calculateLocalDensityOfStates

	Core NanoLanguage elements
calculateDensityOfStates	calculateProjectedHamiltonianEigenstates

Name

calculateLocalDensityOfStates — Calculates the density of states (DOS) for atoms located in the central region of a two-probe system.

Synopsis

Namespace: ATK.TwoProbe

LocalDensityOfStates calculateLocalDensityOfStates(
self_consistent_calculation,
energy,
quantum_number,
green_function_infinitesimal
)

Description

The function calculateLocalDensityOfStates() calculates and returns the spatially resolved density of states

$\displaystyle n(E,\mathbf{r},\mathbf{k}, \sigma) = \sum_{\alpha}|\psi_{\alpha,\mathbf{k},\sigma}(\mathbf{r})|^2 \delta(E-\epsilon_{\alpha,\mathbf{k},\sigma})$

where $E$ is the energy, $\mathbf{k}$ is a point in the 2D Brillouin zone perpendicular to the transport direction, and $\sigma$ is the spin. $\psi_{\alpha,\mathbf{k},\sigma}(\mathbf{r})$ is an eigenstate $\alpha>$ with eigenenergy $\epsilon_{\alpha,\mathbf{k},\sigma}$ .

List of arguments

self_consistent_calculation

An object returned from a previously performed self-consistent calculation for a BulkConfiguration.

Default: None

energy

Energy $E$ for which the local density of states is calculated; e.g. 0.0*eV.

Default: None

quantum_number

Quantum numbers (k,σ) for which the local density of states is to be calculated (see below).

Default: None

green_function_infinitesimal

The imaginary infinitesimal added to the energy of the retarded Green's function.

Default: 1.0e-5*eV

Returned object methods

The returned object has the following two query methods:

Array toArray(): Returns the real-space representation of the local density of states as a NumPy array.
PhysicalUnit toUnit(): Returns the unit of the local density of states.

Usage examples

from ATK.TwoProbe import *
...
scf = executeSelfConsistentCalculation(...)
ldos = calculateLocalDensityOfStates(
    scf,
    energy = 0.0*eV,
    quantum_number=[[0.,0.],Spin.Up]
    )

Notes

The energy is measured relative to the average Fermi level of the two electrodes.

The quantum numbers depend on whether the system is spin-polarized or not, and should be specified as

([k_point], spin) for spin-polarized systems.
[k_point] for unpolarized systems.

where:

k_point is a dimensionless two-dimensional list of coordinates representing a k-point in the 2D Brillouin zone of the unit cell transverse to the transport direction. The coordinates must be given in units of the reciprocal lattice vectors.
spin is the spin σ.

Further examples

Further analysis of two-probe systems


calculateDensityOfStates		calculateProjectedHamiltonianEigenstates