-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathbidirection.py
278 lines (210 loc) · 8 KB
/
bidirection.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
# Prerequisites
from __future__ import division, print_function
#get_ipython().magic(u'matplotlib inline')
import matplotlib.pyplot as plt
import numpy as np
import time
import qmeq
import random
# Quantum dot parameters
vgate = 0.0
bfield = 0.0
omega = 0.0
vbias = 20
cL1,cG1,cm = 1.6, 0.6, 1.0
cL2,c12,c21,cG2 = 0.3, 0.2, 0.2, 0.5
cR2,cR1 = 1.6, 0.3
q10 = 0.0
q20 = 0.0
csigma1 = cL1 + cG1 + cm + c12 + cR1
csigma2 = cR2 + cG2 + cm + c21 + cL2
U1 = (csigma2/(csigma1*csigma2-cm**2))/6.24*1000
U2 = (csigma1/(csigma1*csigma2-cm**2))/6.24*1000
Um = (cm/(csigma1*csigma2 - cm**2))/6.24*1000
print(U1)
print(U2)
print(Um)
vgate1, vgate2, vbiasL, vbiasR = 0.0, 0.0, 10.0, 0.0
q1 = (c12*vgate2 + cG1*vgate1 + cL1*vbiasL + cR1*vbiasR)*6.24/1000 + q10
q2 = (c21*vgate1 + cG2*vgate2 + cL2*vbiasL + cR2*vbiasR)*6.24/1000 + q10
mu1 = Um*q2 + U1*q1 - U1/2
mu2 = Um*q1 + U2*q2 - U2/2
omegapres, omegaflip = 0.01*U1, 0.00*U1
Jev = 0.01 * random.random()
Jt1v = 0.01 * random.random()
Jt2v = 0.01 * random.random()
Je = 0.03*U1
Jp = 0.00*U1
Jt1 = 0.00*U1
Jt2 = 0.00*U1
print(Je)
print(Jt1)
print(Jt2)
Eq1 = 0.5 * U1
Eq2 = 0.0 * U1
Eq1h = 0.5 * U1
Eq2h = 0.0 * U1
# Lead parameters
temp = 0.5
dband = 2000
# Tunneling amplitudes
gam = 0.005
t0 = np.sqrt(gam/(2*np.pi))
t00 = 0.0*t0
nsingle = 4
hsingle = {(0,0): Eq1-mu1+bfield/2,
(1,1): Eq1-mu1-bfield/2,
(2,2): Eq2-mu2+bfield/2,
(3,3): Eq2-mu2-bfield/2,
(0,2): -omegapres,
(1,3): -omegapres,
(0,3): -omegaflip,
(1,2): -omegaflip
}
# 0 is up, 1 is down
coulomb = {(0,1,1,0):U1,
(1,2,2,1):Um,
(0,2,2,0):Um-Je,
(1,3,3,1):Um-Je,
(0,3,3,0):Um,
(2,3,3,2):U2,
(1,2,3,0):-Je,
(0,3,2,1):-Je,
(2,3,0,1):-Jp,
(0,1,2,3):-Jp,
(0,1,3,0):-Jt1,
(0,1,1,2):-Jt1,
(1,2,2,3):-Jt2,
(1,3,3,2):-Jt2,
(0,3,1,0):-Jt1,
(1,2,0,1):-Jt2,
(2,3,0,3):-Jt2}
tleads = {(0, 0):-t0, # L, up <-- up
(1, 0):-t00, # R, up <-- up
(2, 1):-t0, # L, down <-- down
(3, 1):-t00,
(4, 2):-t00,
(5, 2):-t0,
(6, 3):-t00,
(7, 3):-t0} # R, down <-- down
# lead label, lead spin <-- level spin
nleads = 8
vbiasL = vbias/2
vblasR = -vbias/2
# L,up R,up L,down R,down
mulst = {0: -vbiasL, 1: -vbiasR, 2: -vbiasL, 3: -vbiasR,
4: -vbiasL, 5: -vbiasR, 6: -vbiasL, 7: -vbiasR}
tlst = {0: temp, 1: temp, 2: temp, 3: temp,
4: temp, 5: temp, 6: temp, 7: temp}
system = qmeq.Builder(nsingle, hsingle, coulomb,
nleads, tleads, mulst, tlst, dband,
kerntype='Lindblad')
system.solve(masterq=False)
system.solve(qdq=False)
print(system.current[0] + system.current[2] + system.current[4] + system.current[6])
# Here we have chosen to use **Pauli master equation** (*kerntype='Pauli'*) to describe the stationary state. Let's calculate the current through the system:
# In[11]:
#system.solve()
#print('Current:')
#print(system.current)
#print(system.energy_current)
# The four entries correspond to current in $L\uparrow$, $R\uparrow$, $L\downarrow$, $R\downarrow$ lead channels. We see that the current through left lead and right lead channels is conserved up to numerical errors:
# In[12]:
#print('Current continuity:')
#print(np.sum(system.current))
#print(system.indexing)
for i in range(0,4):
print("#####################")
#system.print_state(i)
def stab_calc(system, bfield, vlst, vglst, dV=0.0001):
vpnt, vgpnt = vlst.shape[0], vglst.shape[0]
stab = np.zeros((vpnt, vgpnt))
stab_re = np.zeros((vpnt, vgpnt))
print(vpnt)
for j1 in range(vgpnt):
vgate1 = vglst[j1]
print(j1)
#print(vgate1)
