Search for the production of deuterons and antideuterons in e^+e^- annihilation at center-of-mass energies between 4. 13 and 4. 70 GeV

Using a data sample of e^+e^- collision data corresponding to an integrated luminosity of 19 fb^-1 collected with the BESIII detector at the BEPCII collider, we search for the production of deuterons and antideuterons via e^+e^- pp^-d+c. c. for the first time at center-of-mass energies between 4. 13 and 4. 70 GeV. No significant signal is observed and the upper limit of the e^+e^- pp^-d+c. c. cross section is determined to be from 9. 0 to 145 fb depending on the center-of-mass energy at the 90\% confidence level.