  In multi-band systems, electrons from different orbitals coexist at the Fermi
surface. An attractive interaction among these quasi-particles gives rise to
inter-band or hybrid pairs which eventually condense in a superconducting
state. These quasi-particles have a natural mismatch of their Fermi
wave-vectors, $\delta k_F$, which depends on the strength of the hybridization
between their orbitals. The existence of this natural scale suggests the
possibility of inhomogeneous superconducting ground states in these systems,
even in the absence of an applied magnetic field. Furthermore, since
hybridization $V$ depends on pressure, this provides an external parameter to
control the wave-vectors mismatch at the Fermi surface. In this work, we study
the phase diagram of a two-dimensional, two-band metal with inter-band pairing.
We show that as the mismatch between the Fermi wave-vectors of the two hybrid
bands is reduced, the system presents a normal-to-inhomogeneous superconductor
quantum phase transition at a critical value of the hybridization
$V_c=\Delta_0$. The superconducting ground state for $V<V_c$ is characterized
by a wave-vector with magnitude $|\mathbf{q}_c|=q_c=2 \Delta_0/\bar{v}_f$. Here
$\Delta_0$ is the superconducting gap in the homogeneous state and $\bar{v}_f$
the average Fermi velocity. We discuss the nature of the quantum critical point
(QCP) at $V_c$ and obtain the associated quantum critical exponents.
