Microscopic origin of three-dimensional criticality in the CoSi surface CDW

Identify the specific microscopic mechanism by which coupling between CoSi (001) surface Fermi-arc states and the bulk topology supplies sufficient phase stiffness to produce 3D XY criticality in the nominally two-dimensional surface charge-density wave.

Background

The measured CoSi (001) surface CDW exhibits a critical exponent consistent with the 3D XY universality class, despite the ordering being confined to the surface. The authors attribute this behavior to intrinsic three-dimensional structure arising from an approximately π phase relationship between CDW modulations in different surface sublayers within the unit cell.

The proposed explanation invokes coupling between surface Fermi-arc states and the three-dimensional bulk topology to provide the phase stiffness needed to avoid a purely two-dimensional BKT transition. Although the observations support this interpretation, the microscopic origin of the coupling itself is not determined by the SHG measurements and is explicitly left unresolved.