The Experts below are selected from a list of 420 Experts worldwide ranked by ideXlab platform
Emilian M. Nica - One of the best experts on this subject based on the ideXlab platform.
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Glide Reflection symmetry, Brillouin zone folding, and superconducting pairing for the P4/nmm space group
Physical Review B, 2015Co-Authors: Emilian M. NicaAbstract:Motivated by the studies of the superconducting pairing states in the iron-based superconductors, we analyze the effects of Brillouin zone folding procedure from a space group symmetry perspective for a general class of materials with the $P4/nmm$ space group. The Brillouin zone folding amounts to working with an effective one-Fe unit cell, instead of the crystallographic two-Fe unit cell. We show that the folding procedure can be justified by the validity of a Glide Reflection symmetry throughout the crystallographic Brillouin zone and by the existence of a minimal double degeneracy along the edges of the latter. We also demonstrate how the folding procedure fails when a local spin-orbit coupling is included although the latter does not break any of the space group symmetries of the bare Hamiltonian. In light of these general symmetry considerations, we further discuss the implications of the Glide Reflection symmetry for the superconducting pairing in an effective multi-orbital $t-J_{1}-J_{2}$ model. We find that the $P4/nmm$ space group symmetry allows only pairing states with even parity under the Glide Reflection and zero total momentum.
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Glide Reflection symmetry brillouin zone folding and superconducting pairing for the p4 nmm space group
Physical Review B, 2015Co-Authors: Emilian M. NicaAbstract:Motivated by the studies of the superconducting pairing states in the iron-based superconductors, we analyze the effects of Brillouin zone folding procedure from a space group symmetry perspective for a general class of materials with the $P4/nmm$ space group. The Brillouin zone folding amounts to working with an effective one-Fe unit cell, instead of the crystallographic two-Fe unit cell. We show that the folding procedure can be justified by the validity of a Glide Reflection symmetry throughout the crystallographic Brillouin zone and by the existence of a minimal double degeneracy along the edges of the latter. We also demonstrate how the folding procedure fails when a local spin-orbit coupling is included although the latter does not break any of the space group symmetries of the bare Hamiltonian. In light of these general symmetry considerations, we further discuss the implications of the Glide Reflection symmetry for the superconducting pairing in an effective multi-orbital $t-J_{1}-J_{2}$ model. We find that the $P4/nmm$ space group symmetry allows only pairing states with even parity under the Glide Reflection and zero total momentum.
Marin Soljačić - One of the best experts on this subject based on the ideXlab platform.
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Symmetry-protected topological photonic crystal in three dimensions
Nature Physics, 2016Co-Authors: Chen Fang, Steven G. Johnson, John D. Joannopoulos, Marin SoljačićAbstract:Crystal symmetries may protect single Dirac cones on the surface of a photonic crystal, creating a photonic analogue of a three-dimensional solid-state topological insulator. Topology of electron wavefunctions was first introduced to characterize the quantum Hall states in two dimensions discovered in 1980 (ref. 1 ). Over the past decade, it has been recognized that symmetry plays a crucial role in the classification of topological phases, leading to the broad notion of symmetry-protected topological phases^ 2 . As a primary example, topological insulators^ 3 , 4 are distinguished from normal insulators in the presence of time-reversal symmetry ( ). A three-dimensional (3D) topological insulator^ 3 , 4 , 5 , 6 exhibits an odd number of protected surface Dirac cones, a unique property that cannot be realized in any 2D systems. Importantly, the existence of topological insulators requires Kramers’ degeneracy in spin–orbit coupled electronic materials; this forbids any direct analogue in boson systems^ 7 . In this report, we discover a 3D topological photonic crystal phase hosting a single surface Dirac cone, which is protected by a crystal symmetry^ 8 , 9 , 10 —the nonsymmorphic Glide Reflection^ 11 , 12 , 13 rather than . Such a gapless surface state is fully robust against random disorder of any type^ 14 , 15 . This bosonic topological band structure is achieved by applying alternating magnetization to gap out the 3D ‘generalized Dirac points’ discovered in the bulk of our crystal. The Z _2 bulk invariant is characterized through the evolution of Wannier centres^ 16 . Our proposal—readily realizable using ferrimagnetic materials at microwave frequencies^ 17 , 18 —expands the scope of 3D topological materials from fermions to bosons.
Yuzuru Yoshii - One of the best experts on this subject based on the ideXlab platform.
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A SEARCH FOR NONTOROIDAL TOPOLOGICAL LENSING IN THE SLOAN DIGITAL SKY SURVEY QUASAR CATALOG
The Astrophysical Journal, 2013Co-Authors: Hirokazu Fujii, Yuzuru YoshiiAbstract:Flat space models with multiply connected topology, which have compact dimensions, are tested against the distribution of high-redshift (z ≥ 4) quasars of the Sloan Digital Sky Survey (SDSS). When the compact dimensions are smaller in size than the observed universe, topological lensing occurs, in which multiple images of single objects (ghost images) are observed. We improve on the recently introduced method to identify ghost images by means of four-point statistics. Our method is valid for any of the 17 multiply connected flat models, including nontoroidal ones that are compacted by screw motions or Glide Reflection. Applying the method to the data revealed one possible case of topological lensing caused by sixth-turn screw motion, however, it is consistent with the simply connected model by this test alone. Moreover, simulations suggest that we cannot exclude the other space models despite the absence of their signatures. This uncertainty mainly originates from the patchy coverage of SDSS in the south Galactic cap, and this situation will be improved by future wide-field spectroscopic surveys.
