Recently, alternating twist multilayer graphene (ATMG) has emerged as a family of moiré systems that share several fundamental properties with twisted bilayer graphene, and are expected to host similarly strong electron-electron interactions near the magic angle. Here, we study alternating twist quadrilayer graphene (ATQG) samples with twist angles of 1.96° and 1.52°, which are slightly removed from the magic angle of 1.68°. At the larger angle, we find signatures of correlated insulators only when the ATQG is hole doped, and no signatures of superconductivity, and for the smaller angle we find evidence of superconductivity, while signs of the correlated insulators weaken. Our results provide insight into the twist angle dependence of correlated phases in ATMG and shed light on the nature of correlations in the intermediate coupling regime at the edge of the magic angle range where dispersion and interaction are of the same order.
The recently observed unconventional ferroelectricity in AB bilayer graphene sandwiched by hexagonal Boron Nitride (hBN) presents a new platform to manipulate correlated phases in multilayered van der Waals heterostructures. We present a low-energy continuum model for AB bilayer graphene encapsulated by the top and bottom layers of either hBN or graphene, with two independent twist angles. For the graphene/hBN heterostructures, we show that twist angle asymmetry leads to a layer polarization of the valence and conduction bands. We also show that an out-of-plane displacement field not only tune…
We show that the superconducivity in twisted graphene multilayers originates from a common feature, which is the strong valley symmetry breaking characteristic of these moiré systems at the magic angle. This leads to a breakdown of the rotational symmetry of the flat moiré bands down to $C_3$, and to ground states in which the time-reversal symmetry is broken for a given spin projection. However, this symmetry can be recovered upon exchange of spin-up and spin-down electrons, as we illustrate by means of a self-consistent microscopic Hartree-Fock resolution where the states for the two spin pr…
When two monolayers of graphene are stacked with a small relative twist angle, the resulting band structure exhibits a remarkably flat pair of bands at a sequence of 'magic angles' where correlation effects can induce a host of exotic phases. Here, we study a class of related models of $n$-layered graphene with alternating relative twist angle $\pm θ$ which exhibit magic angle flat bands coexisting with several Dirac dispersing bands at the Moiré K point. Remarkably, we find that the Hamiltonian for the multilayer system can be mapped exactly to a set of decoupled bilayers at {\it different} a…
In-plane magnetic response and Maki parameter of alternating-twist multilayers
Quantum Advanced Research Center (QuARC), CSIC（量子先进研究中心，西班牙国家科学研究委员会）；Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所，西班牙国家科学研究委员会）；Universidad Internacional Menéndez Pelayo（门德斯·佩拉约国际大学）；Department of Mathematics, and Institute for Physical Science and Technology, University of Maryland（马里兰大学数学系及物理科学与技术研究所）；Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理系、尼古拉斯·卡布雷拉研究所及凝聚态物理中心）
The emergence of alternating twist multilayer graphene (ATMG) as a generalization of twisted bilayer graphene (TBG) raises the question - in what important ways do these systems differ? Here, we utilize ab-initio relaxation and single-particle theory, analytical strong coupling analysis, and Hartree-Fock to contrast ATMG with $n=3,4,5,\ldots$ layers and TBG. $\textbf{I}$: We show how external fields enter in the decomposition of ATMG into TBG and graphene subsystems. The parallel magnetic field has little effect for $n$ odd due to mirror symmetry, but surprisingly also for any $n > 2$ if we ar…
We construct a van der Waals heterostructure consisting of three graphene layers stacked with alternating twisting angles $\pmθ$. At the average twist angle $θ\sim 1.56^{\circ}$, a theoretically predicted magic angle for the formation of flat electron bands, narrow conduction and valence moiré bands appear together with a linearly dispersing Dirac band. Upon doping the half-filled moiré valence band with holes, or the half-filled moiré conduction band with electrons, displacement field tunable superconductivity emerges, reaching a maximum critical temperature of 2.1 K at optimal doping and dis…
Twisted graphene systems have draw significant attention due to the discoveries of various correlated and topological phases. In particular, recently the alternating twisted trilayer graphene is discovered to exhibit unconventional superconductivity, which motivates us to study the electronic structures and possible interesting correlation effects of this class of alternating twisted graphene systems. In this work we consider generic alternating twisted multilayer graphene (ATMG) systems with $M$-$L$-$N$ stacking configurations, in which the $M$ ($L$) graphene layers and the $L$ ($N$) layers a…
We calculate the electronic structure of AA'AA'...-stacked alternating twist N-layer (tNG) graphene for N = 3, 4, 5, 6, 8, 10, 20 layers and bulk alternating twist (AT) graphite systems where the lattice relaxations are modeled by means of molecular dynamics simulations. We show that the symmetric AA'AA'... stacking is energetically preferred among all interlayer sliding geometries for progressively added layers up to N=6. Lattice relaxations enhance electron-hole asymmetry, and reduce the magic angles with respect to calculations with fixed tunneling strengths that we quantify from few layers…
