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Commit 2e5b4c14 authored by Hélène Spring's avatar Hélène Spring
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Add different chemical potentials for different sublattices, effect of external out of plane field

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code/.ipynb_checkpoints/testing_ground-checkpoint.py
+ 34
− 6
View file @ 2e5b4c14
# +
import kwant
import numpy as np
import matplotlib.pyplot as plt
from modules.diamond_chain import diamond_chain_system
from modules.analysis_funcs import ldos_from_kpm
from modules.analysis_funcs import ldos_from_kpm, ldos_modes_from_leads
# -
system_params = dict(
j2 = 0,
mu_a = 0,
mu_b = 0,
mu_c = 0,
j2 = 1,
j3 = 1,
semi_infinite = True
phi = np.pi/2,
phi_d = 0
)
chain = diamond_chain_system(20,system_params)
kwant.plot(chain)
inf_chain = diamond_chain_system(5,system_params, semi_infinite = True)
fin_chain = diamond_chain_system(5,system_params, semi_infinite = False)
# o = kwant.plot(fin_chain)
# +
# ldos_modes_from_leads(fin_chain.finalized(), system_params) #doesn't work for flat bands
# -
o = ldos_from_kpm(fin_chain.finalized(), system_params, vmax = 10, energy = 0 )
o = ldos_from_kpm(fin_chain.finalized(), system_params, vmax = 1, energy = 2*system_params['j2'] )
o = ldos_from_kpm(fin_chain.finalized(), system_params, vmax = 10, energy = 2*np.sqrt(2)*system_params['j2'] )
kwant.plotter.bands(inf_chain.finalized(), momenta = np.linspace(-np.pi,np.pi,1000))
ham = fin_chain.finalized().hamiltonian_submatrix()
ev, es = np.linalg.eigh(ham)
ev
plt.plot(ev, marker='o',lw=0)
ldos_from_kpm(chain.finalized(), system_params, vmax = 3)
np.exp(1j*np.pi/2).imag
code/modules/.ipynb_checkpoints/diamond_chain-checkpoint.py
+ 25
− 18
View file @ 2e5b4c14
# -*- coding: utf-8 -*-
import kwant
import numpy as np
......@@ -10,12 +11,14 @@ def diamond_chain_system(N_c, system_params, semi_infinite = False, leads = Fals
| C_i_- | ...
/ ------- \ ______ /
... | A_i_+ | ...
| A_i_- |
\ ______ / ------- \
Φ | A_i_- |
\ ______ //------- \
... | B_i_+ | ...
| B_i_- |
-------
The Φ represents an out-of-plane magnetic field. The phase is added along the // bond in each unit cell
:param int N_c: number of unit cells to include in the cell
:param dict system_params: parameters
:param bool semi_infinite: whether to make a semi-infinite chain or not
......@@ -40,20 +43,20 @@ def diamond_chain_system(N_c, system_params, semi_infinite = False, leads = Fals
#staggered point
sp = i
syst[a_lat_pos(sp,0)] = system_params['mu_a']
syst[a_lat_neg(sp,0)] = system_params['mu_a']
syst[b_lat_pos(sp,0)] = system_params['mu_b']
syst[b_lat_neg(sp,0)] = system_params['mu_b']
syst[c_lat_pos(sp,0)] = system_params['mu_c']
syst[c_lat_neg(sp,0)] = system_params['mu_c']
syst[a_lat_pos(sp,0)] = system_params['mu_a_pos']
syst[a_lat_neg(sp,0)] = system_params['mu_a_neg']
syst[b_lat_pos(sp,0)] = system_params['mu_b_pos']
syst[b_lat_neg(sp,0)] = system_params['mu_b_neg']
syst[c_lat_pos(sp,0)] = system_params['mu_c_pos']
syst[c_lat_neg(sp,0)] = system_params['mu_c_neg']
if i < N_c - 1:
syst[c_lat_pos(sp+1,0)] = system_params['mu_c']
syst[b_lat_pos(sp+1,0)] = system_params['mu_b']
syst[c_lat_neg(sp+1,0)] = system_params['mu_c']
syst[b_lat_neg(sp+1,0)] = system_params['mu_b']
syst[c_lat_pos(sp+1,0)] = system_params['mu_c_pos']
syst[b_lat_pos(sp+1,0)] = system_params['mu_b_pos']
syst[c_lat_neg(sp+1,0)] = system_params['mu_c_neg']
syst[b_lat_neg(sp+1,0)] = system_params['mu_b_neg']
