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# -*- coding: utf-8 -*-
import kwant
import numpy as np
def diamond_chain_system(N_c, system_params, semi_infinite = False, leads = False):
'''
Create a diamond chain of trimer unit cells. Each atom of the trimer has two orbital angular momentum states, + and -
_______
... | C_i_+ |
| C_i_- | ...
/ ------- \ ______ /
... | A_i_+ | ...
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Φ | A_i_- |
\ ______ //------- \
... | B_i_+ | ...
| B_i_- |
-------
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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
:param bool leads: whether to include leads
:rtype kwant.system.FiniteSystem:
'''
# make lattices and sublattices
lat = kwant.lattice.Polyatomic(prim_vecs = [[1,0],[0,1]], basis = [[1,0],[1,0], [0,-1],[0,-1], [0,1],[0,1]], norbs = 1)
a_lat_pos, a_lat_neg, b_lat_pos, b_lat_neg, c_lat_pos, c_lat_neg = lat.sublattices
#make builder and populate with onsite and hoppings
if semi_infinite == True:
syst = kwant.Builder(symmetry=kwant.lattice.TranslationalSymmetry([1,0]))
else:
syst = kwant.Builder()
for i in range(N_c):
#staggered point
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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:
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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']
syst[a_lat_pos(sp,0), b_lat_pos(sp+1,0)] = system_params['j2']
syst[a_lat_neg(sp,0), c_lat_neg(sp+1,0)] = system_params['j2']
syst[a_lat_neg(sp,0), b_lat_neg(sp+1,0)] = system_params['j2']
syst[a_lat_pos(sp,0), b_lat_neg(sp+1,0)] = system_params['j3']
syst[a_lat_neg(sp,0), b_lat_pos(sp+1,0)] = system_params['j3']
# + <--> - hopping with phase
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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']
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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']
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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
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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:
lead_syst = kwant.Builder(symmetry=kwant.lattice.TranslationalSymmetry([1,0]))
lead_syst[a_lat_pos(0,0)] = 0
lead_syst[a_lat_neg(0,0)] = 0
lead_syst[b_lat_pos(0,0)] = 0
lead_syst[b_lat_neg(0,0)] = 0
lead_syst[c_lat_pos(0,0)] = 0
lead_syst[c_lat_neg(0,0)] = 0
lead_syst[lat.neighbors(n=1)] = 1
syst.attach_lead(lead_syst)
syst.attach_lead(lead_syst.reversed())
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def tilted_diamond_chain_system(l, N_c, system_params, semi_infinite = False, leads = False, closed_chain = False):
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'''
Create a diamond chain of trimer unit cells. Each atom of the trimer has two orbital angular momentum states, + and -
_______
... __| B_i_+ |
| B_i_- |
-------
| Φ ||
_______ _______
| C_i_+ |__| A_i_+ |__ ...
| C_i_- | | A_i_- |
------- -------
|
...
The Φ represents an out-of-plane magnetic field. The phase is added along the == bond in each unit cell
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:param int l: the orbital angular momentum number. p bands have l=1, and d have l=2.
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: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
:param bool leads: whether to include leads
:param bool closed_chain: whether to close the chain by adding one additional A site on the open trimer at one end of the chain.
:rtype kwant.system.FiniteSystem:
'''
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if l == 0:
raise ValueError('l cannot be 0: use s_tilted_diamond_chain_system instead.')
