Chimie Théorique » QMX

import numpy as np

from ase.transport.tools import dagger

from ase.transport.selfenergy import LeadSelfEnergy

from ase.transport.greenfunction import GreenFunction

import time

from gpaw.mpi import world

class STM:

    def __init__(self, h1, s1, h2, s2 ,h10, s10, h20, s20, eta1, eta2, w=0.5, pdos=[], logfile = None):

        """XXX

        1. Tip

        2. Surface

        h1: ndarray

            Hamiltonian and overlap matrix for the isolated tip

            calculation.  Note, h1 should contain (at least) one

            principal layer.

        h2: ndarray

            Same as h1 but for the surface.

        h10: ndarray

            periodic part of the tip. must include two and only

            two principal layers.

        h20: ndarray

            same as h10, but for the surface

        The s* are the corresponding overlap matrices.  eta1, and eta

        2 are (finite) infinitesimals.  """

        self.pl1 = len(h10) // 2 #principal layer size for the tip

        self.pl2 = len(h20) // 2 #principal layer size for the surface

        self.h1 = h1 

        self.s1 = s1

        self.h2 = h2

        self.s2 = s2

        self.h10 = h10 

        self.s10 = s10 

        self.h20 = h20 

        self.s20 = s20

        self.eta1 = eta1

        self.eta2 = eta2

        self.w = w #asymmetry of the applied bias (0.5=>symmetric)

        self.pdos = []

        self.log = logfile

    def initialize(self, energies, bias=0):

        """

            energies: list of energies 

            for which the transmission function should be evaluated.

            bias.

            Will precalculate the surface greenfunctions of the tip and

            surface.

        """

        self.bias = bias

        self.energies = energies

        nenergies = len(energies)

        pl1, pl2 = self.pl1, self.pl2

        nbf1, nbf2 = len(self.h1), len(self.h2)

        #periodic part of the tip

        hs1_dii = self.h10[:pl1, :pl1], self.s10[:pl1, :pl1]

        hs1_dij = self.h10[:pl1, pl1:2*pl1], self.s10[:pl1, pl1:2*pl1]

        #coupling betwen per. and non. per part of the tip

        h1_im = np.zeros((pl1, nbf1), complex) 

        s1_im = np.zeros((pl1, nbf1), complex)

        h1_im[:pl1, :pl1], s1_im[:pl1, :pl1] = hs1_dij

        hs1_dim = [h1_im, s1_im]

        #periodic part the surface 

        hs2_dii = self.h20[:pl2, :pl2], self.s20[:pl2, :pl2]

        hs2_dij = self.h20[pl2:2*pl2, :pl2], self.s20[pl2:2*pl2, :pl2]

        #coupling betwen per. and non. per part of the surface

        h2_im = np.zeros((pl2, nbf2), complex)

        s2_im = np.zeros((pl2, nbf2), complex) 

        h2_im[-pl2:, -pl2:], s2_im[-pl2:, -pl2:] = hs2_dij

        hs2_dim = [h2_im, s2_im]

        #tip and surface greenfunction 

        self.selfenergy1 = LeadSelfEnergy(hs1_dii, hs1_dij, hs1_dim, self.eta1)

        self.selfenergy2 = LeadSelfEnergy(hs2_dii, hs2_dij, hs2_dim, self.eta2)

        self.greenfunction1 = GreenFunction(self.h1-self.bias*self.w*self.s1, self.s1, 

                                            [self.selfenergy1], self.eta1)

        self.greenfunction2 = GreenFunction(self.h2-self.bias*(self.w-1)*self.s2, self.s2, 

                                            [self.selfenergy2], self.eta2)

        #Shift the bands due to the bias.

        bias_shift1 = -bias * self.w

        bias_shift2 = -bias * (self.w - 1)

        self.selfenergy1.set_bias(bias_shift1)

        self.selfenergy2.set_bias(bias_shift2)

        #tip and surface greenfunction matrices.

