  The sensitivity of current and planned gravitational wave interferometric
detectors is limited, in the most critical frequency region around 100 Hz, by a
combination of quantum noise and thermal noise. The latter is dominated by
Brownian noise: thermal motion originating from the elastic energy dissipation
in the dielectric coatings used in the interferometer mirrors. The energy
dissipation is a material property characterized by the mechanical loss angle.
We have identified mixtures of titanium dioxide (TiO$_2$) and germanium dioxide
(GeO$_2$) that show internal dissipations at a level of 1 $\times 10^{-4}$, low
enough to provide almost a factor of two improvement on the level of Brownian
noise with respect to the state-of-the-art materials. We show that by using a
mixture of 44% TiO$_2$ and 56% GeO$_2$ in the high refractive index layers of
the interferometer mirrors, it would be possible to achieve a thermal noise
level in line with the design requirements. These results are a crucial step
forward to produce the mirrors needed to meet the thermal noise requirements
for the planned upgrades of the Advanced LIGO and Virgo detectors.
