Surface Functional Renormalization Group for Layered Quantum Materials

TL;DR

This paper extends the functional renormalization group method to surface and interface interactions in layered 3D materials, analyzing emergent correlated states in a semi-infinite Hubbard model with interlayer coupling.

Contribution

It introduces an efficient surface-focused FRG approach and applies it to a layered Hubbard model, revealing complex phase behavior including potential chiral spin-bond order.

Findings

Surface FRG effectively captures surface and interface interactions.

Interlayer coupling influences the stability of magnetic and superconducting states.

Intermediate couplings can lead to incommensurate spin-density-wave and spin-bond order.

Abstract

We present an extension to the two-dimensional functional renormalization group to efficiently treat interactions on the surface or at interfaces of three-dimensional systems. As an application, we consider a semi-infinite stack of two-dimensional square lattices, including a Hubbard interaction on the surface layer and an alternating interlayer coupling. We investigate how strongly correlated states of the decoupled two-dimensional Hubbard model on the surface evolve under inclusion of such an SSH-like interlayer coupling. For large parts of the phase diagram as a function of the interlayer hopping parameters, the physics of the two-dimensional system prevails, with antiferromagnetic, superconducting $d$-wave, and ferromagnetic correlations taking center stage. However, for intermediate interlayer couplings the superconducting state at intermediate interaction strengths separates into two regimes by a small region of incommensurate spin-density-wave and spin-bond order, enabling the potential realization of chiral spin-bond order.