Question

In models of strained graphene one seems to obtain a position-dependent Fermi velocity. By this I mean that if the original Dirac operator is

H=v0(σ1p1+σ2p2),

with constant Fermi velocity v0
, then after the straining procedure one obtains, see this reference (20) for instance

H=σivij(r)pj+ potential terms

I am curious if there is any model in physics that produces a position-dependent Fermi velocity that is the same for both p1,p2
, i.e. I want

H=v(r)(σ1p1+σ2p2)+ potential terms.

My understanding is that although the latter is a special case of the strain in graphene, one cannot design any non-trivial examples of strain fields to get an operator of this type.

Answer 1

In strained graphene models, the Fermi velocity can become position-dependent, resulting in a position-dependent Dirac operator. However, obtaining a position-dependent Fermi velocity that is the same for both p1 and p2 is difficult, as it requires designing non-trivial strain fields.

Step-by-step explanation:

In models of strained graphene, the Fermi velocity can become position-dependent after the straining procedure. While the original Dirac operator is H = v0(σ1p1+σ2p2), with a constant Fermi velocity v0, the strained graphene model can result in H = vij(r)(σ1p1+σ2p2)+ potential terms, where vij(r) represents a position-dependent Fermi velocity. While it is possible to obtain a position-dependent Fermi velocity that is the same for both p1 and p2 in this model, it is challenging to design non-trivial examples of strain fields to achieve this operator type.