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An improved cosmic crystallography method to detect holonomies in flat spaces
Astronomy & Astrophysics, 2011Co-Authors: Hirokazu Fujii, Yuzuru YoshiiAbstract:A new, improved version of a cosmic crystallography method for constraining cosmic topology is introduced. Like the circles-inthe-sky method using CMB data, we work in a thin, shell-like region containing plenty of objects. Two pairs of objects (quadruplet) linked by a holonomy show a specific distribution pattern, and three filters of separation, vectorial condition ,a ndlifetime of objects extract these quadruplets. Each object Pi is assigned an integer si, which is the number of candidate quadruplets including Pi as their members. Then an additional device of si-histogram is used to extract topological ghosts, which tend to have high values of si .I n this paper we consider flat spaces with Euclidean geometry, and the filters are designed to constrain their holonomies. As the second filter, we prepared five types that are specialized for constraining specific holonomies: one for translation, one for half-turn corkscrew motion and Glide Reflection, and three for nth turn corkscrew motion for n = 4,3, and 6. Every multiconnected space has holonomies that are detected by at least one of these five filters. Our method is applied to the catalogs of toy quasars in flat Λ-CDM universes whose typical sizes correspond to z ∼ 5. With these simulations our method is found to work quite well. These are the situations in which type-II pair crystallography methods are insensitive because of the tiny number of ghosts. Moreover, in the flat cases, our method should be more sensitive than the type-I pair (or, in general, n-tuplet) methods because of its multifilter construction and its independence from n.
Yoshii Yuzuru - One of the best experts on this subject based on the ideXlab platform.
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A search for nontoroidal topological lensing in the Sloan Digital Sky Survey quasar catalog
'IOP Publishing', 2013Co-Authors: Fujii Hirokazu, Yoshii YuzuruAbstract:Flat space models with multiply connected topology, which have compact dimensions, are tested against the distribution of high-redshift ($z \geq 4$) quasars of the Sloan Digital Sky Survey (SDSS). When the compact dimensions are smaller in size than the observed universe, topological lensing occurs, in which multiple images of single objects (ghost images) are observed. We improve on the recently introduced method to identify ghost images by means of four-point statistics. Our method is valid for any of the 17 multiply connected flat models, including nontoroial ones that are compactified by screw motions or Glide Reflection. Applying the method to the data revealed one possible case of topological lensing caused by sixth-turn screw motion, however, it is consistent with the simply connected model by this test alone. Moreover, simulations suggest that we cannot exclude the other space models despite the absence of their signatures. This uncertainty mainly originates from the patchy coverage of SDSS in the South Galactic cap, and the situation will be improved by future wide-field spectroscopic surveys.Comment: accepted for publication in Ap
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An improved cosmic crystallography method to detect holonomies in flat spaces
'EDP Sciences', 2011Co-Authors: Fujii Hirokazu, Yoshii YuzuruAbstract:A new, improved version of a cosmic crystallography method for constraining cosmic topology is introduced. Like the circles-in-the-sky method using CMB data, we work in a thin, shell-like region containing plenty of objects. Two pairs of objects (quadruplet) linked by a holonomy show a specific distribution pattern, and three filters of \emph{separation, vectorial condition}, and \emph{lifetime of objects} extract these quadruplets. Each object $P_i$ is assigned an integer $s_i$, which is the number of candidate quadruplets including $P_i$ as their members. Then an additional device of $s_i$-histogram is used to extract topological ghosts, which tend to have high values of $s_i$. In this paper we consider flat spaces with Euclidean geometry, and the filters are designed to constrain their holonomies. As the second filter, we prepared five types that are specialized for constraining specific holonomies: one for translation, one for half-turn corkscrew motion and Glide Reflection, and three for $n$-th turn corkscrew motion for $n=4, 3,$ and 6. {Every multiconnected space has holonomies that are detected by at least one of these five filters.} Our method is applied to the catalogs of toy quasars in flat $\Lambda$-CDM universes whose typical sizes correspond to $z\sim 5$. With these simulations our method is found to work quite well. {These are the situations in which type-II pair crystallography methods are insensitive because of the tiny number of ghosts. Moreover, in the flat cases, our method should be more sensitive than the type-I pair (or, in general, $n$-tuplet) methods because of its multifilter construction and its independence from $n$.}Comment: 12 pages, 8 figures, accepted for publication in A&A (2011
Guo Chuan Thiang - One of the best experts on this subject based on the ideXlab platform.
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Crystallographic bulk-edge correspondence: Glide Reflections and twisted mod 2 indices
Letters in Mathematical Physics, 2019Co-Authors: Kiyonori Gomi, Guo Chuan ThiangAbstract:A 2-torsion topological phase exists for Hamiltonians symmetric under the wallpaper group with Glide Reflection symmetry, corresponding to the unorientable cycle of the Klein bottle fundamental domain. We prove a mod 2 twisted Toeplitz index theorem, which implies a bulk-edge correspondence between this bulk phase and the exotic topological zero modes that it acquires along a boundary Glide axis.