  Recent and on-going large ground-based multi-object spectroscopic surveys
allow to significantly increase the sample of spectroscopic binaries to get
insight into their statistical properties. We investigate the repeated spectral
observations of the Gaia-ESO Survey (GES) internal data release 5 to identify
and characterize spectroscopic binaries with one visible component (SB1) in
fields covering the discs, the bulge, the CoRot fields, and stellar clusters
and associations. A statistical chi2-test is performed on spectra of the iDR5
sub-sample of approximately 43500 stars characterized by at least 2
observations and a S/N > 3. Our sample of RV variables is cleaned from
contamination by pulsation/convection-induced variables using Gaia DR2
parallaxes and photometry. Monte-Carlo simulations using the SB9 catalogue of
spectroscopic orbits allow to estimate our detection efficiency and to correct
the SB1 rate to evaluate the GES SB1 binary fraction and its dependence with
effective temperature and metallicity. We find 641 (resp., 803) FGK SB1
candidates at the 5 sigma (resp., 3 sigma) level. The orbital-period
distribution is estimated from the RV standard-deviation distribution and
reveals that the detected SB1 probe binaries with log(P[d]) < 4. We estimate
the global GES SB1 fraction to be in the range 7-14% with a typical uncertainty
of 4%. The GES SB1 frequency decreases with metallicity at a rate of
-9+/-3%/dex in the metallicity range -2.7<FeH<+0.6. This anticorrelation is
obtained with a confidence level higher than 93% on a homogeneous sample
covering spectral types FGK and a large range of metallicities. When the
present-day mass function is accounted for, this rate turns to 4+/-2%/dex with
a confidence level higher than 88%. In addition we provide the variation of the
SB1 fraction with metallicity separately for F, G, and K spectral types, as
well as for dwarf and giant primaries.
