Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0209382

Degeneracy analysis for a super cell of a photonic crystal and its application to the creation of band gaps

Liang Wu·Sailing He
View original source ↗Read source document ↗Export metadata ↓

Abstract

A method is introduced to analyze the degeneracy properties of the band structure of a photonic crystal making use of the super cells. The band structure associated with a super cell of a photonic crystal has degeneracies at the edge of the Brillouin zone if the photonic crystal has some kind of point group symmetry. Both E-polarization and H-polarization cases have the same degeneracies for a 2-dimensional (2D) photonic crystal. Two theorems are given and proved. These degeneracies can be lifted to create photonic band gaps by changing the transform matrix between the super cell and the smallest unit cell. The existence of the photonic band gaps for many known 2D photonic crystals is explained through the degeneracy analysis.

Explore related subjects

cond-mat.mtrl-sci

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Liang Wu, Sailing He. 2002-09-18. Degeneracy analysis for a super cell of a photonic crystal and its application to the creation of band gaps. https://doi.org/10.1103/physreve.67.026612

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Symmetry-induced magnetic fullerene

Defect-free, charge-neutral, pure-carbon materials are generally viewed as intrinsically non-magnetic. Here we challenge this view by establishing a fundamental principle of symmetry-induced magnetism in pure-carbon fullerene systems through molecular orbital theory. We show that high-order symmetry of fullerene molecules or their crystalline lattices induces degenerate energy levels and hence, quantised magnetic moments at half filling. This mechanism holds for all high-order symmetries. It suggests a plausible intrinsic origin for the previously debated magnetic fullerene. Additionally, recent experimental advances in the synthesis of monolayer fullerene networks provide a feasible platform to implement our prediction on the deep link between symmetry and magnetism in these systems. Our results create new, broad frontiers of quantum magnetism by introducing molecular or crystalline symmetries in any lattice.

cond-mat.mtrl-sci↗
arXiv2026

Tritium for Nanoscale Hydrogen Analysis by Atom Probe Tomography

Accurate nanoscale detection of hydrogen is essential for understanding hydrogen-related phenomena in materials, yet conventional tracing with deuterium is often complicated by residual background hydrogen. This study evaluates tritium as a highly resolvable isotopic marker for nanoscale hydrogen analysis in metals using atom probe tomography. Titanium was selected for its ability to incorporate hydrogen isotopes, providing a suitable platform for tritium detection. Time of flight secondary ion mass spectrometry and electron backscatter diffraction were performed prior to tritium charging to characterize the initial composition and microstructure. Atom probe tomography in laser mode before and after tritium charging, at three post-charging time intervals, enables tracking of tritium incorporation over time. Thermal desorption analysis confirmed the presence of tritium and complemented the secondary ion mass spectrometry measurements, highlighting the role of the surface oxide layer in modulating tritium release. While tritium, deuterium, and protium differ in their diffusion and trapping behavior, the distinct mass signal associated with tritium provides a practical advantage for resolving hydrogen at very low concentrations. This work serves as a fundamental benchmarking study for leveraging tritium and atom probe tomography as a combined tool for understanding hydrogen in materials, relevant for interpreting local processes such as hydrogen embrittlement.

cond-mat.mtrl-sci↗
arXiv2026

Interfacial melting as a thermodynamic indicator of solid-state synthesizability

Computational materials discovery commonly ranks candidate materials by their thermodynamic stability on the formation energy convex hull, yet many predicted-stable phases resist synthesis. We propose that solid-state synthesizability through interfacial-melt-mediated routes requires an additional thermodynamic condition: the interfacial melt at the target composition must itself remain locally stable against spinodal decomposition. We examine this in the classical Fe--B system, where thermodynamically stable FeB$_4$ has been reported under high-pressure synthesis but not in low-pressure synthesis attempts. Using melt--quench molecular dynamics driven by a fine-tuned machine-learning interatomic potential, we find that, at ambient pressure, the B-rich interfacial melt near the FeB$_4$ composition develops a concave free-energy landscape, signaling a demixing instability that is corroborated by the concentration--concentration structure factor and correlated with low-energy icosahedral and pentagonal-pyramidal boron motifs. In contrast to FeB$_4$, metastable Fe$_3$B and Fe$_{23}$B$_6$ remain synthesizable because their corresponding melts are stable. Applied pressure introduces a convex $PV$ contribution that strongly suppresses this instability, reducing the curvature at the FeB$_4$ composition to within the uncertainty of our fit at 1800~K, consistent with the experimental synthesis boundary. Comparison with CrB$_4$ further shows that weaker melt instability correlates with easier experimental synthesis. Interfacial-melt stability, which atomistic simulations can assess via the low-$k$ concentration--concentration structure factor, is thus proposed as a practical thermodynamic screening descriptor of synthesizability for AI-assisted materials discovery.

cond-mat.mtrl-sci↗