From fc973fdde063eb9667e0562fbbba4ce049791d17 Mon Sep 17 00:00:00 2001
From: Joseph Weston <joseph@weston.cloud>
Date: Tue, 16 Jul 2019 16:22:16 +0200
Subject: [PATCH] add 'add_peierls_phase'
This function adds a Peierls phase to a Builder
---
kwant/builder.py | 171 +++++++++++++++++++++++++++++++++++-
kwant/tests/test_builder.py | 25 ++++++
2 files changed, 193 insertions(+), 3 deletions(-)
diff --git a/kwant/builder.py b/kwant/builder.py
index 2ca81a94..89ec7c24 100644
--- a/kwant/builder.py
+++ b/kwant/builder.py
@@ -13,6 +13,7 @@ import collections
import copy
from functools import total_ordering, wraps, update_wrapper
from itertools import islice, chain
+import textwrap
import inspect
import tinyarray as ta
import numpy as np
@@ -20,13 +21,14 @@ from scipy import sparse
from . import system, graph, KwantDeprecationWarning, UserCodeError
from .linalg import lll
from .operator import Density
-from .physics import DiscreteSymmetry
+from .physics import DiscreteSymmetry, magnetic_gauge
from ._common import (ensure_isinstance, get_parameters, reraise_warnings,
- interleave, deprecate_args)
+ interleave, deprecate_args, memoize)
__all__ = ['Builder', 'Site', 'SiteFamily', 'SimpleSiteFamily', 'Symmetry',
- 'HoppingKind', 'Lead', 'BuilderLead', 'SelfEnergyLead', 'ModesLead']
+ 'HoppingKind', 'Lead', 'BuilderLead', 'SelfEnergyLead', 'ModesLead',
+ 'add_peierls_phase']
################ Sites and site families
@@ -1803,6 +1805,169 @@ class Builder:
inter_cell_hopping = cell_hamiltonian = precalculated = \
_require_system
+
+def _add_peierls_phase(syst, peierls_parameter):
+
+ @memoize
+ def wrap_hopping(hop):
+ def f(*args):
+ a, b, *args, phi = args
+ return hop(a, b, *args) * phi(a, b)
+
+ params = ('_site0', '_site1')
+ if callable(hop):
+ params += get_parameters(hop)[2:] # cut off both site parameters
+ params += (peierls_parameter,)
+
+ f.__signature__ = inspect.Signature(
+ inspect.Parameter(name, inspect.Parameter.POSITIONAL_ONLY)
+ for name in params)
+
+ return f
+
+ const_hoppings = {}
+
+ def const_hopping(a, b, phi):
+ return const_hoppings[a, b] * phi(a, b)
+
+ # fix the signature
+ params = ('_site0', '_site1', peierls_parameter)
+ const_hopping.__signature__ = inspect.Signature(
+ inspect.Parameter(name, inspect.Parameter.POSITIONAL_ONLY)
+ for name in params)
+
+ ret = Builder(
+ syst.symmetry,
+ # No time reversal, as magnetic fields break it
+ conservation_law=syst.conservation_law,
+ particle_hole=syst.particle_hole,
+ chiral=syst.chiral,
+ )
+ for i, lead in enumerate(syst.leads):
+ ret.leads.append(
+ BuilderLead(
+ _add_peierls_phase(
+ lead.builder,
+ peierls_parameter + '_lead{}'.format(i),
+ ),
+ lead.interface,
+ lead.padding,
+ )
+ )
+
+ for site, val in syst.site_value_pairs():
+ ret[site] = val
+
+ for hop, val in syst.hopping_value_pairs():
+ if callable(val):
+ ret[hop] = wrap_hopping(val)
+ else:
+ const_hoppings[hop] = val
+ ret[hop] = const_hopping
+
+ return ret
+
+
+def add_peierls_phase(syst, peierls_parameter='phi', fix_gauge=True):
+ """Add a Peierls phase parameter to a Builder.
+
+ Parameters
+ ----------
+ syst : kwant.Builder
+ The system to which to add a Peierls phase.
+ peierls_parameter : str
+ The name of the Peierls phase parameter to value functions.
+ fix_gauge : bool (default: True)
+ If True, fix the gauge of the system and return it also
+
+ Returns
+ -------
+ syst : kwant.builder.Finitesystem or kwant.builder.InfiniteSystem
+ A system where all hoppings are given by value functions
+ that have an additional parameter 'phi' that should be
+ the Peierls phase returned by `kwant.physics.magnetic_gauge`.