# + <--> +
syst[a_lat_pos(sp,0), c_lat_pos(sp+1,0)] = system_params['j2']
......@@ -68,21 +71,25 @@ def diamond_chain_system(N_c, system_params, semi_infinite = False, leads = Fals
syst[a_lat_neg(sp,0), b_lat_pos(sp+1,0)] = system_params['j3']
# + <--> - hopping with phase
syst[a_lat_pos(sp,0), c_lat_neg(sp+1,0)] = -system_params['j3'] #phase e^i pi
syst[a_lat_neg(sp,0), c_lat_pos(sp+1,0)] = -system_params['j3'] #phase e^i pi
syst[a_lat_pos(sp,0), c_lat_neg(sp+1,0)] = system_params['j3']*np.exp(1j*2*system_params['phi']) #phase e^i phi
syst[a_lat_neg(sp,0), c_lat_pos(sp+1,0)] = system_params['j3']*np.exp(1j*2*system_params['phi']) #phase e^i phi
# + <--> +
syst[a_lat_pos(sp,0), c_lat_pos(sp,0)] = system_params['j2']
syst[a_lat_pos(sp,0), b_lat_pos(sp,0)] = system_params['j2']
if i == 0:
added_phase = 1
else:
added_phase = np.exp(1j*2*system_params['phi_d'])
syst[a_lat_pos(sp,0), b_lat_pos(sp,0)] = system_params['j2']*added_phase #phase e^i phi_d due to mag field
# - <--> -
syst[a_lat_neg(sp,0), c_lat_neg(sp,0)] = system_params['j2']
syst[a_lat_neg(sp,0), b_lat_neg(sp,0)] = system_params['j2']
syst[a_lat_neg(sp,0), b_lat_neg(sp,0)] = system_params['j2']*added_phase #phase e^i phi_d due to mag field
# + <--> -
syst[a_lat_pos(sp,0), c_lat_neg(sp,0)] = system_params['j3']
syst[a_lat_neg(sp,0), c_lat_pos(sp,0)] = system_params['j3']
# + <--> - hopping with phase
syst[a_lat_pos(sp,0), b_lat_neg(sp,0)] = -system_params['j3'] #phase e^i pi
syst[a_lat_neg(sp,0), b_lat_pos(sp,0)] = -system_params['j3'] #phase e^i pi
syst[a_lat_pos(sp,0), b_lat_neg(sp,0)] = system_params['j3']*np.exp(1j*2*system_params['phi'])*added_phase #phase e^i phi_d due to mag field #phase e^i phi
syst[a_lat_neg(sp,0), b_lat_pos(sp,0)] = system_params['j3']*np.exp(1j*2*system_params['phi'])*added_phase #phase e^i phi_d due to mag field #phase e^i phi
if leads:
......
code/modules/diamond_chain.py
+ 25
− 18
View file @ 2e5b4c14
# -*- coding: utf-8 -*-
import kwant
import numpy as np
......@@ -10,12 +11,14 @@ def diamond_chain_system(N_c, system_params, semi_infinite = False, leads = Fals
| C_i_- | ...
/ ------- \ ______ /
... | A_i_+ | ...
| A_i_- |
\ ______ / ------- \
Φ | A_i_- |
\ ______ //------- \
... | B_i_+ | ...
| B_i_- |
-------
The Φ represents an out-of-plane magnetic field. The phase is added along the // bond in each unit cell
:param int N_c: number of unit cells to include in the cell
:param dict system_params: parameters
:param bool semi_infinite: whether to make a semi-infinite chain or not
......@@ -40,20 +43,20 @@ def diamond_chain_system(N_c, system_params, semi_infinite = False, leads = Fals
#staggered point
sp = i
syst[a_lat_pos(sp,0)] = system_params['mu_a']
syst[a_lat_neg(sp,0)] = system_params['mu_a']
syst[b_lat_pos(sp,0)] = system_params['mu_b']
syst[b_lat_neg(sp,0)] = system_params['mu_b']
syst[c_lat_pos(sp,0)] = system_params['mu_c']
syst[c_lat_neg(sp,0)] = system_params['mu_c']
syst[a_lat_pos(sp,0)] = system_params['mu_a_pos']
syst[a_lat_neg(sp,0)] = system_params['mu_a_neg']
syst[b_lat_pos(sp,0)] = system_params['mu_b_pos']
syst[b_lat_neg(sp,0)] = system_params['mu_b_neg']
syst[c_lat_pos(sp,0)] = system_params['mu_c_pos']
syst[c_lat_neg(sp,0)] = system_params['mu_c_neg']
if i < N_c - 1:
syst[c_lat_pos(sp+1,0)] = system_params['mu_c']
syst[b_lat_pos(sp+1,0)] = system_params['mu_b']
syst[c_lat_neg(sp+1,0)] = system_params['mu_c']
syst[b_lat_neg(sp+1,0)] = system_params['mu_b']
syst[c_lat_pos(sp+1,0)] = system_params['mu_c_pos']
syst[b_lat_pos(sp+1,0)] = system_params['mu_b_pos']
