Sharp announced a new 5.5" 4K IGZO LCD display (2160x3840) - that is the world's highest density display at 806 PPI (!). This takes the crowd from the previous record setting display - SDC's 5.1" QHD (577 PPI) Super AMOLED.
While it's a bit debatable whether we need such high-density displays in our mobile phones, it seems this race won't stop soon. Samsung is also reportedly working on a 4K panel for the Galaxy Note 5, for example (rumors suggest this will be a 5.9" 4K panel). Some other reports say that Samsung is also developing a 5" 4K panel (which will reach 860PPI).
In November 2014, Japan's SEL demonstrated a 2.8" 2560x1440 panel - that reaches a PPI of 1058! This is just a prototype panel at this stage, and is based on SEL's CAAS-OS (C-Axis Aligned Crystalline Oxide Semiconductor) backplane, and a WRGB structure.