Like many of the more respected makes of guitar, Martin and Lowden don't have a zero fret, Fyldes do.

I prefer Martins and Lowdens, but I have friends who swear by their Fyldes.

I've always regarded the zero fret as being a bit of a cop-out on the part of the luthier or manufacturer, it must make it easier to fit the frets on a jig.

See Wikipedia on the subject

A properly made nut with accurately-cut grooves made of bone or ivory is far better, IMHO

Alan