Dichalcogenide

class dichalcogenide.Dichalcogenide(material=<dichalcogenides.model.material.Material object>, system=<dichalcogenides.model.system.System object>, root='')

Model for a dichalcogenide.

Inherits from model.Model.

at

Product of the lattice constant and hopping energy.

Returns:\(at\) Return type:float

Δ

Valance band conduction band energy splitting.

Returns:\(Δ\) Return type:float

λ

Half the valence band spin splitting.

Returns:\(λ\) Return type:float

class dichalcogenide.Energy(dichalcogenide)

Dichalcogenide properties related to the energy.

Instantiate with a Dichalcogenide instance, e.g.,

energy = Energy(Dichalcogenide('mos2', 'default'))
energy.e(0, 1, 1, 1)

e(k, n, τ, σ)

Band energy.

Parameters:

• k (float) – Momentum \(k\).
• n (int) – Band index \(n = ±1\).
• τ (int) – Valley index \(τ = ±1\).
• σ (int) – Spin index \(σ = ±1\).

Returns:

\(E^n_{τ σ} (k)\)

Return type:

float

k(e, n, τ, σ)

Inverse energy-momentum relation.

Parameters:

• e (float) – Energy \(E\).
• n (int) – Band index \(n = ±1\).
• τ (int) – Valley index \(τ = ±1\).
• σ (int) – Spin index \(σ = ±1\).

Returns:

\(k(E)\)

Return type:

float

class dichalcogenide.UpperValenceBand(dichalcogenide)

Dichalcogenide properties related to the upper valence band energy.

For this class, the energy is assumed to be in the upper valence band: \(n = -1\) and \(τ = σ\).

Instantiate with a Dichalcogenide instance, e.g.,

uvb = UpperValenceBand(Dichalcogenide('mos2', 'default'))
uvb.ρ(0)

trig(name)

Trigonometric functions of the energy.

• sin θ - \(\sin θ(E)\)
• cos θ - \(\cos θ(E)\)
• sin^2 θ/2 - \(\sin^2 \frac{θ(E)}{2}\)
• cos^2 θ/2 - \(\cos^2 \frac{θ(E)}{2}\)

Parameters:name (str) – One of the above function names. Returns:Corresponding function of the energy \(E\). Return type:function

Δμ

Chemical potential offset.

The distance of the chemical potential from the top of the upper valence band.

Returns:\(Δμ\) Return type:float Default:\(-λ\)

μ

Chemical potential.

Determined by the chemical potential offset.

Returns:\(μ = λ - Δ / 2 + Δμ\) Return type:float

ξ_bounds

Allowed range for the variable \(ξ = E - μ\).

Returns:\((\left|Δμ\right| - 2 λ, \left|Δμ\right|)\) Return type:tuple

ρ(e)

Density of states.

Parameters:e (float) – Energy \(E\). Returns:\(ρ(E) = \left|k'(E) k(E)\right|\) Return type:float

class dichalcogenide.Optical(dichalcogenide)

Dichalcogenide properties related to optical transitions.

Instantiate with a Dichalcogenide instance, e.g.,

optical = Optical(Dichalcogenide('mos2', 'default'))

p_circular(e, τ, ε)

Matrix element for optical transitions (circular polarization): \(\left|P^{+-}_α \left(E, \mathbf{ϵ_±} \right)\right|^2\).

Transitions are from the upper valance band to the lower conduction band. Given in units of \(\text{GeV}^2\).

Parameters:

• e (float) – Energy \(E\).
• τ (int) – Valley index \(τ = ±1\).
• ϵ (int) – Polarization index \(ϵ = ±1\).