the phase of wave functions
Hello all,
My question is about modifying the phase of wave functions. I want to calculate derivative of scattering matrix with respect to energy and they come out to be discontinuous because of the phases.
To remedy this I need to modify these phases. Following the suggestion of Anton Akhmerov in this mail group I understood how to modify the phase of modes in the leads.
But I also need to change the phase of wave functions in the scattering region to obtain continuous scattering matrices at different energies.
I wonder if there is an another way to call wave functions in the scattering region (apart from kwant.solvers.default.wave_function) or a method to modify these phases.
Thank you in advance.
Nur
Hi Nur,
I don't think you need to do anything inside the scattering region to modify the phase of the scattering matrix. Are you sure this is the problem?
Best, Anton
On Sun, Jan 24, 2016 at 6:04 PM, Fahriye Nur Gursoy fahriyetortop@sabanciuniv.edu wrote:
Hello all,
My question is about modifying the phase of wave functions. I want to calculate derivative of scattering matrix with respect to energy and they come out to be discontinuous because of the phases.
To remedy this I need to modify these phases. Following the suggestion of Anton Akhmerov in this mail group I understood how to modify the phase of modes in the leads.
But I also need to change the phase of wave functions in the scattering region to obtain continuous scattering matrices at different energies.
I wonder if there is an another way to call wave functions in the scattering region (apart from kwant.solvers.default.wave_function) or a method to modify these phases.
Thank you in advance.
Nur
Hello Anton,
I checked my code, I think the problem is still about the modes of the leads. I can modify the phase of the modes in the leads. When I call the modes (using lead.info), I obtain modified wave functions but the scattering matrix is the same. I guess,the scattering matrix is still calculated with original wave functions.
I posted my code below. Thank you
Nur
import sys as systemCommands import kwant import numpy as np
class WavefunctionLead(kwant.builder.InfiniteSystem): def __init__(self, lead): self.__dict__ = lead.__dict__ def modes(self, energy, args=()): prop_modes_fix, stab_modes_fix = \ super(WavefunctionLead, self).modes(energy=0.4, args=args) size_fix = prop_modes_fix.wave_functions.shape[1] fix = [] for i in range(size_fix): fix0 = prop_modes_fix.wave_functions[0][i] fix.append(fix0) prop_modes, stab_modes = \ super(WavefunctionLead, self).modes(energy=energy, args=args) wf_size = prop_modes.wave_functions.shape[0] #number of orbital num_modes = prop_modes.wave_functions.shape[1]#number of modes (2*num_modes) ## change of the phase for i in range(wf_size): for j in range(num_modes): f = fix[j] prop_modes.wave_functions[i,j]=prop_modes.wave_functions[i,j]*(prop_modes.wave_functions[i,j]/f) if prop_modes.wave_functions[i,j].real >= 0 : prop_modes.wave_functions[i,j] = 1 * prop_modes.wave_functions[i,j] else : continue return prop_modes, stab_modes def make_system(a, t, L, f, r, rcc, kso, w): lat = kwant.lattice.square(a) sys = kwant.Builder() def myShape(pos): (x, y) = pos if (L/2f<= y < L/2+f) and (0<=x <2): return True elif (L/2f<= y < L/2+f) and (L1<= x< L+1): return True elif ( 2 <= x < L1 ) and ( 0 <= y < L1) and rcc ** 2 <(x ** 2 + y ** 2) and (3*r ** 2 < ((x(L/2)) ** 2 + (y(L/2)) ** 2)): return True def onsite(site1, tm):## Electric field in x direction x1 =site1.pos[0] y1 = site1.pos[1] return 4*t + np.sin(w*tm)*w*x1*kso sys[lat.shape(myShape, (0, L/2))] = onsite sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = t sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = t ##leads## lead0 = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) def lead_shape_0(pos): (x, y) = pos return ( L/2f <= y < L/2+f)
lead0[lat.shape(lead_shape_0, (0, L/2))] = 4*t lead0[kwant.builder.HoppingKind((1, 0), lat, lat)] = t lead0[kwant.builder.HoppingKind((0, 1), lat, lat)] = t lead1 = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) def lead_shape_1(pos): (x, y) = pos return ( L/2f <= y < L/2+f)
lead1[lat.shape(lead_shape_1, (0, L/2))] = 4*t lead1[kwant.builder.HoppingKind((1, 0), lat, lat)] = t lead1[kwant.builder.HoppingKind((0, 1), lat, lat)] = t sys.attach_lead(lead0) sys.attach_lead(lead1) fsys = sys.finalized() ### fsys.leads = [WavefunctionLead(lead) for lead in fsys.leads] ### return fsys
def main(): ## w = frequency ## kso = Rashba spin orbit coupling sys = make_system(a=1, t=1, L=50, f=2, r=6, rcc=5, kso = 0.3/50, w = 0.001) energies=[0.00001 * i+0.40 for i in xrange(300)] tm =1000 #time parameter for energy in energies: S = kwant.smatrix(sys, energy, args=[tm]) mode = S.lead_info wf =mode[0].wave_functions print wf if __name__ == '__main__': main()
On 24 January 2016 at 22:52, Anton Akhmerov anton.akhmerov+kd@gmail.com wrote:
Hi Nur,
I don't think you need to do anything inside the scattering region to modify the phase of the scattering matrix. Are you sure this is the problem?
Best, Anton
On Sun, Jan 24, 2016 at 6:04 PM, Fahriye Nur Gursoy fahriyetortop@sabanciuniv.edu wrote:
Hello all,
My question is about modifying the phase of wave functions. I want to calculate derivative of scattering matrix with respect to energy and they come out to be discontinuous because of the phases.
