ratios. We apply our theory to monolayer black phosphorus (phosphorene).
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Symmetry breaking in two-dimensional layered materials plays a significant role in their macroscopic electrical, optical, magnetic and topological properties, including but not limited to spin-polarization effects, valley-contrasting physics, nonlinear Hall effects, nematic order, ferroelectricity, Bose-Einstein condensation and unconventional superconductivity. Engineering symmetry breaking of two-dimensional layered materials not only offers extraordinary opportunities to tune their physical properties, but also provides unprecedented possibilities to introduce completely new physics and technological innovations in electronics, photonics and optoelectronics. Indeed, over the past 15 years, a wide variety of physical, structural and chemical approaches have been developed to engineer symmetry breaking of two-dimensional layered materials. In this Review, we focus on the recent progresses on engineering the breaking of inversion, rotational, time reversal and spontaneous gauge symmetries in two-dimensional layered materials, and illustrate our perspectives on how these may lead to potential new physics and applications.
We present a theoretical and computational framework to compute the symmetry number of a flexible sphere cluster in $mathbb{R}^3$, using a definition of symmetry that arises naturally when calculating the equilibrium probability of a cluster of spheres in the sticky-sphere limit. We define the sticky symmetry group of the cluster as the set of permutations and
We compute the absolute Poissons ratio $ u$ and the bending rigidity exponent $eta$ of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality $d = 2 + d_c$, $d_c gg 1$. We demonstrate that, in the regime of anomalous Hookes law, the absolute Poissons ratio approaches material independent value determined solely by the spatial dimensionality $d_c$: $ u = -1 +2/d_c-a/d_c^2+dots$ where $aapprox 1.76pm 0.02$. Also, we find the following expression for the exponent of the bending rigidity: $eta = 2/d_c+(73-68zeta(3))/(27 d_c^2)+dots$. These results cannot be captured by self-consistent screening approximation.
Two-dimensional (2D) topological materials (TMs) have attracted tremendous attention due to the promise of revolutionary devices with non-dissipative electric or spin currents. Unfortunately, the scarcity of 2D TMs holds back the experimental realization of such devices. In this work, based on our recently developed, highly efficient TM discovery algorithm using symmetry indicators, we explore the possible 2D TMs in all non-magnetic compounds in four recently proposed materials databases for possible 2D materials. We identify hundreds of 2D TM candidates, including 205 topological (crystalline) insulators and 299 topological semimetals. In particular, we highlight MoS, with a mirror Chern number of -4, as a possible experimental platform for studying the interaction-induced modification to the topological classification of materials. Our results winnow out the topologically interesting 2D materials from these databases and provide a TM gene pool which for further experimental studies.
We derive electronic tight-binding Hamiltonians for strained graphene, hexagonal boron nitride and transition metal dichalcogenides based on Wannier transformation of {it ab initio} density functional theory calculations. Our microscopic models include strain effects to leading order that respect the hexagonal crystal symmetry and local crystal configuration, and are beyond the central force approximation which assumes only pair-wise distance dependence. Based on these models, we also derive and analyze the effective low-energy Hamiltonians. Our {it ab initio} approaches complement the symmetry group representation construction for such effective low-energy Hamiltonians and provide the values of the coefficients for each symmetry-allowed term. These models are relevant for the design of electronic device applications, since they provide the framework for describing the coupling of electrons to other degrees of freedom including phonons, spin and the electromagnetic field. The models can also serve as the basis for exploring the physics of many-body systems of interesting quantum phases.
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