There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Materials with flat electronic bands often exhibit exotic quantum phenomena owing to strong correlations. An isolated low-energy flat band can be induced in bilayer graphene by simply rotating the layers by 1.1°, resulting in the appearance of gate-tunable superconducting and correlated insulating phases. In this study, we demonstrate that in addition to the twist angle, the interlayer coupling can be varied to precisely tune these phases. We induce superconductivity at a twist angle larger than 1.1°—in which correlated phases are otherwise absent—by varying the interlayer spacing with hydrostatic pressure. Our low-disorder devices reveal details about the superconducting phase diagram and its relationship to the nearby insulator. Our results demonstrate twisted bilayer graphene to be a distinctively tunable platform for exploring correlated states.

https://science.sciencemag.org/content/sci/early/2019/01/23/science.aav1910.full.pdf

Tuning superconductivity in twisted bilayer graphene.

Superconductivity can occur under conditions approaching broken-symmetry parent states1. In bilayer graphene, the twisting of one layer with respect to the other at ‘magic’ twist angles of around 1 degree leads to the emergence of ultra-flat moire superlattice minibands. Such bands are a rich and highly tunable source of strong-correlation physics2–5, notably superconductivity, which emerges close to interaction-induced insulating states6,7. Here we report the fabrication of magic-angle twisted bilayer graphene devices with highly uniform twist angles. The reduction in twist-angle disorder reveals the presence of insulating states at all integer occupancies of the fourfold spin–valley degenerate flat conduction and valence bands—that is, at moire band filling factors ν = 0, ±1, ±2, ±3. At ν ≈ −2, superconductivity is observed below critical temperatures of up to 3 kelvin. We also observe three new superconducting domes at much lower temperatures, close to the ν = 0 and ν = ±1 insulating states. Notably, at ν = ± 1 we find states with non-zero Chern numbers. For ν = −1 the insulating state exhibits a sharp hysteretic resistance enhancement when a perpendicular magnetic field greater than 3.6 tesla is applied, which is consistent with a field-driven phase transition. Our study shows that broken-symmetry states, interaction-driven insulators, orbital magnets, states with non-zero Chern numbers and superconducting domes occur frequently across a wide range of moire flat band fillings, including close to charge neutrality. This study provides a more detailed view of the phenomenology of magic-angle twisted bilayer graphene, adding to our evolving understanding of its emergent properties. The fabrication of magic-angle twisted bilayer graphene devices with highly uniform twist angles enables the observation of new superconducting domes, orbital magnets and Chern insulating states.

Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene

When two sheets of graphene are stacked at a small twist angle, the resulting flat superlattice minibands are expected to strongly enhance electron-electron interactions. Here, we present evidence that near three-quarters ([Formula: see text]) filling of the conduction miniband, these enhanced interactions drive the twisted bilayer graphene into a ferromagnetic state. In a narrow density range around an apparent insulating state at [Formula: see text], we observe emergent ferromagnetic hysteresis, with a giant anomalous Hall (AH) effect as large as 10.4 kilohms and indications of chiral edge states. Notably, the magnetization of the sample can be reversed by applying a small direct current. Although the AH resistance is not quantized, and dissipation is present, our measurements suggest that the system may be an incipient Chern insulator.

https://science.sciencemag.org/content/sci/early/2019/07/24/science.aaw3780.full.pdf

Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene

The competition between the kinetic energy of electrons in a crystal and the inter-electron Coulomb repulsion underlies many fascinating phenomena in quantum materials. Superlattices formed from moir\'e patterns in graphene structures have emerged as tunable platforms for such physics. This paper shows that in many graphene moir\'e structures not only are the electronic bands narrow enough for Coulomb interaction to be important, but they are also topologically nontrivial. This setting of a strong correlated partially filled topological band promises to lead to many novel phenomena.

