Looking for a dye which emits around 680 nm
There are two dyes commonly used in biochemistry research with $\lambda_\mathrm{Ex}$ of around $\pu{650 nm}$. They are Alexa Fluor 647 from ThermoFisher and Cyanine5 (Cy5) from Lumiprobe. Two example of these two categories are illustrated in the following figure. Either probe can be ordered according to the way you want to conjugate to your substrate (azide and alkyne groups are shown here). For example, IgG conjugate of Alexa Fluor 647 with amide linkage is shown in the insert.