syst[c_lat_neg(sp+1,0)] = system_params['mu_c_neg']
syst[b_lat_neg(sp+1,0)] = system_params['mu_b_neg']
# + <--> +
syst[a_lat_pos(sp,0), c_lat_pos(sp+1,0)] = system_params['j2']
......@@ -68,21 +71,25 @@ def diamond_chain_system(N_c, system_params, semi_infinite = False, leads = Fals
syst[a_lat_neg(sp,0), b_lat_pos(sp+1,0)] = system_params['j3']
# + <--> - hopping with phase
syst[a_lat_pos(sp,0), c_lat_neg(sp+1,0)] = -system_params['j3'] #phase e^i pi
syst[a_lat_neg(sp,0), c_lat_pos(sp+1,0)] = -system_params['j3'] #phase e^i pi
syst[a_lat_pos(sp,0), c_lat_neg(sp+1,0)] = system_params['j3']*np.exp(1j*2*system_params['phi']) #phase e^i phi
syst[a_lat_neg(sp,0), c_lat_pos(sp+1,0)] = system_params['j3']*np.exp(1j*2*system_params['phi']) #phase e^i phi
# + <--> +
syst[a_lat_pos(sp,0), c_lat_pos(sp,0)] = system_params['j2']
syst[a_lat_pos(sp,0), b_lat_pos(sp,0)] = system_params['j2']
if i == 0:
added_phase = 1
else:
added_phase = np.exp(1j*2*system_params['phi_d'])
syst[a_lat_pos(sp,0), b_lat_pos(sp,0)] = system_params['j2']*added_phase #phase e^i phi_d due to mag field
# - <--> -
syst[a_lat_neg(sp,0), c_lat_neg(sp,0)] = system_params['j2']
syst[a_lat_neg(sp,0), b_lat_neg(sp,0)] = system_params['j2']
syst[a_lat_neg(sp,0), b_lat_neg(sp,0)] = system_params['j2']*added_phase #phase e^i phi_d due to mag field
# + <--> -
syst[a_lat_pos(sp,0), c_lat_neg(sp,0)] = system_params['j3']
syst[a_lat_neg(sp,0), c_lat_pos(sp,0)] = system_params['j3']
# + <--> - hopping with phase
syst[a_lat_pos(sp,0), b_lat_neg(sp,0)] = -system_params['j3'] #phase e^i pi
syst[a_lat_neg(sp,0), b_lat_pos(sp,0)] = -system_params['j3'] #phase e^i pi
syst[a_lat_pos(sp,0), b_lat_neg(sp,0)] = system_params['j3']*np.exp(1j*2*system_params['phi'])*added_phase #phase e^i phi_d due to mag field #phase e^i phi
syst[a_lat_neg(sp,0), b_lat_pos(sp,0)] = system_params['j3']*np.exp(1j*2*system_params['phi'])*added_phase #phase e^i phi_d due to mag field #phase e^i phi
if leads:
......
code/testing_ground.py
+ 18
− 7
View file @ 2e5b4c14
......@@ -9,24 +9,33 @@ from modules.analysis_funcs import ldos_from_kpm, ldos_modes_from_leads
# -
system_params = dict(
mu_a = 0,
mu_b = 0,
mu_c = 0,
mu_a_pos = 0.4,
mu_a_neg = -0.2,
mu_b_pos = -0.3,
mu_b_neg = 0.3,
mu_c_pos = 0.1,
mu_c_neg = -0.1,
j2 = 1,
j3 = 1,
phi = np.pi/2,
phi_d = 0.3
)
inf_chain = diamond_chain_system(20,system_params, semi_infinite = True)
fin_chain = diamond_chain_system(20,system_params, semi_infinite = False)
inf_chain = diamond_chain_system(5,system_params, semi_infinite = True)
fin_chain = diamond_chain_system(5,system_params, semi_infinite = False)
# o = kwant.plot(fin_chain)
# +
# ldos_modes_from_leads(fin_chain.finalized(), system_params) #doesn't work for flat bands
# -
o = ldos_from_kpm(fin_chain.finalized(), system_params, vmax = 10, energy = -2.82842712)
o = ldos_from_kpm(fin_chain.finalized(), system_params, vmax = 10, energy = 0 )
kwant.plotter.bands(inf_chain.finalized(), momenta = np.linspace(-4,4,100))
o = ldos_from_kpm(fin_chain.finalized(), system_params, vmax = 1, energy = 2*system_params['j2'] )
o = ldos_from_kpm(fin_chain.finalized(), system_params, vmax = 10, energy = 2*np.sqrt(2)*system_params['j2'] )
kwant.plotter.bands(inf_chain.finalized(), momenta = np.linspace(-np.pi,np.pi,1000))
ham = fin_chain.finalized().hamiltonian_submatrix()
......@@ -36,4 +45,6 @@ ev
plt.plot(ev, marker='o',lw=0)
np.exp(1j*np.pi/2).imag
notes/diamond_chain.pptx
+ 0
− 0
View file @ 2e5b4c14
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