Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains

Many-body interactions give rise to the appearance of exotic phases in Hermitian physics. Despite their importance, many-body effects remain an open problem in non-Hermitian physics due to the complexity of treating many-body interactions. Here, we present a family of exact and numerical phase diagrams for non-Hermitian interacting Kitaev chains. In particular, we establish the exact phase boundaries for the dimerized Kitaev-Hubbard chain with complex-valued Hubbard interactions. Our results reveal that some of the Hermitian phases disappear as non-Hermiticty is enhanced. Based on our analytical findings, we explore the regime of the model that goes beyond the solvable regime, revealing regimes where non-Hermitian topological degeneracy remains. The combination of our exact and numerical phase diagrams provides an extensive description of a family of non-Hermitian interacting models. Our results provide a stepping stone toward characterizing non-Hermitian topology in realistic interacting quantum many-body systems.Comment: 4+4 pages, 5+9 figure

Magnetic Edge Anisotropy in Graphenelike Honeycomb Crystals

The independent predictions of edge ferromagnetism and the quantum spin Hall phase in graphene have inspired the quest of other two-dimensional honeycomb systems, such as silicene, germanene, stanene, iridates, and organometallic lattices, as well as artificial superlattices, all of them with electronic properties analogous to those of graphene, but a larger spin-orbit coupling. Here, we study the interplay of ferromagnetic order and spin-orbit interactions at the zigzag edges of these graphenelike systems. We find an in-plane magnetic anisotropy that opens a gap in the otherwise conducting edge channels that should result in large changes of electronic properties upon rotation of the magnetization.J. F. R. acknowledges financial support by MEC-Spain (FIS2010-21883-C02-01) and Generalitat Valenciana (ACOMP/2010/070), Prometeo. This work has been financially supported in part by FEDER funds. We acknowledge financial support by Marie-Curie-ITN 607904-SPINOGRAPH

Quantum anomalous Hall effect in graphene coupled to skyrmions

Skyrmions are topologically protected spin textures, characterized by a topological winding number N, that occur spontaneously in some magnetic materials. Recent experiments have demonstrated the capability to grow graphene on top Fe/Ir, a system that exhibits a two-dimensional skyrmion lattice. Here we show that a weak exchange coupling between the Dirac electrons in graphene and a two-dimensional skyrmion lattice withN = ±1 drives graphene into a quantum anomalous Hall phase, with a band gap in bulk, a Chern number C = 2N, and chiral edge states with perfect quantization of conductance G = 2N e2 h . Our findings imply that the topological properties of the skyrmion lattice can be imprinted in the Dirac electrons of graphene.J.F.R. acknowledges financial support by MEC-Spain (Grant No. FIS2013-47328-C2-2-P) and Generalitat Valenciana (Grant No. ACOMP/2010/070), Prometeo. This work has been financially supported in part by FEDER funds. We acknowledge financial support by Marie-Curie-ITN Grant No. 607904-SPINOGRAPH

Unconventional Yu–Shiba–Rusinov states in hydrogenated graphene

Conventional in-gap Yu–Shiba–Rusinov (YSR) states require two ingredients: magnetic atoms and a superconducting host that, in the normal phase, has a finite density of states at the Fermi energy. Here we show that hydrogenated graphene can host YSR states without any of those two ingredients. Atomic hydrogen chemisorbed in graphene is known to act as paramagnetic center with a weakly localized magnetic moment. Our calculations for hydrogenated graphene in proximity to a superconductor show that individual adatoms induce in-gap YSR states with an exotic spectrum whereas chains of adatoms result in a gapless YSR band. Our predictions can be tested using state of the art techniques, combining recent progress of atomic manipulation of atomic hydrogen on graphene together with the well tested proximity effect in graphene.JFR acknowledges financial supported by MEC-Spain (FIS2013-47328-C2-2-P) and Generalitat Valenciana (ACOMP/2010/070), Prometeo. This work has been financially supported in part by FEDER funds. We acknowledge financial support by Marie-Curie-ITN 607904-SPINOGRAPH

