  A new class of universal "three-body" bound states has been recently
predicted theoretically for identical fermions interacting at p-wave resonance
in two dimensions. This phenomenon is called the super Efimov effect since the
binding energies of the states follow a intriguing double exponential scaling.
However, experimental resolution of this scaling is expected to meet formidable
challenges. In this work, we introduce a new thermodynamic quantity, the
three-body contact $C_\theta$, to quantify three-body correlations in a two
dimensional gas composed of the resonantly interacting fermions; the contact
$C_\theta$ is the consequence of the underlying universal super Efimov effect
in the many-body context. We show how $C_\theta$ affects physical observables
such as the radio-frequency spectrum, the momentum distribution and the atom
loss rate. Signature of the elusive super Efimov effect in the thermodynamic
system can be pinned down by the detection of the three-body contact $C_\theta$
via these observables.
