Effective low-energy Hamiltonians for interacting nanostructures

TL;DR

This paper develops a functional renormalization group approach to derive low-energy Hamiltonians for interacting trigonal graphene nanodiscs, demonstrating the robustness of zero-energy state degeneracy and analyzing the effects of excited states.

Contribution

It introduces a systematic fRG method to derive effective low-energy Hamiltonians for nanostructures, including excited state effects, and confirms the robustness of zero-energy degeneracy.

Findings

Zero-energy state degeneracy remains robust against higher level influences.

The effective Hamiltonian captures interaction effects accurately.

Degeneracy is preserved for various nanodisc sizes and shapes.

Abstract

We present a functional renormalization group (fRG) treatment of trigonal graphene nanodiscs and composites thereof, modeled by finite-size Hubbard-like Hamiltonians with honeycomb lattice structure. At half filling, the noninteracting spectrum of these structures contains a certain number of half-filled states at the Fermi level. For the case of trigonal nanodiscs, including interactions between these degenerate states was argued to lead to a large ground state spin with potential spintronics applications. Here we perform a systematic fRG flow where the excited single-particle states are integrated out with a decreasing energy cutoff, yielding a renormalized low-energy Hamiltonian for the zero-energy states that includes effects of the excited levels. The numerical implementation corroborates the results obtained with a simpler Hartree-Fock treatment of the interaction effects within the zero-energy states only. In particular, for trigonal nanodiscs the degeneracy of the one-particle-states with zero-energy turns out to be very robust against influences of the higher levels. As an explanation, we give a general argument that within this fRG scheme the zero-energy degeneracy remains unsplit under quite general conditions and for any size of the trigonal nanodisc. We furthermore discuss the differences in the effective Hamiltonian and their ground states of single nanodiscs and composite bow-tie-shaped systems.