transport.rst 3.66 KB
 jensj committed Jul 28, 2014 1 .. module:: ase.transport  carstenr committed Aug 14, 2008 2 3 4 5 6 7  :synopsis: Electron transport ================== Electron transport ==================  jensj committed Jul 28, 2014 8 9 The :mod:ase.transport module of ASE assumes the generic setup of the system in question sketched below:  carstenr committed Aug 14, 2008 10 11 12 13 14 15 16 17 18 19  . . . |setup| . . . .. |setup| image:: transport_setup.png :align: middle There is a central region (blue atoms plus the molecule) connected to two semi-infinite leads constructed by infinitely repeated *principal layers* (red atoms). The entire structure may be periodic in the transverse direction, which can be effectively sampled using  carstenr committed Aug 15, 2008 20 **k**-points (yellowish atoms).  carstenr committed Aug 14, 2008 21 22 23 24 25 26 27 28 29 30 31 32 33  The system is described by a Hamiltonian matrix which must be represented in terms of a localized basis set such that each element of the Hamiltonian can be ascribed to either the left, central, or right region, *or* the coupling between these. The Hamiltonian can thus be decomposed as: .. math:: H = \begin{pmatrix} \ddots & V_L & & & \\ V_L^\dagger & H_L & V_L & & \\  jensj committed Jul 28, 2014 34 35 36  & V_L^\dagger & H_C & V_R & \\ & & V_R^\dagger & H_R & V_R \\ & & & V_R^\dagger & \ddots  carstenr committed Aug 14, 2008 37 38 39 40  \end{pmatrix} where H_{L/R} describes the left/right principal layer, and H_C the central region. V_{L/R} is the coupling between principal  carstenr committed Aug 14, 2008 41 layers, *and* from the principal layers into the central region. The  carstenr committed Aug 14, 2008 42 43 44 central region must contain at least one principal layer on each side, and more if the potential has not converged to its bulk value at this size. The central region is assumed to be big enough that there is no  carstenr committed Aug 14, 2008 45 46 direct coupling between the two leads. The principal layer must be so big that there is only coupling between nearest neighbor layers.  carstenr committed Aug 14, 2008 47 48  Having defined H_{L/R}, V_{L/R}, and H_C, the elastic  dulak committed May 30, 2013 49 transmission function can be determined using the Non-equilibrium  carstenr committed Aug 23, 2008 50 Green Function (NEGF) method. This is achieved by the class:  carstenr committed Aug 14, 2008 51 52 53 54 :class:~ase.transport.calculators.TransportCalculator (in ase.transport.calculators) which makes no requirement on the origin of these five matrices.  Mikkel Strange committed Feb 24, 2016 55 .. autoclass:: TransportCalculator  carstenr committed Aug 23, 2008 56 57 58   Mikkel Strange committed Feb 24, 2016 59 .. .. class:: ase.transport.calculators.TransportCalculator(energies, h, h1, h2, s=None, s1=None, s2=None, align_bf=False)  carstenr committed Aug 23, 2008 60   Mikkel Strange committed Feb 24, 2016 61 62  Determine transport properties of device sandwiched between semi-infinite leads using non-equillibrium Green function methods.  carstenr committed Aug 23, 2008 63   Mikkel Strange committed Feb 24, 2016 64 65  energies is the energy grid on which the transport properties should be determined.  carstenr committed Aug 23, 2008 66   Mikkel Strange committed Feb 24, 2016 67 68 69 70 71 72 73 74 75 76 77 78 79 80  h1 (h2) is a matrix representation of the Hamiltonian of two principal layers of the left (right) lead, and the coupling between such layers. h is a matrix representation of the Hamiltonian of the scattering region. This must include at least on lead principal layer on each side. The coupling in (out) of the scattering region is assumed to be identical to the coupling between left (right) principal layers. s, s1, and s2 are the overlap matrices corresponding to h, h1, and h2. Default is the identity operator. If align_bf is True, the onsite elements of the Hamiltonians will be shifted to a common fermi level.  carstenr committed Aug 23, 2008 81 82 83 84 85 86  This module is stand-alone in the sense that it makes no requirement on the origin of these five matrices. They can be model Hamiltonians or derived from different kinds of electronic structure codes.  Jens Jørgen Mortensen committed Mar 19, 2019 87 88 For an example of how to use the :mod:ase.transport module, see section 9.2 in the ASE-paper:  carstenr committed Aug 14, 2008 89   Jens Jørgen Mortensen committed Mar 19, 2019 90 91 92 93  J. Phys. Condens. Matter: The Atomic Simulation Environment | A Python library for working with atoms __ (7 June 2017).