Correlation-induced valley topology in buckled graphene superlattices

Flat bands emerging in buckled monolayer graphene superlattices have been recently shown to realize correlated states analogous to those observed in twisted graphene multilayers. Here, we demonstrate the emergence of valley topology driven by competing electronic correlations in buckled graphene superlattices. We show, both by means of atomistic models and a low-energy description, that the existence of long-range electronic correlations leads to a competition between antiferromagnetic and charge density wave instabilities, that can be controlled by means of screening engineering. Interestingly, we find that the emergent charge density wave has a topologically non-trivial electronic structure, leading to a coexistent quantum valley Hall insulating state. In a similar fashion, the antiferromagnetic phase realizes a spin-polarized quantum valley-Hall insulating state. Our results put forward buckled graphene superlattices as a new platform to realize interaction-induced topological matter.Comment: 7 pages, 6 figure

Ferroelectric valley valves with graphene/MoTe2_2 van der Waals heterostructures

Ferroelectric van der Waals heterostructures provide a natural platform to design a variety of electrically controllable devices. In this work, we demonstrate that AB bilayer graphene encapsulated in MoTe$_2$ acts as a valley valve that displays a switchable built-in topological gap, leading to ferroelectrically driven topological channels. Using a combination of ab initio calculations and low energy models, we show that the ferroelectric order of MoTe$_2$ allows the control of the gap opening in bilayer graphene and leads to topological channels between different ferroelectric domains. Moreover, we analyze the effect that the moir\'e modulation between MoTe$_2$ and graphene layers has in the topological modes, demonstrating that the edge states are robust against moir\'e modulations of the ferroelectrically-induced electric potential. Our results put forward ferroelectric/graphene heterostructures as versatile platforms to engineer switchable built-in topological channels without requiring an external electric bias.Comment: 8 pages, 4 figure

Electrically controllable magnetism in twisted bilayer graphene

Twisted graphene bilayers develop highly localised states around AA-stacked regions for small twist angles. We show that interaction effects may induce either an antiferromagnetic (AF) and a ferromagnetic (F) polarization of said regions, depending on the electrical bias between layers. Remarkably, F-polarised AA regions under bias develop spiral magnetic ordering, with a relative $120^\circ$ misalignment between neighbouring regions due to a frustrated antiferromagnetic exchange. This remarkable spiral magnetism emerges naturally without the need of spin-orbit coupling, and competes with the more conventional lattice-antiferromagnetic instability, which interestingly develops at smaller bias under weaker interactions than in monolayer graphene, due to Fermi velocity suppression. This rich and electrically controllable magnetism could turn twisted bilayer graphene into an ideal system to study frustrated magnetism in two dimensions, with interesting potential also for a range of applications.Comment: 7 pages, 3 figures. Minor correction

Hamiltonian learning with real-space impurity tomography in topological moire superconductors

Extracting Hamiltonian parameters from available experimental data is a challenge in quantum materials. In particular, real-space spectroscopy methods such as scanning tunneling spectroscopy allow probing electronic states with atomic resolution, yet even in those instances extracting effective Hamiltonian is an open challenge. Here we show that impurity states in modulated systems provide a promising approach to extracting non-trivial Hamiltonian parameters of a quantum material. We show that by combining the real-space spectroscopy of different impurity locations in a moire topological superconductor, modulations of exchange and superconducting parameters can be inferred via machine learning. We demonstrate our strategy with a physically-inspired harmonic expansion combined with a fully-connected neural network that we benchmark against a conventional convolutional architecture. We show that while both approaches allow extracting exchange modulations, only the former approach allows inferring the features of the superconducting order. Our results demonstrate the potential of machine learning methods to extract Hamiltonian parameters by real-space impurity spectroscopy as local probes of a topological state.Comment: 11 pages, 8 figure