Electronic transport properties of molecules, nano-wires, and bulks such as superlattice structures can be calculated based on a non-equilibrium Green function (NEGF) method within the collinear and non-collinear DFT methods. The features and capabilities are listed below:

- SCF calculation of system with two leads under zero and finite bias voltage
- SCF calculation under gate bias voltage
- Compatible with the LDA+U method
- Spin-dependent transmission and current
**k**-resolved transmission and current along perpendicular to the current axis- Calculation of current-voltage curve
- Accurate and efficient contour integration scheme
- Interpolation of the effect by the bias voltage
- Quick calculation for periodic systems under zero bias
- The eigen-channel analysis [97]
- The real-space charge and spin current [95]

The details of the implementation can be found in Ref. [58]. First the usage of the functionalities for the collinear case is explained in the following subsections. After then, the non-collinear case will be discussed.

**System we consider**

In the current implementation of OpenMX Ver. 3.8, a system shown in Fig. 31(a) is treated
by the NEGF method. The system consists of a central region connected with
infinite left and right leads, and the two dimensional periodicity spreads
over the **bc**-plane. Considering the two dimensional periodicity, the
system can be cast into a one-dimensional problem depending on
the Bloch wave vector shown in Fig. 31(b).
Also, the Green function of the region
is self-consistently
determined in order to take account of relaxation of electronic structure around
the interface between the central region and the region .
It should be noted that the electronic transport is assumed to be along
the **a**-axis in the current implementation. Thus, users have to keep in mind
the specification when the geometrical structure is constructed.
See also the subsection 'Step 1: The calculations for leads'.

**Computational flow**

The NEGF calculation is performed by the following three steps:

** Step 1 Step 2 Step 3
**

Each step consists of

**Step 1**The band structure calculations are performed for the left and right leads using a program code 'openmx'. The calculated results will be used to represent the Hamiltonian of the leads in the NEGF calculation of the step 2.

**Step 2**The NEGF calculation is performed for the structure shown in Fig. 31 under zero or a finite bias voltage using a program code 'openmx', where the result in the step 1 is used for the construction of the leads.

**Step 3**By making use of the result of the step 2, the transmission, charge/spin current density, and the eigenchannel are calculated by a program code 'openmx'.

**An example: carbon chain**

As a first trial, let us illustrate the three steps by employing a carbon chain. Before going to the illustration,

**Step 1**

%./openmx Lead-Chain.dat | tee lead-chain.std

A file 'negf-chain.hks' is generated by the step 1.

**Step 2**

%./openmx NEGF-Chain.dat | tee negf-chain.std

A file 'negf-chain.tranb' is generated by the step 2.

**Step 3**

`openmx`

starts step 3 immediately after it finishes step 2.
If we perform separately the step2 and the step 3, we run `openmx`

as follows:

%./openmx Lead-Chain.dat | tee lead-chain.std

In the step 3, `openmx`

reads a file 'negf-chain.tranb' and
calculates the transmission, current, and eigen channels.

negf-chain.conductance negf-chain.tranec0_0_0_2_r.cube negf-chain.current negf-chain.tranec0_0_0_3_i.cube negf-chain.tran0_0 negf-chain.tranec0_0_0_3_r.cube negf-chain.tranec0_0_0_0_i.cube negf-chain.tranec0_0_0_4_i.cube negf-chain.tranec0_0_0_0_r.cube negf-chain.tranec0_0_0_4_r.cube negf-chain.tranec0_0_0_1_i.cube negf-chain.traneval0_0_0 negf-chain.tranec0_0_0_1_r.cube negf-chain.tranevec0_0_0 negf-chain.tranec0_0_0_2_i.cubeare generated by the step 3.

The calculations can be traced by using the input files stored in a directory of 'work/negf_example'. By plotting the sixth column in 'negf-chain.tran0_0' as a function of the fourth column, you can see a transmission curve as shown in Fig. 32.

2016-04-03