root / ase / transport / stm.py @ 1
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| 1 | 1 | tkerber | import numpy as np |
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| 2 | 1 | tkerber | from ase.transport.tools import dagger |
| 3 | 1 | tkerber | from ase.transport.selfenergy import LeadSelfEnergy |
| 4 | 1 | tkerber | from ase.transport.greenfunction import GreenFunction |
| 5 | 1 | tkerber | import time |
| 6 | 1 | tkerber | from gpaw.mpi import world |
| 7 | 1 | tkerber | |
| 8 | 1 | tkerber | |
| 9 | 1 | tkerber | class STM: |
| 10 | 1 | tkerber | def __init__(self, h1, s1, h2, s2 ,h10, s10, h20, s20, eta1, eta2, w=0.5, pdos=[], logfile = None): |
| 11 | 1 | tkerber | """XXX
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| 12 | 1 | tkerber |
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| 13 | 1 | tkerber | 1. Tip
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| 14 | 1 | tkerber | 2. Surface
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| 15 | 1 | tkerber |
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| 16 | 1 | tkerber | h1: ndarray
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| 17 | 1 | tkerber | Hamiltonian and overlap matrix for the isolated tip
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| 18 | 1 | tkerber | calculation. Note, h1 should contain (at least) one
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| 19 | 1 | tkerber | principal layer.
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| 20 | 1 | tkerber |
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| 21 | 1 | tkerber | h2: ndarray
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| 22 | 1 | tkerber | Same as h1 but for the surface.
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| 23 | 1 | tkerber |
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| 24 | 1 | tkerber | h10: ndarray
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| 25 | 1 | tkerber | periodic part of the tip. must include two and only
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| 26 | 1 | tkerber | two principal layers.
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| 27 | 1 | tkerber |
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| 28 | 1 | tkerber | h20: ndarray
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| 29 | 1 | tkerber | same as h10, but for the surface
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| 30 | 1 | tkerber |
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| 31 | 1 | tkerber | The s* are the corresponding overlap matrices. eta1, and eta
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| 32 | 1 | tkerber | 2 are (finite) infinitesimals. """
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| 33 | 1 | tkerber | |
| 34 | 1 | tkerber | self.pl1 = len(h10) // 2 #principal layer size for the tip |
| 35 | 1 | tkerber | self.pl2 = len(h20) // 2 #principal layer size for the surface |
| 36 | 1 | tkerber | self.h1 = h1
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| 37 | 1 | tkerber | self.s1 = s1
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| 38 | 1 | tkerber | self.h2 = h2
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| 39 | 1 | tkerber | self.s2 = s2
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| 40 | 1 | tkerber | self.h10 = h10
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| 41 | 1 | tkerber | self.s10 = s10
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| 42 | 1 | tkerber | self.h20 = h20
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| 43 | 1 | tkerber | self.s20 = s20
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| 44 | 1 | tkerber | self.eta1 = eta1
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| 45 | 1 | tkerber | self.eta2 = eta2
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| 46 | 1 | tkerber | self.w = w #asymmetry of the applied bias (0.5=>symmetric) |
| 47 | 1 | tkerber | self.pdos = []
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| 48 | 1 | tkerber | self.log = logfile
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| 49 | 1 | tkerber | |
| 50 | 1 | tkerber | def initialize(self, energies, bias=0): |
| 51 | 1 | tkerber | """
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| 52 | 1 | tkerber | energies: list of energies
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| 53 | 1 | tkerber | for which the transmission function should be evaluated.
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| 54 | 1 | tkerber | bias.
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| 55 | 1 | tkerber | Will precalculate the surface greenfunctions of the tip and
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| 56 | 1 | tkerber | surface.
