In [1]:
%pylab inline
import matplotlib.pyplot as plt
from scipy.integrate import * # az integráló rutinok betöltése
Single-electron tunneling in SIN and SIS junctions.¶
I-V curve of superconductor–insulator–normal junctions¶
See Chapter 34.6, and Eq. (34.6.16) and Fig. 34.17. in Jenő Sólyom: Fundamentals of the Physics of Solids, Volume 3: Normal, Broken-Symmetry, and Correlated Systems (A modern szilárdtestfizika alpajai I. A szilárd testek szerkezete és dinamikája) see here.
I-V curve of superconductor–insulator–superconductor junctions¶
See Chapter 34.6, and Eq. (34.6.44) and Fig. 34.21. in Jenő Sólyom's book
In [2]:
# Az abra kimentesehez az alabbiakat a plt.show() ele kell tenni!!!
#savefig('fig_rainbow_p2_1ray.pdf'); # Abra kimentese
#savefig('fig_rainbow_p2_1ray.eps'); # Abra kimentese
# Abra es fontmeretek
xfig_meret= 8 # 12 nagy abrahoz
yfig_meret= 6 # 12 nagy abrahoz
xyticks_meret= 15 # 20 nagy abrahoz
xylabel_meret= 21 # 30 nagy abrahoz
legend_meret= 21 # 30 nagy abrahoz
In [3]:
def Fermi_Dirac(x,t):
# Herer the chemical potential is zero!!!!
return(1/(exp(x/t)+1))
def kivagas(x,x0):
tmp=piecewise(x, [x < x0, x >= x0], [0, 1])+piecewise(x, [x < -x0, x >= -x0], [1, 0])
return(tmp)
def current_SN_mag(x,ev,DL,t):
if (abs(x) > DL):
tmp = abs(x)/sqrt(x**2-DL**2)*(Fermi_Dirac(x,t)-Fermi_Dirac(x+ev,t))
else:
tmp = 0
return(tmp)
def current_SNS_mag(x,ev,DL,DR,t):
if (abs(x) > DL and abs(x+ev) > DR):
tmp = abs(x)/sqrt(x**2-DL**2)*abs(x+ev)/sqrt((x+ev)**2-DR**2)*(Fermi_Dirac(x,t)-Fermi_Dirac(x+ev,t))
else:
tmp = 0
return(tmp)
def current_SN(ev,DL,t):
tmp = quad(current_SN_mag,-xm,xm,args=(ev,DL,t))[0]
return tmp
def current_SNS(ev,DL,DR,t):
tmp = quad(current_SNS_mag,-xm,xm,args=(ev,DL,DR,t))[0]
return tmp
In [4]:
def ff(x,*params):
y=0
for i in range(len(params)):
y=y+params[i]*x**i
return y
I-V for SN¶
see Eq. (34.6.16) and Fig. 34.17. in Jenő Sólyom's book
In [5]:
xm=200
t = 0.25
DL = 3.0
evmax = 1.25*(DL)
xx = []
yy = []
for ev in linspace(0,evmax,500):
xx.append(ev)
yy.append(current_SN(ev,DL,t))
#yy=array(yy)
figsize(xfig_meret,xfig_meret)
plot(xx,yy);
axvline(x= DL, color='k', linestyle='--')
xlabel(r'$e V$',fontsize=20)
ylabel(r'$I$',fontsize=20)
cim="I-V for SN," + r'$\quad T = $' + str(t) + r'$\quad \Delta_L= $' +str(DL)
title(cim,fontsize=20)
#ylim(0,1)
grid();
In [6]:
xm=100
DL = 3.0
tvec = [0.5,0.25,0.1]
#szin=['k','brown','g','b','r']
szin=['k','b','r']
evmax = 1.5*(DL)
figsize(xfig_meret,xfig_meret)
for j in range(len(tvec)):
xx = []
yy = []
for ev in linspace(0,evmax,100):
xx.append(ev)
yy.append(current_SN(ev,DL,tvec[j]))
#yy=array(yy)
plot(xx,yy,label=r'$T = $'+str(tvec[j]),color=szin[j]);
legend(loc='upper left',fontsize=legend_meret)
axvline(x= DL, color='k', linestyle='--')
xlabel(r'$e V$',fontsize=20)
ylabel(r'$I$',fontsize=20)
cim= "I-V for SN," + r'$\quad \Delta_L= $' +str(DL)
title(cim,fontsize=20)
#ylim(0,1)
grid();
I-V for SNS¶
see Eq. (34.6.44) and Fig. 34.21. in Jenő Sólyom's book
In [7]:
xm=50
t = 1.5
DL = 2.
DR = 3.
#DL = 1.*t
#DR = 2.*t
print("|DL-DR| = ", abs(DR-DL))
print("DL+DR = ", DR+DL)
evmax = 1.25*(DL+DR)
xx = []
yy = []
for ev in linspace(0,evmax,500):
xx.append(ev)
yy.append(current_SNS(ev,DL,DR,t))
#yy=array(yy)
figsize(xfig_meret,xfig_meret)
plot(xx,yy);
axvline(x=abs(DL-DR), color='k', linestyle='--')
axvline(x= DL+DR, color='k', linestyle='--')
xlabel(r'$e V$',fontsize=20)
ylabel(r'$I$',fontsize=20)
cim="I-V for SNS," + r'$\quad T = $' + str(t) + r'$\quad \Delta_L= $' +str(DL) + r'$\quad \Delta_R= $' + str(DR)
title(cim,fontsize=20)
#ylim(0,1)
grid();
In [8]:
xm=20
DL = 0.5
DR = 1.
tvec = [1,0.5,0.25]
#szin=['k','brown','g','b','r']
szin=['k','b','r']
evmax = 1.25*(DL+DR)
figsize(xfig_meret,xfig_meret)
for j in range(len(tvec)):
xx = []
yy = []
for ev in linspace(0,evmax,200):
xx.append(ev)
yy.append(current_SNS(ev,DL,DR,tvec[j]))
#yy=array(yy)
plot(xx,yy,label=r'$T = $'+str(tvec[j]),color=szin[j]);
legend(loc='upper left',fontsize=legend_meret)
axvline(x=abs(DL-DR), color='k', linestyle='--')
axvline(x= DL+DR, color='k', linestyle='--')
xlabel(r'$e V$',fontsize=20)
ylabel(r'$I$',fontsize=20)
cim= "I-V for SNS," +r'$\quad \Delta_L= $' +str(DL) + r'$\quad \Delta_R= $' + str(DR)
title(cim,fontsize=20)
#ylim(0,1)
grid();
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