Cd_xHg_1-xTe: topologically nontrivial material#

Last update: 2026-08-04

Tags: status:under_development topological_insulators CdHgTe bulk 8-band_kp

Summary#

This example calculates electronic band dispersion of HgTe, CdTe, and of the alloy Cd_xHg_1-xTe using 8-band \(\mathbf{k} \cdot \mathbf{p}\) method. It allows exploring phase transition of the Cd_xHg_1-xTe from the trivial one, for HgTe, to nontrivial one, for CdTe.

Example information#

Dimensionality: 1D
Structure/Device: Bulk crystal
Material system: CdHgTe
Physical models: 8-band \(\mathbf{k} \cdot \mathbf{p}\)
Difficulty: Easy
Total runtime (order of magnitude): Seconds
Memory consumption (order of magnitude): 10 MB
Prepared with software version: 3.0.0

Files#

bulk_CdHgTe_1d.nnp - complete input file for this example

Physical system#

Bulk Cd_xHg_1-xTe at 4.2 K.

Models and assumptions#

The example uses 8-band \(\mathbf{k} \cdot \mathbf{p}\) method with rescaled Luttinger parameters and 1-band effective-mass models for bulk band structure. Strain effects are included.

Simulation setup#

Uniform slab of Cd_xHg_1-xTe spanning from -1 to 1 is defined to initialize 1D simulation. Bulk band structure is calculated for the material at the position 0. It could be any position within the simulation domain as it is uniformly defined. Both \(\mathbf{k} \cdot \mathbf{p}\) and 1-band models for heavy-hole, light-hole, spin-orbit split-off hole, and electron bands in vicinity of the \(\Gamma\) point are triggered to allow comparison of the two approaches. The band structures are plotted from 1 nm^-1 towards \(L\) point, through the \(\Gamma\) point, until 1 nm^-1 towards the \(X\) point of the first Brilloun zone. Negative effective masses are enabled explicitly to inform solver that it is expected for this material system. Substrate is set to Cd_xHg_1-xTe with an independent alloy content.

Main functionalities of this simulation can be conveniently controlled using variables:

$strain: when set to 1 then strain effects are included, if set to 0 then otherwise
$temperature: the temperature expressed in K,
$alloy_x_bulk: alloy content \(x\) in CdxHg1-xTe of the analyzed bulk material,
$alloy_x_substrate: alloy content \(x\) in CdxHg1-xTe substrate.

Running the example#

Run the input file directly as provided.

Output files#

./Bulk_dispersions/kp8/bulk_dispersion_HgCdTe.dat
bulk band structure using 8-band \(\mathbf{k} \cdot \mathbf{p}\) method

./Bulk_dispersions/Gamma/bulk_dispersion_HgCdTe.dat
bulk band structure using 1-band model for electrons near the \(\Gamma\) point

./Bulk_dispersions/HH/bulk_dispersion_HgCdTe.dat
bulk band structure using 1-band model for heavy-hole valence band

./Bulk_dispersions/LH/bulk_dispersion_HgCdTe.dat
bulk band structure using 1-band model for light-hole valence band

./Bulk_dispersions/SO/bulk_dispersion_HgCdTe.dat
bulk band structure using 1-band model for split-off-hole valence band

Results#

../../_images/electronic_band_structures.png — Figure 379 TEMPORARY FIGURE: Electronic band structures of bulk (a) CdTe, (b) Cd_0.16Hg_0.84Te, and (c) HgTe calculated using 8-band \(\mathbf{k} \cdot \mathbf{p}\) model.#

CdxHg1-xTe: topologically nontrivial material#