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| 57 | 1 | tkerber | """
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| 58 | 1 | tkerber | self.bias = bias
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| 59 | 1 | tkerber | self.energies = energies
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| 60 | 1 | tkerber | nenergies = len(energies)
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| 61 | 1 | tkerber | pl1, pl2 = self.pl1, self.pl2 |
| 62 | 1 | tkerber | nbf1, nbf2 = len(self.h1), len(self.h2) |
| 63 | 1 | tkerber | |
| 64 | 1 | tkerber | #periodic part of the tip
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| 65 | 1 | tkerber | hs1_dii = self.h10[:pl1, :pl1], self.s10[:pl1, :pl1] |
| 66 | 1 | tkerber | hs1_dij = self.h10[:pl1, pl1:2*pl1], self.s10[:pl1, pl1:2*pl1] |
| 67 | 1 | tkerber | #coupling betwen per. and non. per part of the tip
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| 68 | 1 | tkerber | h1_im = np.zeros((pl1, nbf1), complex)
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| 69 | 1 | tkerber | s1_im = np.zeros((pl1, nbf1), complex)
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| 70 | 1 | tkerber | h1_im[:pl1, :pl1], s1_im[:pl1, :pl1] = hs1_dij |
| 71 | 1 | tkerber | hs1_dim = [h1_im, s1_im] |
| 72 | 1 | tkerber | |
| 73 | 1 | tkerber | #periodic part the surface
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| 74 | 1 | tkerber | hs2_dii = self.h20[:pl2, :pl2], self.s20[:pl2, :pl2] |
| 75 | 1 | tkerber | hs2_dij = self.h20[pl2:2*pl2, :pl2], self.s20[pl2:2*pl2, :pl2] |
| 76 | 1 | tkerber | #coupling betwen per. and non. per part of the surface
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| 77 | 1 | tkerber | h2_im = np.zeros((pl2, nbf2), complex)
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| 78 | 1 | tkerber | s2_im = np.zeros((pl2, nbf2), complex)
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| 79 | 1 | tkerber | h2_im[-pl2:, -pl2:], s2_im[-pl2:, -pl2:] = hs2_dij |
| 80 | 1 | tkerber | hs2_dim = [h2_im, s2_im] |
| 81 | 1 | tkerber | |
| 82 | 1 | tkerber | #tip and surface greenfunction
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| 83 | 1 | tkerber | self.selfenergy1 = LeadSelfEnergy(hs1_dii, hs1_dij, hs1_dim, self.eta1) |
| 84 | 1 | tkerber | self.selfenergy2 = LeadSelfEnergy(hs2_dii, hs2_dij, hs2_dim, self.eta2) |
| 85 | 1 | tkerber | self.greenfunction1 = GreenFunction(self.h1-self.bias*self.w*self.s1, self.s1, |
| 86 | 1 | tkerber | [self.selfenergy1], self.eta1) |
| 87 | 1 | tkerber | self.greenfunction2 = GreenFunction(self.h2-self.bias*(self.w-1)*self.s2, self.s2, |
| 88 | 1 | tkerber | [self.selfenergy2], self.eta2) |
| 89 | 1 | tkerber | |
| 90 | 1 | tkerber | #Shift the bands due to the bias.
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| 91 | 1 | tkerber | bias_shift1 = -bias * self.w
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| 92 | 1 | tkerber | bias_shift2 = -bias * (self.w - 1) |
| 93 | 1 | tkerber | self.selfenergy1.set_bias(bias_shift1)
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| 94 | 1 | tkerber | self.selfenergy2.set_bias(bias_shift2)
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| 95 | 1 | tkerber | |
| 96 | 1 | tkerber | #tip and surface greenfunction matrices.
