As per Wikipedia:
Space elevator cable would need a cable material with a specific strength of at least 100,000 kN/(kg/m).
Modern fibre materials such as kevlar, fibreglass and carbon/graphite fibre have breaking lengths of 100–400 km/m.
Nanoengineered materials such as carbon nanotubes and, more recently discovered, graphene ribbons (perfect two-dimensional sheets of carbon) are expected to have breaking lengths of 5000–6000 km/m.
So in short... no. A breakthrough of double the strength of graphene gets us maybe 10% there. Space elevators just aren't going to happen for at least few hundred years, at best.