hR1-Hg (Direct)

hR1–Hg (Direct)

Image of hR1–Hg (Direct), generated by Vesta

Lattice Vectors:

\[\begin{split}a_1 &= ~\hat{x}\\ a_2 &= 0.3333132676~\hat{x} + \sqrt{8}/\sqrt{9}~\hat{y}\\ a_3 &= 0.3333132676~\hat{x} + \sqrt{2}/6~\hat{y} + \sqrt{5}/\sqrt{6}~\hat{z}\\\end{split}\]

Space Group: 166

Point Group of Structure: \(\bar{3}m\)

Structure DOI: https://doi.org/10.1103/PhysRev.19.444.3

Photonics DOI: Gap(s) for space group 166 above band 2 theorized in: https://doi.org/10.1103/PhysRevLett.121.263903,

Gap(s) above band(s) 5, 6, 13, 18 not previously studied

Source: Inorganic Crystallographic Database #53771

MPB Epsilon Input File: Download

Gap Atlas for \(\varepsilon = 16\)

Gap Atlas for \(\varepsilon\) = 16 across filling fraction \(\phi\) and frequency \(\omega\).

Gap Atlas for \(\varepsilon = 14\)

Gap Atlas for \(\varepsilon\) = 14 across filling fraction \(\phi\) and frequency \(\omega\).

Gap Atlas for \(\varepsilon = 12\)

Gap Atlas for \(\varepsilon\) = 12 across filling fraction \(\phi\) and frequency \(\omega\).

Gap Atlas for \(\varepsilon = 10\)

Gap Atlas for \(\varepsilon\) = 10 across filling fraction \(\phi\) and frequency \(\omega\).

Gap Atlas for \(\varepsilon = 8\)

Gap Atlas for \(\varepsilon\) = 8 across filling fraction \(\phi\) and frequency \(\omega\).

Gap between Bands 2-3

Below is the band structure and isosurface of hR1–Hg (Direct) at dielectric contrast \(\varepsilon = 16\), radius \(r = 0.43\) and filling fraction \(\phi = 0.387\).

Band Structure across first Brillouin Zone.

View along \(a_1\).

Gap between Bands 5-6

Below is the band structure and isosurface of hR1–Hg (Direct) at dielectric contrast \(\varepsilon = 16\), radius \(r = 0.28\) and filling fraction \(\phi = 0.107\).

Band Structure across first Brillouin Zone.

View along \(a_1\).

Gap between Bands 6-7

Below is the band structure and isosurface of hR1–Hg (Direct) at dielectric contrast \(\varepsilon = 16\), radius \(r = 0.28\) and filling fraction \(\phi = 0.107\).

Band Structure across first Brillouin Zone.

View along \(a_1\).

Gap between Bands 13-14

Below is the band structure and isosurface of hR1–Hg (Direct) at dielectric contrast \(\varepsilon = 16\), radius \(r = 0.46\) and filling fraction \(\phi = 0.474\).

Band Structure across first Brillouin Zone.

View along \(a_1\).

Gap between Bands 18-19

Below is the band structure and isosurface of hR1–Hg (Direct) at dielectric contrast \(\varepsilon = 16\), radius \(r = 0.32\) and filling fraction \(\phi = 0.159\).

Band Structure across first Brillouin Zone.

View along \(a_1\).