+ Any leads have similar parameters named 'phi_lead0',
+ 'phi_lead1' etc.
+ gauge : callable
+ Only returned if 'fix_gauge' is True. Called with magnetic
+ field(s), and returns a parameter dictionary that can be
+ passed to the system as 'params' (see the example below).
+
+ Examples
+ --------
+ >>> import numpy as np
+ >>> import kwant
+ >>>
+ >>> syst = make_system()
+ >>> lead = make_lead()
+ >>> syst.attach_lead(lead)
+ >>> syst.attach_lead(lead.reversed())
+ >>>
+ >>> fsyst, phase = kwant.builder.add_peierls_phase(syst)
+ >>>
+ >>> def B_syst(pos):
+ >>> return np.exp(-np.sum(pos * pos))
+ >>>
+ >>> kwant.smatrix(fsyst, parameters=dict(t=-1, **phase(B_syst, 0, 0)))
+ """
+
+ def wrap_gauge(gauge):
+ phase_names = [peierls_parameter]
+ phase_names += [peierls_parameter + '_lead{}'.format(i)
+ for i in range(len(syst.leads))]
+
+ doc = textwrap.dedent("""\
+ Return the Peierls phase for a magnetic field configuration.
+
+ Parameters
+ ----------
+ syst_field : scalar, vector or callable
+ The magnetic field to apply to the scattering region.
+ If callable, takes a position and returns the
+ magnetic field at that position. Can be a scalar if
+ the system is 1D or 2D, otherwise must be a vector.
+ Magnetic field is expressed in units :math:`φ₀ / l²`,
+ where :math:`φ₀` is the magnetic flux quantum and
+ :math:`l` is the unit of length.
+ *lead_fields : scalar, vector or callable
+ The magnetic fields to apply to each of the leads, in
+ the same format as 'syst_field'. In addition, if a callable
+ is provided, then the magnetic field must have the symmetry
+ of the associated lead.
+ tol : float, default: 1E-8
+ The tolerance to which to calculate the flux through each
+ hopping loop in the system.
+ average : bool, default: False
+ If True, estimate the magnetic flux through each hopping loop
+ in the system by evaluating the magnetic field at a single
+ position inside the loop and multiplying it by the area of the
+ loop. If False, then ``scipy.integrate.quad`` is used to integrate
+ the magnetic field. This parameter is only used when 'syst_field'
+ or 'lead_fields' are callable.
+
+ Returns
+ -------
+ phases : dict of callables
+ To be passed directly as the parameters of a system wrapped with
+ 'kwant.builder.add_peierls_phase'.
+ """)
+
+ @wraps(gauge)
+ def f(*args, **kwargs):
+ phases = gauge(*args, **kwargs)
+ return dict(zip(phase_names, phases))
+
+ f.__doc__ = doc
+
+ return f
+
+ ret = _add_peierls_phase(syst, peierls_parameter).finalized()
+
+ if fix_gauge:
+ return ret, wrap_gauge(magnetic_gauge(ret))
+ else:
+ return ret
+
################ Finalized systems
diff --git a/kwant/tests/test_builder.py b/kwant/tests/test_builder.py
index 84e3ef02..3885940a 100644
--- a/kwant/tests/test_builder.py
+++ b/kwant/tests/test_builder.py
@@ -1416,3 +1416,28 @@ def test_finalization_preserves_padding():
syst = syst.finalized()
# The order is guaranteed because the paddings are sorted.
assert [syst.sites[i] for i in syst.lead_paddings[0]] == padding[:-1]
+
+
+def test_add_peierls_phase():
+
+ lat = kwant.lattice.square()
+ syst = kwant.Builder()
+ syst[(lat(i, j) for i in range(5) for j in range(5))] = 4
+ syst[lat.neighbors()] = lambda a, b, t: -t
+
+ lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))
+ lead[(lat(0, j) for j in range(5))] = 4
+ lead[lat.neighbors()] = -1
+
+ syst.attach_lead(lead)
+ syst.attach_lead(lead.reversed())
+
+ syst, phase = builder.add_peierls_phase(syst)
+
+ assert isinstance(syst, builder.FiniteSystem)
+
+ params = phase(1, 0, 0)
+
+ assert all(p in params for p in ('phi', 'phi_lead0', 'phi_lead1'))
+
+ kwant.smatrix(syst, energy=0.1, params=dict(t=-1, **params))
--
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