Hello,
I'm a new kwant user, and i'm trying to reproduce some papers using real units and surges me a lot of questions regarding the internal units in kwant, if anyone understands, could you give me an idea?
Usually the examples in kwant are chosen such that the units are given by (t=a=1), where (t) naturally depends on the value of (a) by means of t=hbar**2/(2ma**2), using this fact then the matrix elements of the hamiltonian are commonly defined , this parameters enter in the hamiltonian by means of
the building of the lattice:
lat = kwant.lattice.square(a=a, norbs=norbs)
the matrix elements of the hamiltonian(e.g. with Rashba SOC):
sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = -t * sigma_0 - 1j * alpha * sigma_y
and from now on, all the calculations are given in terms of this units:
for example, the energy units are in terms of [t] , the time unit are in (hbar/[t]), and the unit of distance in terms of [a], this means that for example 1 step in kwant energy correspond to one step of t in whatever units it has, is this correct? or am I missing something?
Then assuming that i give the following values
t=0.1 #in what units? can I simply assume that are eV?
and for whatever reason i choose
a=1
in this case what unit correspond to a?, I suppose that it has a unit such that
t=hbar**2/(2ma**2)=0.1#in eV?
Is this correct?
and again once I replace this value in kwant, then the unit of energy is given by 0.1 eV, that is in steps of t, or in eV? How the system recognize in what units i want to work?
If you have more comments about the units of the operators this will help me a lot, for example I understand that the units of of the observable are the same that the explicit formulas that appears in the tkwant review? for example the wave density has units of 1/sqrt(E), according to normalization formula and furthermore the current has no units, is this correct?
again thank you and sorry for the stupid questions!