In-plane magnetic response and Maki parameter of alternating-twist multilayers

TL;DR

This paper analytically investigates the in-plane magnetic response of alternating-twist multilayer graphene systems, revealing angle-dependent susceptibilities, negligible responses for odd layers, and implications for superconducting phases.

Contribution

It introduces a method to analyze the orbital magnetic response of alternating-twist multilayers, extending the understanding of their magnetic properties and potential superconducting phases.

Findings

In-plane magnetic response is negligible for odd-layer systems.

Susceptibility diverges near magic angles in TBG.

Response varies significantly with twist angle, being much smaller or larger than TBG at different angles.

Abstract

We analytically study the orbital response of alternating-twist graphene systems with four and five layers to an in-plane magnetic field, using the unitary transformation introduced by Khalaf et al. (Phys. Rev. B 100, 085109 (2019)). This transformation maps an alternating-twist N-layer system onto N/2 decoupled twisted bilayer graphene (TBG) systems with distinct effective twist angles, together with a single decoupled layer for odd N, thereby generating a hierarchy of N/2 magic angles. For five layers, we find that the orbital in-plane magnetic response is negligibly small, and we expect this property to hold for all systems with an odd number of layers. For a tetralayer system, we approximately express the in-plane orbital susceptibility in terms of the corresponding TBG responses, which are large compared to the spin susceptibility and even diverge in the clean limit at charge neutrality near the magic angle. Remarkably, the in-plane magnetic response is strongly angle dependent: compared with TBG, it is about 0.01 times smaller at the first magic angle, whereas at the second it reaches about 3.6 times the value of magic angle TBG. We finally introduce the in-plane Maki parameter as the ratio between the difference in orbital susceptibility of the normal and superconducting states and the paramagnetic Pauli susceptibility. For TBG, we find values up to 2 near the magic angle. Our analysis can be extended to other response functions and suggests that the different effective magic angles in alternating-twist multilayers may host distinct superconducting phases.