Conformal field theory at the critical point of monolayer-bilayer phases of subvalent cations in honeycomb layered materials

Abstract

The rather intriguing experimental result that a wide class of silver (Ag)-based layered materials form stable Ag bilayers, each comprising a pair of triangular sub-lattices, suggests an unexplained bifurcation mechanism for the honeycomb lattice. It is well-known that the honeycomb lattice of graphene requires an additional degree of freedom to describe the orbital wave functions sitting in two different triangular sub-lattices, known as pseudo-spin. In this paper, we exploit the pseudo-spin degree of freedom in the Ag honeycomb lattice to propose a bifurcation mechanism for the Ag triangular sub-lattices, which ultimately requires conformal symmetry breaking within the context of an idealized model, resulting in a cation monolayer-bilayer phase transition in exemplars such as \({\rm Ag_2}M_2\rm TeO_6\) (where \(M\) = Ni, Co, Cu, Mg, Zn). In this description, the critical point of the phase transition is described by Liouville conformal field theory. Our framework is consistent with the following necessary and sufficient conditions for the observation of stable bilayers of cations in layered materials: 1) observation of a pair of cation triangular sub-lattices of the honeycomb lattice; 2) a bond between the subvalent cation and an anion and; 3) existence of weakly attractive cation-cation interactions related to allowed cation subvalent states. Since other materials such as \(\rm Tl_2MnTeO_6\) share the aforementioned conditions with Ag-based systems, the theoretical framework herein also sheds light on the nature of their bilayer structure, with noteworthy applications in the vast field of analogue quantum gravity research.