https://link.aps.org/accepted/10.1103/PhysRevB.99.075127

Nearly flat Chern bands in moiré superlattices

Recently quantum anomalous effects were observed in twisted bilayer graphene. This paper shows that twisted bilayer graphene hosts narrow Chern bands if aligned with hBN substrate, which give rise to quantum anomalous effects through quantum Hall ferromagnetism

https://link.aps.org/pdf/10.1103/PhysRevResearch.1.033126

Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous Hall effect and a lattice model

A recent experiment reported a large anomalous Hall effect in Magic Angle Twisted Bilayer Graphene (TBG) aligned with a hexagonal boron nitride(h-BN) substrate at $\frac{3}{4}$ filling of the conduction band. In this paper we study this system theoretically, and propose explanations of this observation. We emphasize that the physics for this new system is qualitatively different from the pure TBG system. The aligned h-BN breaks in-plane two-fold rotation symmetry and gaps out the Dirac crossings of ordinary TBG. The resulting valence and conduction bands of each valley carry equal and opposite Chern numbers $C=\pm 1$. A useful framework is provided by a lattice extended Hubbard model for this system which we derive. An obvious possible explanation of the anomalous Hall effect is that at $3/4$-filling the system is a spin-valley polarized ferromagnetic insulator where the electrons completely fill a Chern band. We also examine an alternate more radical proposal of a compressible valley polarized but spin unpolarized composite ferm liquid metallic state. We argue that either state is compatible with current experiments, and propose ways to distinguish between them in the future. We also briefly discuss the physics at $1/2$ filling.

Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model.

Collective excitations of bound electron-hole pairs—known as excitons—are ubiquitous in condensed matter, emerging in systems as diverse as band semiconductors, molecular crystals, and proteins. Recently, their existence in strongly correlated electron materials has attracted increasing interest due to the excitons’ unique coupling to spin and orbital degrees of freedom. The non-equilibrium driving of such dressed quasiparticles offers a promising platform for realizing unconventional many-body phenomena and phases beyond thermodynamic equilibrium. Here, we achieve this in the van der Waals correlated insulator NiPS3 by photoexciting its newly discovered spin–orbit-entangled excitons that arise from Zhang-Rice states. By monitoring the time evolution of the terahertz conductivity, we observe the coexistence of itinerant carriers produced by exciton dissociation and a long-wavelength antiferromagnetic magnon that coherently precesses in time. These results demonstrate the emergence of a transient metallic state that preserves long-range antiferromagnetism, a phase that cannot be reached by simply tuning the temperature. More broadly, our findings open an avenue toward the exciton-mediated optical manipulation of magnetism. Previous work has shown the existence of spin-orbit-entangled excitons and their coupling to antiferromagnetism in the correlated insulator NiPS3. Here the authors show that non-equilibrium driving of these excitons produces a transient metallic antiferromagnetic state that cannot be achieved by tuning the temperature in equilibrium.

/pdf/exciton-driven-antiferromagnetic-metal-in-a-correlated-van-4y19zpmp78.pdf

Exciton-driven antiferromagnetic metal in a correlated van der Waals insulator.

We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a $\mathrm{Sp}(N$) principal chiral model with a topological $\mathrm{\ensuremath{\Theta}}$ term, whose boundary is described by a $\mathrm{Sp}(N$) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning $\mathrm{\ensuremath{\Theta}}$ in the field theory, and the phase transition occurs at $\mathrm{\ensuremath{\Theta}}=\ensuremath{\pi}$. The simplest version of these models with $N=1$ is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a $(1+1)\text{D}$ conformal field theory with central charge $c=1$. After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or ${Z}_{2}$ symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely $\mathrm{\ensuremath{\Theta}}=\ensuremath{\pi}$ is a stable $(2+1)\text{D}$ conformal field theory with gapless bosonic modes.

Dan Mao

Papers

Nearly flat Chern bands in moiré superlattices

Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous Hall effect and a lattice model

Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model.

Exciton-driven antiferromagnetic metal in a correlated van der Waals insulator.

Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term