Correlated interlayer quantum Hall state in large-angle twisted trilayer graphene
Daegu Gyeongbuk Institute of Science and Technology (DGIST)（大邱庆北科学技术院）；Ulsan National Institute of Science and Technology（蔚山科学技术院）；University of Seoul（首尔大学）；Pohang University of Science and Technology（浦项科技大学）；National Institute for Materials Science（物质材料研究机构）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究所）
The discovery of alternating superconducting and insulating ground-states in magic angle graphene has suggested an intriguing analogy with cuprate high-$T_c$ materials. Here we argue that the network states of small angle twisted bilayer graphene (TBG) afford a further perspective on the cuprates by emulating their stripe-ordered phases, as in La$_{1.875}$Ba$_{0.125}$CuO$_4$. We show that the spin and valley quantum numbers of stripes in TBG graphene fractionalize, developing characteristic signatures in the tunneling density of states and the magnetic noise spectrum of impurity spins. By exam…
We investigate the electronic structure of alternating-twist triple Bernal-stacked bilayer graphene (t3BG) as a function of interlayer coupling $ω$, twist angle $θ$, interlayer potential difference $Δ$, and top-bottom bilayers sliding vector $\boldsymbolτ$ for three possible configurations AB/AB/AB, AB/BA/AB, and AB/AB/BA. The parabolic low-energy band dispersions in a Bernal-stacked bilayer and gap-opening through a finite interlayer potential difference $Δ$ allows the flattening of bands in t3BG down to $\sim 20$~meV for twist angles $θ\lesssim 2^{\circ}$ regardless of the stacking types. Th…
The interlayer van der Waals interaction in twisted bilayer graphene (tBLG) induces both in-plane and out-of-plane atomic displacements showing complex patterns that depend on the twist angle. In particular, for small twist angles, within each graphene layer, the relaxations give rise to a vortex-like displacement pattern which is known to affect the dispersion of the flat bands. Here, we focus on yet another structural property, the chirality of the twisted bilayer. We perform first-principles calculations based on density functional theory to investigate the properties induced by twist chira…
We study the commensuration torques and layer sliding energetics of alternating twist trilayer graphene (t3G) and twisted bilayer graphene on hexagonal boron nitride (t2G/BN) that have two superposed moire interfaces. Lattice relaxations for typical graphene twist angles of $\sim 1^{\circ}$ in t3G or t2G/BN are found to break the out-of-plane layer mirror symmetry, give rise to layer rotation energy local minima dips of the order of $\sim 10^{-1}$ meV/atom at double moire alignment angles, and have sliding energy landscape minima between top-bottom layers of comparable magnitude. Moire superlu…
The superlattice of alternating graphene/h-BN few-layered heterostructures is found to exhibit strong dependence on the parity of the number of layers within the stack. Odd-parity systems show a unique flamingo-like pattern, whereas their even-parity counterparts exhibit regular hexagonal or rectangular superlattices. When the alternating stack consists of seven layers or more, the flamingo pattern becomes favorable, regardless of parity. Notably, the out-of-plane corrugation of the system strongly depends on the shape of the superstructure resulting in significant parity dependence of its mec…
The discovery of correlated states and superconductivity in magic-angle twisted bilayer graphene (MATBG) has established moiré quantum matter as a new platform to explore interaction-driven and topological quantum phenomena. Multitudes of phases have been realized in moiré systems, but surprisingly, robust superconductivity has been one of the least common of all, initially found in MATBG and only more recently also in magic-angle twisted trilayer graphene (MATTG). While MATBG and MATTG share some similar characteristics, they also exhibit substantial differences, such as in their response to …
Lattice dynamics play a crucial role in the physics of Moiré systems. In twisted bilayer graphene (TBG), it was shown that, in addition to the graphene phonons, there is another set of gapless excitations termed Moiré Phonons [Phys. Rev. B, 075416, 2019] reflecting the lattice dynamics at the Moire superlattice level. These modes were later suggested to be phasons due to the incommensurate stacking of the two graphene layers [Phys. Rev. B, 155426, 2019]. In this work, we elucidate the equivalence of these two seemingly distinct perspectives by identifying an underlying symmetry, which we dub m…
Moire patterns result from setting a 2D material such as graphene on another 2D material with a small twist angle or from the lattice mismatch of 2D heterostructures. We present a continuum model for the elastic energy of these bilayer moire structures that includes an intralayer elastic energy and an interlayer misfit energy that is minimized at two stackings (disregistries). We show by theory and computation that the displacement field that minimizes the global elastic energy subject to a global boundary constraint gives large alternating regions of one of the two energy-minimizing stackings…
