I actually studied one mind-numbing material science book with medieval swords in mind to keep interest. Seems like the vikings got it right with high carbon steel. The only good improvement to it would be boride or hard chrome coating. But the main function of such would be temporary stop to corrosion.
The major problem of swords is fatigue while notched. Low alloy steels are some of the best known materials for this. But they don't stay sharp very well and hardened high carbon steel can just cut through such beam. When you go from high carbon steel to very high carbon steel, you get additionally "left over austenite". A real time hardening method which helps both against nocthing and against fatigue. The stuff spontaneously quenches itself under stress(!). A reaction more commonly known to happen in manganese steel, but here it happens to lesser degree.
The major problem of swords is fatigue while notched. Low alloy steels are some of the best known materials for this. But they don't stay sharp very well and hardened high carbon steel can just cut through such beam. When you go from high carbon steel to very high carbon steel, you get additionally "left over austenite". A real time hardening method which helps both against nocthing and against fatigue. The stuff spontaneously quenches itself under stress(!). A reaction more commonly known to happen in manganese steel, but here it happens to lesser degree.
https://en.wikipedia.org/wiki/Mangalloy