        nbf1_small = nbf1 #XXX Change this for efficiency in the future

        nbf2_small = nbf2 #XXX -||-

        coupling_list1 = range(nbf1_small)# XXX -||-

        coupling_list2 = range(nbf2_small)# XXX -||-

        self.gft1_emm = np.zeros((nenergies, nbf1_small, nbf1_small), complex) 

        self.gft2_emm = np.zeros((nenergies, nbf2_small, nbf2_small), complex)

        for e, energy in enumerate(self.energies):

            if self.log != None: # and world.rank == 0:

                    T = time.localtime()

                    self.log.write(' %d:%02d:%02d, ' % (T[3], T[4], T[5]) +

                                   '%d, %d, %02f\n' % (world.rank, e, energy))

            gft1_mm = self.greenfunction1.retarded(energy)[coupling_list1]

            gft1_mm = np.take(gft1_mm, coupling_list1, axis=1)

            gft2_mm = self.greenfunction2.retarded(energy)[coupling_list2]

            gft2_mm = np.take(gft2_mm, coupling_list2, axis=1)

            self.gft1_emm[e] = gft1_mm

            self.gft2_emm[e] = gft2_mm

            if self.log != None and world.rank == 0:

                self.log.flush()

    def get_transmission(self, v_12, v_11_2=None, v_22_1=None):

        """XXX

        v_12:

            coupling between tip and surface 

        v_11_2:

            correction to "on-site" tip elements due to the 

            surface (eq.16). Is only included to first order.

        v_22_1:

            corretion to "on-site" surface elements due to he

            tip (eq.17). Is only included to first order.

        """

        dim0 = v_12.shape[0]

        dim1 = v_12.shape[1]

        nenergies = len(self.energies)

        T_e = np.empty(nenergies,float)

        v_21 = dagger(v_12)

        for e, energy in enumerate(self.energies):

            gft1 = self.gft1_emm[e]

            if v_11_2!=None:

                gf1 = np.dot(v_11_2, np.dot(gft1, v_11_2)) 

                gf1 += gft1 #eq. 16

            else:

                gf1 = gft1

            gft2 = self.gft2_emm[e]

            if v_22_1!=None:

                gf2 = np.dot(v_22_1,np.dot(gft2, v_22_1))

                gf2 += gft2 #eq. 17

            else:

                gf2 = gft2

            a1 = (gf1 - dagger(gf1))

            a2 = (gf2 - dagger(gf2))

            self.v_12 = v_12

            self.a2 = a2

            self.v_21 = v_21

            self.a1 = a1

            v12_a2 = np.dot(v_12, a2[:dim1])

            v21_a1 = np.dot(v_21, a1[-dim0:])

            self.v12_a2 = v12_a2

            self.v21_a1 = v21_a1

            T = -np.trace(np.dot(v12_a2[:,:dim1], v21_a1[:,-dim0:])) #eq. 11

            T_e[e] = T

            self.T_e = T_e

        return T_e

    def get_current(self, bias, v_12, v_11_2=None, v_22_1=None):

        """Very simple function to calculate the current.

        Asummes zero temperature.

        bias: type? XXX

            bias voltage (V)

        v_12: XXX

            coupling between tip and surface.

        v_11_2:

            correction to onsite elements of the tip

            due to the potential of the surface.

        v_22_1:

            correction to onsite elements of the surface

            due to the potential of the tip.

        """

        energies = self.energies

        T_e = self.get_transmission(v_12, v_11_2, v_22_1)

        bias_window = -np.array([bias * self.w, bias * (self.w - 1)])

        bias_window.sort()

        self.bias_window = bias_window

        #print 'bias window', np.around(bias_window,3)

        #print 'Shift of tip lead do to the bias:', self.selfenergy1.bias

        #print 'Shift of surface lead do to the bias:', self.selfenergy2.bias

        i1 = sum(energies < bias_window[0]) 

        i2 = sum(energies < bias_window[1])

        step = 1 

        if i2 < i1:

            step = -1

        return np.sign(bias)*np.trapz(x=energies[i1:i2:step], y=T_e[i1:i2:step])