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# make lattices and sublattices
lat = kwant.lattice.Polyatomic(prim_vecs = [[1,-1],[1,1]], basis = [[0,0],[0,0], [0,1],[0,1], [-1,0],[-1,0]], norbs = 1)
a_lat_pos, a_lat_neg, b_lat_pos, b_lat_neg, c_lat_pos, c_lat_neg = lat.sublattices
#make builder and populate with onsite and hoppings
if semi_infinite == True:
syst = kwant.Builder(symmetry=kwant.lattice.TranslationalSymmetry([1,-1]))
else:
syst = kwant.Builder()
for i in range(N_c):
#staggered point
sp = i
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 == 0:
added_phase = 1
if closed_chain:
syst[a_lat_pos(-1,0)] = system_params['mu_a_pos']
syst[a_lat_neg(-1,0)] = system_params['mu_a_neg']
syst[a_lat_pos(-1,0), c_lat_pos(0,0)] = system_params['j2']
syst[a_lat_pos(-1,0), b_lat_pos(0,0)] = system_params['j2']
syst[a_lat_neg(-1,0), c_lat_neg(0,0)] = system_params['j2']
syst[a_lat_neg(-1,0), b_lat_neg(0,0)] = system_params['j2']
syst[a_lat_pos(-1,0), b_lat_neg(0,0)] = system_params['j3']*added_phase #phase e^i phi_d due to mag field
syst[a_lat_neg(-1,0), b_lat_pos(0,0)] = system_params['j3']*added_phase #phase e^i phi_d due to mag field
syst[a_lat_pos(-1,0), c_lat_neg(0,0)] = system_params['j3']*np.exp(1j*2*system_params['phi']) #phase e^i phi
syst[a_lat_neg(-1,0), c_lat_pos(0,0)] = system_params['j3']*np.exp(1j*2*system_params['phi']) #phase e^i phi
else:
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added_phase = np.exp(1j*2*system_params['phi_d']*l)
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if i < N_c - 1:
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']
syst[a_lat_pos(sp,0), b_lat_pos(sp+1,0)] = system_params['j2']
# - <--> -
syst[a_lat_neg(sp,0), c_lat_neg(sp+1,0)] = system_params['j2']
syst[a_lat_neg(sp,0), b_lat_neg(sp+1,0)] = system_params['j2']
# + <--> -
syst[a_lat_pos(sp,0), b_lat_neg(sp+1,0)] = system_params['j3']*added_phase #phase e^i phi_d due to mag field
syst[a_lat_neg(sp,0), b_lat_pos(sp+1,0)] = system_params['j3']*added_phase #phase e^i phi_d due to mag field
# + <--> - hopping with phase
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']*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']*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']*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:
lead_syst = kwant.Builder(symmetry=kwant.lattice.TranslationalSymmetry([1,0]))
lead_syst[a_lat_pos(0,0)] = 0
lead_syst[a_lat_neg(0,0)] = 0
lead_syst[b_lat_pos(0,0)] = 0
lead_syst[b_lat_neg(0,0)] = 0
lead_syst[c_lat_pos(0,0)] = 0
lead_syst[c_lat_neg(0,0)] = 0
lead_syst[lat.neighbors(n=1)] = 1
syst.attach_lead(lead_syst)
syst.attach_lead(lead_syst.reversed())
return syst
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def s_tilted_diamond_chain_system(N_c, system_params, semi_infinite = False, leads = False, closed_chain = False):
'''
Create a diamond chain of trimer unit cells.
_______
... __| B_i |
| |
-------
| Φ ||
_______ _______
| C_i |__| A_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
:param bool leads: whether to include leads
:param bool closed_chain: whether to close the chain by adding one additional A site on the open trimer at one end of the chain.
:rtype kwant.system.FiniteSystem:
'''
# make lattices and sublattices
lat = kwant.lattice.Polyatomic(prim_vecs = [[1,-1],[1,1]], basis = [[0,0], [0,1], [-1,0]], norbs = 1)
a_lat, b_lat, c_lat = lat.sublattices
#make builder and populate with onsite and hoppings
if semi_infinite == True:
syst = kwant.Builder(symmetry=kwant.lattice.TranslationalSymmetry([1,-1]))
else:
syst = kwant.Builder()
for i in range(N_c):
#staggered point
sp = i
syst[a_lat(sp,0)] = system_params['mu_a']
syst[b_lat(sp,0)] = system_params['mu_b']
syst[c_lat(sp,0)] = system_params['mu_c']
if i == 0:
added_phase = 1
if closed_chain:
syst[a_lat(-1,0)] = system_params['mu_a']
syst[a_lat(-1,0), c_lat(0,0)] = system_params['j2']
syst[a_lat(-1,0), b_lat(0,0)] = system_params['j2']
else:
added_phase = np.exp(1j*2*system_params['phi_d'])
if i < N_c - 1:
#intercell
syst[c_lat(sp+1,0)] = system_params['mu_c']
syst[b_lat(sp+1,0)] = system_params['mu_b']
syst[a_lat(sp,0), c_lat(sp+1,0)] = system_params['j2']
syst[a_lat(sp,0), b_lat(sp+1,0)] = system_params['j2']
# intracell
syst[a_lat(sp,0), c_lat(sp,0)] = system_params['j2']
syst[a_lat(sp,0), b_lat(sp,0)] = system_params['j2']*added_phase #phase e^i phi_d due to mag field
if leads:
lead_syst = kwant.Builder(symmetry=kwant.lattice.TranslationalSymmetry([1,0]))
lead_syst[a_lat(0,0)] = 0
lead_syst[b_lat(0,0)] = 0
lead_syst[c_lat(0,0)] = 0
lead_syst[lat.neighbors(n=1)] = 1
syst.attach_lead(lead_syst)
syst.attach_lead(lead_syst.reversed())
return syst