Experimental realization of dice-lattice flat band at the Fermi level in layered electride YCl

Flat electronic bands, where interactions among electrons overwhelm their kinetic energies, hold the promise for exotic correlation physics. The dice lattice has long been theorized as a host of flat bands with intriguing band topology. However, to date, no material has ever been found to host the characteristic flat bands of a dice lattice. Here, using angle-resolved photoemission spectroscopy (ARPES), we discover a dice-lattice flat band at $E_F$ in the van der Waals (vdW) electride [YCl]$^{2+}$: 2e-. In this system, excess valence electrons from Y deconfine from the cation framework to form an interstitial anionic electron lattice that constitutes the dice lattice. Our ARPES measurements unambiguously identify two sets of dice-lattice bands in YCl, including a nearly dispersionless band at the Fermi level. The flat bands and other dispersive bands observed in ARPES find excellent agreement with first-principles calculations, and theoretical analysis reveals that the near-$E_F$ electronic structure is well captured by a simple dice-lattice model. Our findings thus end the long quest of a real dice flat band material and establish vdW electride YCl as a prototype of dice metals. Our results further demonstrate the anionic electron lattice as a novel scheme for realizing lattice geometries and electronic structures rare to find in conventional crystalline systems.