Sorry, a typo was in my previous mail. Now it is correct. L. Dear authors, I think the problem relies in that the particle-hole symmetry in the leads is not correctly implemented. Indeed, in the present form H_leads (k) \neq - U H^*_leads (-k) U^{-1} (as it holds instead for the scattering region). To solve the problem, it looks me sufficient just to add a factor (1j) to the hoppings in the leads. In this way, the conductance results symmetric around zero energy (where the Weyl nodes occur) I hope it can help. Best regards, L. L. Il giorno ven 15 mar 2019 alle ore 16:21 Il giorno ven 22 mar 2019 alle ore 16:59 Luca Lepori ha scritto:

Dear authors,

I think the problem relies in that the particle-hole symmetry in the leads is not correctly implemented. Indeed, in the present form H_leads (k) \neq - U H_leads (k) U^{-1} (as it hold instead for the scattering region). To solve the problem, it looks me sufficient just to add a factor (1j) to the hoppings in the leads. In this way, the conductance results symmetric around zero energy (where the Weyl nodes occur)

I hope it can help.

Best regards,

L. L.

Il giorno ven 15 mar 2019 alle ore 16:21 Luca Lepori ha scritto:

...

Dear Joe,

concerning to your answer https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg01808.html ,

I checked that I do not have any sign problem, as those you described, in my system/code. Therefore I am wandering if some fuzzy problem of matching of wavefunctions is known, or expected, to occur when metals (leads) and semimetals (scattering region) are put in contact (perhaps due to symmetries of whatever), not depending on the sign problem.

I also attach below the code that I used, and that looks me correct, after various checks on the spectrum of the scattering region and of the leads. I assumed a cubic lattice with periodic boundary conditions along x and z, while the leads are along y. However, I checked that the problem persists also assuming open boundary conditions.

Thank you very much for the help and best regards

L.

-----------------------------------------------------------------------------------

import kwant import math import cmath import scipy.sparse.linalg as sla import numpy

# For plotting from matplotlib import pyplot

# For matrix support import tinyarray

#-----------------------------------------------------

# We define Pauli-matrices sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]])

# We define the variables and the constants

t = 1.0 v = 1.0 L = 13 # length y W = 13 # length x and z k0 = math.pi/10. #k0 = -0.4636476090008061

m0 = math.cos(k0) vtilde = v/math.sin(k0) h = vtilde*m0 + 2*v a=1

#---------------------------------------------------------------------------------------------------------

syst = kwant.Builder() lat = kwant.lattice.cubic(a)

for i in range(W): for j in range(L): for k in range(W):

# On-site Hamiltonian syst[lat(i, j, k)] = h*sigma_x

# Hopping in x-direction if i > 0: syst[lat(i, j, k), lat(i - 1, j, k)] = -(vtilde/2)*sigma_x

# Hopping in y-direction if j > 0: syst[lat(i, j, k), lat(i, j - 1, k)] = -(v/2)*((1j)*sigma_y + sigma_x)

# Hopping in z-direction if k > 0: syst[lat(i, j, k), lat(i, j, k - 1)] = -(v/2)*((1j)*sigma_z + sigma_x)

# I close hopping in x-direction, connecting W-1 and 0 for j in range(L): for k in range(W): syst[lat(0, j, k), lat(W-1, j, k)] = -(vtilde/2)*sigma_x

# I close the hopping in z-direction, connecting W-1 and 0 for i in range(W): for j in range(L): syst[lat(i, j, 0), lat(i, j, W-1)] = -(v/2)*((1j)*sigma_z + sigma_x)

#---------------------------------------------------------------------------------------------------------

# We define the right lead, along y sym_right_lead = kwant.TranslationalSymmetry((0, a, 0)) right_lead = kwant.Builder(sym_right_lead)

for i in range(W): for k in range(W):

right_lead[lat(i, 0, k)] = mu*sigma_0

if i > 0: right_lead[lat(i, 0, k), lat(i-1, 0, k)] = -t*sigma_0

if k > 0: right_lead[lat(i, 0, k), lat(i, 0, k-1)] = -t*sigma_0

right_lead[lat(i, 1, k), lat(i, 0, k)] = -t*sigma_0

# I close hopping in x-direction, connecting W-1 and 0 for k in range(W): right_lead[lat(0, 0, k), lat(W-1, 0, k)] = -t*sigma_0

