Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

Abstract: In this work, we present a theoretical research on the lattice relaxations, phonon properties, and relaxed electronic structures in magic-angle twisted bilayer graphene (TBG). We construct a continuum elastic model in order to study the lattice dynamics of magic-angle TBG, where both in-plane and out-of-plane lattice displacements are take into account. The fully relaxed lattice structure calculated using such a model is in quantitative agreement with experimental measurements. Furthermore, we investigate the phonon properties in magic-angle TBG using the continuum elastic model, where both the in-plane and out-of-plane phonon modes are included and treated on equal footing. We identify different types of moir\'e phonons including in-plane sliding modes, soft out-of-plane flexural modes, as well as out-of-plane breathing modes. The latter two types of phonon modes exhibit interesting monopolar, dipolar, quadrupolar, and octupolar-type out-of-plane vibration patterns. Additionally, we explore the impact of the relaxed moir\'e superlattice structure on the electronic band structures of magic-angle TBG using an effective continuum model, which shows nearly exact agreement with those calculated using a microscopic atomistic tight-binding approach. Our work lays foundation for further studies on the electron-phonon coupling effects and their interplay with $e$-$e$ interactions in magic-angle TBG.

Abstract: We propose a new class of magnetic proximity effects based on the spin dependent hybridization between the electronic states at the Fermi energy in a non-magnetic conductor and the narrow spin split bands of a ferromagnetic insulator. Unlike conventional exchange proximity, we show this hybridization proximity effect has a very strong influence on the non-magnetic layer and can be further modulated by application of an electric field. We use DFT calculations to illustrate this effect in graphene placed next to a monolayer of CrI$_3$, a ferromagnetic insulator. We find strong hybridization of the graphene bands with the narrow conduction band of CrI$_3$ in one spin channel only. We show that our results are robust with respect to lattice mismatch and twist angle variations. Furthermore, we show that an out-of-plane electric field can be used to modulate the hybridization strength, paving the way for applications.

Abstract: The quantum Hall effect is widely used for the investigation of fundamental phenomena, ranging from topological phases to composite fermions. In particular, the discovery of a room temperature resistance quantum in graphene is significant for compact resistance standards that can operate above cryogenic temperatures. However, this requires large magnetic fields that are accessible only in a few high magnetic field facilities. Here, we report on the quantum Hall effect in graphene encapsulated by the ferroelectric insulator CuInP2S6. Electrostatic gating of the graphene channel enables the Fermi energy to be tuned so that electrons in the localized states of the insulator are in equilibrium with the current-carrying, delocalized states of graphene. Due to the presence of strongly bound states in this hybrid system, a quantum Hall plateau can be achieved at room temperature in relatively modest magnetic fields. This phenomenon offers the prospect for the controlled manipulation of the quantum Hall effect at room temperature.

Abstract: The shift current is part of the second-order optical response of materials with a close connection to topology. Here we report a sign inversion in the band-edge shift photoconductivity of the Haldane model when the system undergoes a topological phase transition. This result is obtained following two complementary schemes. On one hand, we derive an analytical expression for the band-edge shift current in a two-band tight-binding model showing that the sign reversal is driven by the mass term. On the other hand, we perform a numerical evaluation on a continuum version of the Haldane model. This approach allows us to include off-diagonal matrix elements of the position operator, which are discarded in tight-binding models but can contribute significantly to the shift current. Explicit evaluation of the shift current shows that while the model predictions remain accurate in the deep tight-binding regime, significant deviations arise for shallow potential landscapes. Notably, the sign reversal across the topological phase transition is observed in all regimes, implying it is a robust effect that could be observable in a wide range of topological insulators such as $\text{BiTe}_{2}$ and $\text{CsPbI}_{3}$ reported in Phys. Rev. Lett. 116, 237402 (2016).

Abstract: We investigate the effects of introducing a boost (a Zeeman field parallel to the spin quantization axis) at the proximitized helical edge of a two-dimensional (2D) quantum spin Hall insulator. Our self-consistent analysis finds that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting phase may emerge at the edge when the boost is larger than a critical value tied to the induced pairing gap. A non-trivial consequence of retaining the 2D bulk in the model is that this boundary FFLO state supports a finite magnetization as well as finite current (flowing along the edge). This has implications for a proper treatment of the ultra-violet cutoff in analyses employing the effective one-dimensional (1D) helical edge model. Our results may be contrasted with previous studies of such 1D models, which found that the FFLO phase either does not appear for any value of the boost (in non-self-consistent calculations), or that it self-consistently appears even for infinitesimal boost, but carries no current and magnetization.