Magnetic Field and Strain Functions

import pybinding as pb
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from pybinding.constants import phi0
import inspect
from pybinding.repository import graphene
from math import pi

###Note that these are credited to the tutorial from Pybinding, with small edits to their triaxial code to make it uniaxial

def constant_magnetic_field(B):
    @pb.hopping_energy_modifier
    def function(energy, x1, y1, x2, y2):
        # the midpoint between two sites
        y = 0.5 * (y1 + y2)
        # scale from nanometers to meters
        y *= 1e-9

        # vector potential along the x-axis
        A_x = B * y

        # integral of (A * dl) from position 1 to position 2
        peierls = A_x * (x1 - x2)
        # scale from nanometers to meters (because of x1 and x2)
        peierls *= 1e-9

        # the Peierls substitution
        return energy * np.exp(1j * 2*pi/phi0 * peierls)
    return function

def uniaxial_strain(c, beta=3.37):
    """Produce both the displacement and hopping energy modifier"""
    @pb.site_position_modifier
    def displacement(x, y, z):
        uy = c * y**2
        return x, y + uy, z

    @pb.hopping_energy_modifier
    def strained_hopping(energy, x1, y1, z1, x2, y2, z2):
        l = np.sqrt((x1-x2)**2 + (y1-y2)**2 + (z1-z2)**2)
        w = l / graphene.a_cc - 1
        return energy * np.exp(-beta*w)

    return displacement, strained_hopping