# I close hopping in z-direction, connecting W-1 for i in range(W): right_lead[lat(i, 0, 0), lat(i, 0, W-1)] = -t*sigma_0

syst.attach_lead(right_lead) left_lead = right_lead.reversed() syst.attach_lead(left_lead)

Dear Adel, I think I have solved the problem. I wrote again just for completeness, in case somebody encountered the same problem. However, I will try to be more clear. Best, L. Il giorno ven 22 mar 2019 alle ore 17:16 Abbout Adel ha scritto:

Dear Luca,

Your problem is not clear at all. Your code is not well written so that we can follow it easily (a lot of variables and loops). Even with that, there is no error message.

If you specify what you want to do and what is the part which makes problem for you with the corresponding code and error message, someone may help you.

Regards, Adel

On Fri, Mar 15, 2019 at 6:22 PM Luca Lepori wrote:

...

Dear Joe,

concerning to your answer https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg01808.html ,

I checked that I do not have any sign problem, as those you described, in my system/code. Therefore I am wandering if some fuzzy problem of matching of wavefunctions is known, or expected, to occur when metals (leads) and semimetals (scattering region) are put in contact (perhaps due to symmetries of whatever), not depending on the sign problem.

I also attach below the code that I used, and that looks me correct, after various checks on the spectrum of the scattering region and of the leads. I assumed a cubic lattice with periodic boundary conditions along x and z, while the leads are along y. However, I checked that the problem persists also assuming open boundary conditions.

Thank you very much for the help and best regards

L.

-----------------------------------------------------------------------------------

import kwant import math import cmath import scipy.sparse.linalg as sla import numpy

# For plotting from matplotlib import pyplot

# For matrix support import tinyarray

#-----------------------------------------------------

# We define Pauli-matrices sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]])

# We define the variables and the constants

t = 1.0 v = 1.0 L = 13 # length y W = 13 # length x and z k0 = math.pi/10. #k0 = -0.4636476090008061

m0 = math.cos(k0) vtilde = v/math.sin(k0) h = vtilde*m0 + 2*v a=1

#---------------------------------------------------------------------------------------------------------

syst = kwant.Builder() lat = kwant.lattice.cubic(a)

for i in range(W): for j in range(L): for k in range(W):

# On-site Hamiltonian syst[lat(i, j, k)] = h*sigma_x

# Hopping in x-direction if i > 0: syst[lat(i, j, k), lat(i - 1, j, k)] = -(vtilde/2)*sigma_x

# Hopping in y-direction if j > 0: syst[lat(i, j, k), lat(i, j - 1, k)] = -(v/2)*((1j)*sigma_y + sigma_x)

# Hopping in z-direction if k > 0: syst[lat(i, j, k), lat(i, j, k - 1)] = -(v/2)*((1j)*sigma_z + sigma_x)

# I close hopping in x-direction, connecting W-1 and 0 for j in range(L): for k in range(W): syst[lat(0, j, k), lat(W-1, j, k)] = -(vtilde/2)*sigma_x

# I close the hopping in z-direction, connecting W-1 and 0 for i in range(W): for j in range(L): syst[lat(i, j, 0), lat(i, j, W-1)] = -(v/2)*((1j)*sigma_z + sigma_x)

#---------------------------------------------------------------------------------------------------------

# We define the right lead, along y sym_right_lead = kwant.TranslationalSymmetry((0, a, 0)) right_lead = kwant.Builder(sym_right_lead)

for i in range(W): for k in range(W):

right_lead[lat(i, 0, k)] = mu*sigma_0

if i > 0: right_lead[lat(i, 0, k), lat(i-1, 0, k)] = -t*sigma_0

if k > 0: right_lead[lat(i, 0, k), lat(i, 0, k-1)] = -t*sigma_0

right_lead[lat(i, 1, k), lat(i, 0, k)] = -t*sigma_0

# I close hopping in x-direction, connecting W-1 and 0 for k in range(W): right_lead[lat(0, 0, k), lat(W-1, 0, k)] = -t*sigma_0

# I close hopping in z-direction, connecting W-1 for i in range(W): right_lead[lat(i, 0, 0), lat(i, 0, W-1)] = -t*sigma_0

syst.attach_lead(right_lead) left_lead = right_lead.reversed() syst.attach_lead(left_lead)

-- Abbout Adel