On proximity of 4/7 solid phase of ³He adsorbed on graphite-origin of specific-heat anomalies in hole-doped density-ordered solid-

We theoretically study the stability of the solidified second-layer ³He at 4/7 of the first-layer density adsorbed on graphite, which exhibits quantum spin liquid. We construct a lattice model for the secondlayer ³He by taking account of density fluctuations on the third layer together by employing the refined configuration recently found by path integral Monte Carlo simulations. When holes are doped into the 4/7 solid, within the mean-field approximation, the density-ordered fluid emerges. The evolution of hole pockets offers a unified explanation for the measured doping and temperature dependences of specificheat anomalies. We argue that differentiation in momentum space is a key to understanding the physics and accounts for multiscale thermodynamic anomalies in the mono- and double-layered ³He systems beyond the mean-field level.