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

Igor Vasilevskiy, Miguel Sánchez Sánchez, Khadija Challaouy, Dionisios Margetis, Guillermo Gómez-Santos, Tobias Stauber

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.

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

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.
Paper Structure (22 sections, 59 equations, 2 figures)

This paper contains 22 sections, 59 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Response theory for multilayers
  3. Layer-resolved Ohm's law and Kubo formula
  4. Electric and magnetic fields
  5. Electric and magnetic dipoles
  6. In-plane magnetic response
  7. Trilayer response
  8. Tetralayer response
  9. System response near the first magic angle
  10. System response near the second magic angle
  11. Pentalayer response
  12. Discussion
  13. In-plane Maki parameter
  14. Pauli limit and corrections
  15. Bilayer systems
  16. ...and 7 more sections

Figures (2)

  • Figure 1: Schematic of the magnetization profile induced by an in-plane magnetic field in a tetralayer system near the first (A) and second (B) magic angles. The color scale indicates the sign and relative magnitude of the magnetization in each interlayer region.
  • Figure 2: Left-hand side: The orbital magnetic contribution of Eq. (\ref{['SusceptibilityOrb2']}) (black) and the density of states of twisted bilayer graphene obtained from the non-interacting tight-binding model at a twist angle $\theta=1.25^\circ$ (upper panel) and $\theta_m=1.05^\circ$ (lower panel), using the parameters of Ref. Sanchez24. Right-hand side: The in-plane Maki parameter as defined in Eq. (\ref{['Maki']}).