To remedy this I need to modify these phases. Following the suggestion of Anton Akhmerov in this mail group I understood how to modify the phase of modes in the leads.
But I also need to change the phase of wave functions in the scattering region to obtain continuous scattering matrices at different energies.
I wonder if there is an another way to call wave functions in the
scattering
region (apart from kwant.solvers.default.wave_function) or a method to modify these phases.
Thank you in advance.
Nur
Hi Fahriye,
I see now, you're modifying the propagating modes, but not touching the stabilized ones. Solvers, in turn, only use stabilized modes. In order for everything to work the way you want, you need to modify the stabilized modes in the same way. This means that you need to multiply the first entries in StabilizedModes.vecs and StabilizedModes.vecslambdainv by the same phase factors you've used for the propagating modes.
Hope that helps, Anton
On Mon, Jan 25, 2016, 13:50 Fahriye Nur Gursoy < fahriyetortop@sabanciuniv.edu> wrote:
Hello Anton,
I checked my code, I think the problem is still about the modes of the leads. I can modify the phase of the modes in the leads. When I call the modes (using lead.info), I obtain modified wave functions but the scattering matrix is the same. I guess,the scattering matrix is still calculated with original wave functions.
I posted my code below. Thank you
Nur
import sys as systemCommands import kwant import numpy as np
class WavefunctionLead(kwant.builder.InfiniteSystem): def __init__(self, lead): self.__dict__ = lead.__dict__ def modes(self, energy, args=()): prop_modes_fix, stab_modes_fix = \ super(WavefunctionLead, self).modes(energy=0.4, args=args) size_fix = prop_modes_fix.wave_functions.shape[1] fix = [] for i in range(size_fix): fix0 = prop_modes_fix.wave_functions[0][i] fix.append(fix0) prop_modes, stab_modes = \ super(WavefunctionLead, self).modes(energy=energy, args=args) wf_size = prop_modes.wave_functions.shape[0] #number of orbital num_modes = prop_modes.wave_functions.shape[1]#number of modes (2*num_modes) ## change of the phase for i in range(wf_size): for j in range(num_modes): f = fix[j]
prop_modes.wave_functions[i,j]=prop_modes.wave_functions[i,j]*(prop_modes.wave_functions[i,j]/f) if prop_modes.wave_functions[i,j].real >= 0 : prop_modes.wave_functions[i,j] = 1 * prop_modes.wave_functions[i,j] else : continue return prop_modes, stab_modes def make_system(a, t, L, f, r, rcc, kso, w): lat = kwant.lattice.square(a) sys = kwant.Builder() def myShape(pos): (x, y) = pos if (L/2f<= y < L/2+f) and (0<=x <2): return True elif (L/2f<= y < L/2+f) and (L1<= x< L+1): return True elif ( 2 <= x < L1 ) and ( 0 <= y < L1) and rcc ** 2 <(x ** 2 + y ** 2) and (3*r ** 2 < ((x(L/2)) ** 2 + (y(L/2)) ** 2)): return True def onsite(site1, tm):## Electric field in x direction x1 =site1.pos[0] y1 = site1.pos[1] return 4*t + np.sin(w*tm)*w*x1*kso sys[lat.shape(myShape, (0, L/2))] = onsite sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = t sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = t ##leads## lead0 = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) def lead_shape_0(pos): (x, y) = pos return ( L/2f <= y < L/2+f)
lead0[lat.shape(lead_shape_0, (0, L/2))] = 4*t lead0[kwant.builder.HoppingKind((1, 0), lat, lat)] = t lead0[kwant.builder.HoppingKind((0, 1), lat, lat)] = t lead1 = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) def lead_shape_1(pos): (x, y) = pos return ( L/2f <= y < L/2+f)
lead1[lat.shape(lead_shape_1, (0, L/2))] = 4*t lead1[kwant.builder.HoppingKind((1, 0), lat, lat)] = t lead1[kwant.builder.HoppingKind((0, 1), lat, lat)] = t sys.attach_lead(lead0) sys.attach_lead(lead1) fsys = sys.finalized() ### fsys.leads = [WavefunctionLead(lead) for lead in fsys.leads] ### return fsys
def main(): ## w = frequency ## kso = Rashba spin orbit coupling sys = make_system(a=1, t=1, L=50, f=2, r=6, rcc=5, kso = 0.3/50, w = 0.001) energies=[0.00001 * i+0.40 for i in xrange(300)] tm =1000 #time parameter for energy in energies: S = kwant.smatrix(sys, energy, args=[tm]) mode = S.lead_info wf =mode[0].wave_functions print wf if __name__ == '__main__': main()
On 24 January 2016 at 22:52, Anton Akhmerov anton.akhmerov+kd@gmail.com wrote:
Hi Nur,
I don't think you need to do anything inside the scattering region to modify the phase of the scattering matrix. Are you sure this is the problem?
Best, Anton
On Sun, Jan 24, 2016 at 6:04 PM, Fahriye Nur Gursoy fahriyetortop@sabanciuniv.edu wrote:
Hello all,
My question is about modifying the phase of wave functions. I want to calculate derivative of scattering matrix with respect to energy and
they
come out to be discontinuous because of the phases.
To remedy this I need to modify these phases. Following the suggestion
of
Anton Akhmerov in this mail group I understood how to modify the phase
of
modes in the leads.
But I also need to change the phase of wave functions in the scattering region to obtain continuous scattering matrices at different energies.
I wonder if there is an another way to call wave functions in the
scattering
region (apart from kwant.solvers.default.wave_function) or a method to modify these phases.
Thank you in advance.
Nur
participants (2)

Anton Akhmerov

Fahriye Nur Gursoy