Small-twist-angle transition metal dichalcogenide (TMD) heterobilayers develop isolated flat moire bands that are approximately described by triangular lattice generalized Hubbard models [PhysRevLett.121.026402]. In this article we explore the metall
ic and insulating states that appear under different control conditions at a density of one-electron per moire period, and the transitions between them. By combining fully self-consistent Hartree-Fock theory calculations with strong-coupling expansions around the atomic limit, we identify four different magnetic states and one nonmagnetic state near the model phase diagrams metal-insulator phase-transition line. Ferromagnetic insulating states, stabilized by non-local direct exchange interactions, are surprisingly prominent.
The Hall effect, in which current flows perpendicular to an applied electrical bias, has played a prominent role in modern condensed matter physics over much of the subjects history. Appearing variously in classical, relativistic and quantum guises,
it has among other roles contributed to establishing the band theory of solids, to research on new phases of strongly interacting electrons, and to the phenomenology of topological condensed matter. The dissipationless Hall current requires time-reversal symmetry breaking. For over a century it has either been ascribed to externally applied magnetic field and referred to as the ordinary Hall effect, or ascribed to spontaneous non-zero total internal magnetization (ferromagnetism) and referred to as the anomalous Hall effect. It has not commonly been associated with antiferromagnetic order. More recently, however, theoretical predictions and experimental observations have identified large Hall effects in some compensated magnetic crystals, governed by neither of the global magnetic-dipole symmetry breaking mechanisms mentioned above. The goals of this article are to systematically organize the present understanding of anomalous antiferromagnetic materials that generate a non-zero Hall effect, which we will call anomalous Hall antiferromagnets, and to discuss this class of materials in a broader fundamental and applied research context. Our motivation in drawing attention to anomalous Hall antiferromagnets is two-fold. First, since Hall effects that are not governed by magnetic dipole symmetry breaking are at odds with the traditional understanding of the phenomenon, the topic deserves attention on its own. Second, this new reincarnation has again placed the Hall effect in the middle of an emerging field of physics at the intersection of multipole magnetism, topological condensed matter, and spintronics.
Topological insulator thin films with surface magnetism are expected to exhibit a quantized anomalous Hall effect when the magnetizations on the top and bottom surfaces are parallel, and a quantized topological magnetoelectric (QTME) response when th
e magnetizations have opposing orientations and the films are sufficiently thick. We present a unified picture of both effects that associates finite thickness corrections to the QTME with non-locality in the side-wall current response function. Using realistic tight-binding model calculations, we show that finite-thickness corrections in Bi$_2$Se$_3$ topological insulator (TI) thin films are reduced in size when the exchange coupling of band states to surface magnetization is strengthened.
CrSb is an attractive material for room-temperature antiferromagnetic spintronic applications because of its high N{e}el temperature $sim$700 K and semi-metallic character. We study the magnetic properties of CrSb bilayers on few-layer topological in
sulator thin films using emph{ab initio} density functional theory. We find that the intrinsic parts of the total anomalous Hall conductivities of the thin films are non-zero, and approximately quantized. The N{e}el temperature of CrSb bilayers on few-layer topological insulator thin films is found to be approximately two times larger than that of an isolated CrSb thin film. Due to the low Fermi level density of states of CrSb, Hall quantization might be achievable by introducing disorder. CrSb bilayers on topological insulator surfaces are therefore attractive candidates for high-temperature quantum anomalous Hall effects.
Donors in silicon can now be positioned with an accuracy of about one lattice constant, making it possible in principle to form donor arrays for quantum computation or quantum simulation applications. However the multi-valley character of the silicon
conduction band combines with central cell corrections to the donor state Hamiltonian to translate atomic scale imperfections in donor placement into strongly disordered inter-donor hybridization. We present a simple model that is able to account accurately for central-cell corrections, and use it to assess the impact of donor-placement disorder on donor array properties in both itinerant and localized limits.
It has recently been shown that superconductivity in magic-angle twisted trilayer graphene survives to in-plane magnetic fields that are well in excess of the Pauli limit, and much stronger than the in-plane critical magnetic fields of magic-angle tw
isted bilayer graphene. The difference is surprising because twisted bilayers and trilayers both support the magic-angle flat bands thought to be the fountainhead of twisted graphene superconductivity. We show here that the difference in critical magnetic fields can be traced to a $mathcal{C}_2 mathcal{M}_{h}$ symmetry in trilayers that survives in-plane magnetic fields, and also relative displacements between top and bottom layers that are not under experimental control at present. An gate electric field breaks the $mathcal{C}_2 mathcal{M}_{h}$ symmetry and therefore limits the in-plane critical magnetic field.
Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct symmetry prop
erties. In this paper, we show how to create maximally expressive models for quantum states with specific symmetry properties by drawing on literature from the machine learning community. We implement group equivariant convolutional networks (G-CNN) cite{cohen2016group}, and demonstrate that performance improvements can be achieved without increasing memory use. We show that G-CNNs achieve very good accuracy for Heisenberg quantum spin models in both ordered and spin liquid regimes, and improve the ground state accuracy on the triangular lattice over other variational Monte-Carlo methods.
The quantum anomalous Hall (QAH) effect has recently been realized in thin films of intrinsic magnetic topological insulators (IMTIs) like MnBi$_2$Te$_4$. Here we point out that that the QAH gaps of these IMTIs can be optimized, and that both axion i
nsulator/semimetal and Chern insulator/semimetal transitions can be driven by electrical gate fields on the $sim 10$ meV/nm scale. This effect is described by combining a simplified coupled-Dirac-cone model of multilayer thin films with Schr{o}dinger-Poisson self-consistent-field equations.
Near a magic twist angle, bilayer graphene transforms from a weakly correlated Fermi liquid to a strongly correlated two-dimensional electron system with properties that are extraordinarily sensitive to carrier density and to controllable environment
al factors such as the proximity of nearby gates and twist-angle variation. Among other phenomena magic-angle twisted bilayer graphene hosts superconductivity, interaction induced insulating states, magnetism, electronic nematicity, linear-in-T low-temperature resistivity, and quantized anomalous Hall states. We highlight some key research results in this field, point to important questions that remain open, and comment on the place of magic angle twisted bilayer graphene in the strongly correlated quantum matter world.
We discuss the magnetic and topological properties of bulk crystals and quasi-two-dimensional thin films formed by stacking intrinsic magnetized topological insulator ( for example Mn(Sb$_{x}$Bi$_{1-x}$)$_2$X$_4$ with X = Se,Te, including MnBi$_2$Te$
_4$) septuple layers and topological insulator quintuple layers in arbitrary order. Our analysis makes use of a simplified model that retains only Dirac-cone degrees of freedom on both surfaces of each septuple or quintuple layer. We demonstrate the models applicability and estimate its parameters by comparing with {it ab initio } density-functional-theory(DFT) calculations. We then employ the coupled Dirac cone model to provide an explanation for the dependence of thin-film properties, particularly the presence or absence of the quantum anomalous Hall effect, on film thickness, magnetic configuration, and stacking arrangement, and to comment on the design of Weyl superlattices.