#print(vgate2)
for j2 in range(vpnt):
vgate2 = vlst[j2]
q1 = (c12*vgate2 + cG1*vgate1 + cL1*vbiasL + cR1*vbiasR)*6.24/1000 + q10
q2 = (c21*vgate1 + cG2*vgate2 + cL2*vbiasL + cR2*vbiasR)*6.24/1000 + q20
mu1 = Um*q2 + U1*q1 - U1/2
mu2 = Um*q1 + U2*q2 - U2/2
gg = 0.01*U1
system.change(hsingle={(0,0): Eq1-mu1+bfield/2,
(1,1): Eq1h-mu1-bfield/2,
(2,2): Eq2-mu2+bfield/2,
(3,3): Eq2h-mu2-bfield/2,
(0,2): -gg,
(1,3): -gg,
(0,3): -omegaflip,
(1,2): -omegaflip})
system.solve(masterq=False)
system.change(mulst = {0: -vbiasL, 1: -vbiasR, 2: -vbiasL, 3: -vbiasR,
4: -vbiasL, 5: -vbiasR, 6: -vbiasL, 7: -vbiasR})
system.solve(qdq=False)
stab[j1, j2] = system.current[0] + system.current[2] + system.current[4] + system.current[6]
stab[j1, j2] = abs(stab[j1, j2])
#############################################################################
q1 = (c12*vgate2 + cG1*vgate1 + cL1*vbiasR + cR1*vbiasL)*6.24/1000 + q10
q2 = (c21*vgate1 + cG2*vgate2 + cL2*vbiasR + cR2*vbiasL)*6.24/1000 + q20
mu1 = Um*q2 + U1*q1 - U1/2
mu2 = Um*q1 + U2*q2 - U2/2
system.change(hsingle={(0,0): Eq1-mu1+bfield/2,
(1,1): Eq1h-mu1-bfield/2,
(2,2): Eq2-mu2+bfield/2,
(3,3): Eq2h-mu2-bfield/2,
(0,2): -gg,
(1,3): -gg,
(0,3): -omegaflip,
(1,2): -omegaflip})
system.solve(masterq=False)
system.change(mulst = {0: -vbiasR, 1: -vbiasL, 2: -vbiasR, 3: -vbiasL,
4: -vbiasR, 5: -vbiasL, 6: -vbiasR, 7: -vbiasL})
system.solve(qdq=False)
stab_re[j1, j2] = system.current[0] + system.current[2] + system.current[4] + system.current[6]
stab_re[j1, j2] = abs(stab_re[j1, j2])
#0.000000001 good
#stab[j1, j2] = np.log(stab[j1, j2])
#stab[j1,j2] = mu1-mu2
#
#system.add(mulst={0: dV/2, 1: -dV/2,
#2: dV/2, 3: -dV/2})
#system.solve(qdq=False)
#stab_cond[j1, j2] = (system.current[0] + system.current[2] - stab[j1, j2])/dV
#
return stab, stab_re
# We changed the single particle Hamiltonian by calling the function **system.change** and specifying which matrix elements to change. The function **system.add** adds a value to a specified parameter. Also the option *masterq=False* in **system.solve** indicates just to diagonalise the quantum dot Hamiltonian and the master equation is not solved. Similarly, the option *qdq=False* means that the quantum dot Hamiltonian is not diagonalized (it was already diagonalized previously) and just master equation is solved.
# In[19]:
start_time = time.time()
system.kerntype = 'Lindblad'
vpnt, vgpnt = 101, 101
vlst = np.linspace(-200, 600, vpnt)
vglst = np.linspace(-200, 600, vgpnt)
stab, stab_re = stab_calc(system, bfield, vlst, vglst)
# The stability diagram has been produced. Let's see how it looks like:
# In[20]:
def stab_plot(stab, stab_cond, vlst, vglst, gam):
(xmin, xmax, ymin, ymax) = np.array([vglst[0], vglst[-1], vlst[0], vlst[-1]])
fig = plt.figure(figsize=(12,4.2))
#
p1 = plt.subplot(1, 2, 1)
p1.set_xlabel('$V_{g1}(mV)$', fontsize=20)
p1.set_ylabel('$V_{g2}(mV)$', fontsize=20)
p1_im = plt.imshow(stab.T, extent=[xmin, xmax, ymin, ymax], aspect='auto', origin='lower', cmap = plt.get_cmap('Spectral'))
cbar1 = plt.colorbar(p1_im)
cbar1.set_label('Current [unit]', fontsize=20)
#
p2 = plt.subplot(1, 2, 2)
p2.set_xlabel('$V_{g1}(mV)$', fontsize=20);
p2.set_ylabel('$V_{g2}(mV)$', fontsize=20);
p2_im = plt.imshow(stab_cond.T, extent=[xmin, xmax, ymin, ymax], aspect='auto', origin='lower', cmap = plt.get_cmap('Spectral'))
cbar2 = plt.colorbar(p2_im)
cbar2.set_label('Current [unit]', fontsize=20)
#
plt.tight_layout()
plt.show()
print("--- %s seconds ---" % (time.time() - start_time))
stab_plot(stab, stab_re, vlst, vglst, gam)