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| 97 | 1 | tkerber | nbf1_small = nbf1 #XXX Change this for efficiency in the future
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| 98 | 1 | tkerber | nbf2_small = nbf2 #XXX -||-
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| 99 | 1 | tkerber | coupling_list1 = range(nbf1_small)# XXX -||- |
| 100 | 1 | tkerber | coupling_list2 = range(nbf2_small)# XXX -||- |
| 101 | 1 | tkerber | self.gft1_emm = np.zeros((nenergies, nbf1_small, nbf1_small), complex) |
| 102 | 1 | tkerber | self.gft2_emm = np.zeros((nenergies, nbf2_small, nbf2_small), complex) |
| 103 | 1 | tkerber | |
| 104 | 1 | tkerber | for e, energy in enumerate(self.energies): |
| 105 | 1 | tkerber | if self.log != None: # and world.rank == 0: |
| 106 | 1 | tkerber | T = time.localtime() |
| 107 | 1 | tkerber | self.log.write(' %d:%02d:%02d, ' % (T[3], T[4], T[5]) + |
| 108 | 1 | tkerber | '%d, %d, %02f\n' % (world.rank, e, energy))
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| 109 | 1 | tkerber | gft1_mm = self.greenfunction1.retarded(energy)[coupling_list1]
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| 110 | 1 | tkerber | gft1_mm = np.take(gft1_mm, coupling_list1, axis=1)
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| 111 | 1 | tkerber | |
| 112 | 1 | tkerber | gft2_mm = self.greenfunction2.retarded(energy)[coupling_list2]
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| 113 | 1 | tkerber | gft2_mm = np.take(gft2_mm, coupling_list2, axis=1)
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| 114 | 1 | tkerber | |
| 115 | 1 | tkerber | self.gft1_emm[e] = gft1_mm
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| 116 | 1 | tkerber | self.gft2_emm[e] = gft2_mm
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| 117 | 1 | tkerber | |
| 118 | 1 | tkerber | if self.log != None and world.rank == 0: |
| 119 | 1 | tkerber | self.log.flush()
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| 120 | 1 | tkerber | |
| 121 | 1 | tkerber | def get_transmission(self, v_12, v_11_2=None, v_22_1=None): |
| 122 | 1 | tkerber | """XXX
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| 123 | 1 | tkerber |
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| 124 | 1 | tkerber | v_12:
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| 125 | 1 | tkerber | coupling between tip and surface
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| 126 | 1 | tkerber | v_11_2:
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| 127 | 1 | tkerber | correction to "on-site" tip elements due to the
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| 128 | 1 | tkerber | surface (eq.16). Is only included to first order.
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| 129 | 1 | tkerber | v_22_1:
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| 130 | 1 | tkerber | corretion to "on-site" surface elements due to he
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| 131 | 1 | tkerber | tip (eq.17). Is only included to first order.
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| 132 | 1 | tkerber | """
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| 133 | 1 | tkerber | |
| 134 | 1 | tkerber | dim0 = v_12.shape[0]
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| 135 | 1 | tkerber | dim1 = v_12.shape[1]
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| 136 | 1 | tkerber | |
| 137 | 1 | tkerber | nenergies = len(self.energies) |
| 138 | 1 | tkerber | T_e = np.empty(nenergies,float)
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| 139 | 1 | tkerber | v_21 = dagger(v_12) |
| 140 | 1 | tkerber | for e, energy in enumerate(self.energies): |
| 141 | 1 | tkerber | gft1 = self.gft1_emm[e]
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| 142 | 1 | tkerber | if v_11_2!=None: |
| 143 | 1 | tkerber | gf1 = np.dot(v_11_2, np.dot(gft1, v_11_2)) |
| 144 | 1 | tkerber | gf1 += gft1 #eq. 16
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| 145 | 1 | tkerber | else:
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| 146 | 1 | tkerber | gf1 = gft1 |
| 147 | 1 | tkerber | |
| 148 | 1 | tkerber | gft2 = self.gft2_emm[e]
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| 149 | 1 | tkerber | if v_22_1!=None: |
| 150 | 1 | tkerber | gf2 = np.dot(v_22_1,np.dot(gft2, v_22_1)) |
| 151 | 1 | tkerber | gf2 += gft2 #eq. 17
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| 152 | 1 | tkerber | else:
