  Positroids are certain representable matroids originally studied by Postnikov
in connection with the totally nonnegative Grassmannian and now used widely in
algebraic combinatorics. The positroids give rise to determinantal equations
defining positroid varieties as subvarieties of the Grassmannian variety.
Rietsch, Knutson-Lam-Speyer and Pawlowski studied geometric and cohomological
properties of these varieties. In this paper, we continue the study of the
geometric properties of positroid varieties by establishing several equivalent
conditions characterizing smooth positroid varieties using a variation of
pattern avoidance defined on decorated permutations, which are in bijection
with positroids. Furthermore, we give a combinatorial method for determining
the dimension of the tangent space of a positroid variety at key points using
an induced subgraph of the Johnson graph. We also give a Bruhat interval
characterization of positroids.