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| 153 | 1 | tkerber | gf2 = gft2 |
| 154 | 1 | tkerber | |
| 155 | 1 | tkerber | a1 = (gf1 - dagger(gf1)) |
| 156 | 1 | tkerber | a2 = (gf2 - dagger(gf2)) |
| 157 | 1 | tkerber | self.v_12 = v_12
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| 158 | 1 | tkerber | self.a2 = a2
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| 159 | 1 | tkerber | self.v_21 = v_21
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| 160 | 1 | tkerber | self.a1 = a1
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| 161 | 1 | tkerber | v12_a2 = np.dot(v_12, a2[:dim1]) |
| 162 | 1 | tkerber | v21_a1 = np.dot(v_21, a1[-dim0:]) |
| 163 | 1 | tkerber | self.v12_a2 = v12_a2
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| 164 | 1 | tkerber | self.v21_a1 = v21_a1
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| 165 | 1 | tkerber | T = -np.trace(np.dot(v12_a2[:,:dim1], v21_a1[:,-dim0:])) #eq. 11
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| 166 | 1 | tkerber | T_e[e] = T |
| 167 | 1 | tkerber | self.T_e = T_e
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| 168 | 1 | tkerber | return T_e
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| 169 | 1 | tkerber | |
| 170 | 1 | tkerber | |
| 171 | 1 | tkerber | def get_current(self, bias, v_12, v_11_2=None, v_22_1=None): |
| 172 | 1 | tkerber | """Very simple function to calculate the current.
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| 173 | 1 | tkerber |
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| 174 | 1 | tkerber | Asummes zero temperature.
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| 175 | 1 | tkerber |
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| 176 | 1 | tkerber | bias: type? XXX
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| 177 | 1 | tkerber | bias voltage (V)
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| 178 | 1 | tkerber |
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| 179 | 1 | tkerber | v_12: XXX
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| 180 | 1 | tkerber | coupling between tip and surface.
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| 181 | 1 | tkerber |
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| 182 | 1 | tkerber | v_11_2:
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| 183 | 1 | tkerber | correction to onsite elements of the tip
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| 184 | 1 | tkerber | due to the potential of the surface.
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| 185 | 1 | tkerber | v_22_1:
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| 186 | 1 | tkerber | correction to onsite elements of the surface
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| 187 | 1 | tkerber | due to the potential of the tip.
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| 188 | 1 | tkerber | """
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| 189 | 1 | tkerber | energies = self.energies
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| 190 | 1 | tkerber | T_e = self.get_transmission(v_12, v_11_2, v_22_1)
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| 191 | 1 | tkerber | bias_window = -np.array([bias * self.w, bias * (self.w - 1)]) |
| 192 | 1 | tkerber | bias_window.sort() |
| 193 | 1 | tkerber | self.bias_window = bias_window
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| 194 | 1 | tkerber | #print 'bias window', np.around(bias_window,3)
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| 195 | 1 | tkerber | #print 'Shift of tip lead do to the bias:', self.selfenergy1.bias
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| 196 | 1 | tkerber | #print 'Shift of surface lead do to the bias:', self.selfenergy2.bias
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| 197 | 1 | tkerber | i1 = sum(energies < bias_window[0]) |
| 198 | 1 | tkerber | i2 = sum(energies < bias_window[1]) |
| 199 | 1 | tkerber | step = 1
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| 200 | 1 | tkerber | if i2 < i1:
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| 201 | 1 | tkerber | step = -1
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| 202 | 1 | tkerber | |
| 203 | 1 | tkerber | return np.sign(bias)*np.trapz(x=energies[i1:i2:step], y=T_e[i1:i2:step])
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| 204 | 1 | tkerber | |
| 205 | 1 | tkerber | |
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| 207 | 1 | tkerber | |
| 208 | 1 | tkerber |