Topological insulators (TIs) have been found in strained binary HgTe and ternary I-III-VI 2 chalcopyrite compounds such as CuTlSe 2 which have inverted band structures. However, the nontrivial band gaps of these existing binary and ternary TIs are limited to small values, usually around 10 meV or less. In this work, we reveal that a large non-trivial band gap requires the material having a large negative crystal field splitting ∆ CF at top of the valence band and a moderately large negative s − p band gap E s−p g . These parameters can be better tuned through chemical ordering in multinary compounds. Based on this understanding, we show that a series of quaternary I 2 -II-IV-
sensors and nonvolatile memories that require a high data density with a long retention time. [7] In order to engineer the potential of these 2D magnets, it is crucial to investigate their intrinsic spin-phonon coupling (SPC) systematically, which is a key mechanism behind magnetic fluctuations, magnon dissipation, and establishing long-range ferromagnetic. [8] Lattice dynamics and electronic properties of 2D materials have been widely quantified by Raman spectroscopy. [9] Similar methods can be used to observe SPC in 2D magnets [10] such as FeF 2 , FePS 3 , and Cr 2 Ge 2 Te 6 . However, many previous experimental studies have focused on the effects of magnetism on phonon frequencies. Additionally, some theoretical models approximate the interaction between magnons and phonons with localized spin, which has successfully predicted magnon softening [11] and phonon frequency shifts at low temperature. [12] In contrast, there have been a limited number of theoretical studies that examine SPC in 2D magnets, [8h,13] while concentrating on spin-induced phonon shifts. Therefore, a comprehensive study of SPC in 2D magnets is needed to understand the effect of spin and lattice degrees of freedom on the directions and amplitudes of phonon shifts.We investigated the crystal structure, magnetic exchange interactions, critical temperatures, and phonon properties of Novel 2D magnets exhibit intrinsic electrically tunable magnetism down to the monolayer limit, which has significant value for nonvolatile memory and emerging computing device applications. In these compounds, spin-phonon coupling (SPC) typically plays a crucial role in magnetic fluctuations, magnon dissipation, and ultimately establishing long-range ferromagnetic order. However, a systematic understanding of SPC in 2D magnets that combines theory and experiment is still lacking. In this work, monolayer chromium tribromide is studied to investigate SPC in 2D magnets via Raman spectroscopy and first principle calculations. The experimental Curie temperature and phonon shifts are found to be in good agreement with the numerical simulations. Specifically, it is demonstrated how magnetic exchange interactions affect phonon vibrations, which helps establish design fundamentals for 2D magnetic materials and other related devices.
It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron-electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling (SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state.
We introduce an efficient training framework for constructing machine learning-based emulators and demonstrate its capability by training an artificial neural network to predict the time evolution of quantum wave packets propagating through a potential landscape. This approach is based on the idea of knowledge distillation and uses elements of curriculum learning. It works by constructing a set of simple, but rich-in-physics training examples (a curriculum). These examples are used by the emulator to learn the general rules describing the time evolution of a quantum system (knowledge distillation). We show that this emulator is capable of learning the rules of quantum dynamics from a curriculum of simple training examples (wave packet interacting with a single rectangular potential barrier), and subsequently generalizes this knowledge to solve more challenging cases (propagation through an arbitrarily complex potential landscape). Furthermore, we demonstrate, that using this framework we can not only make high-fidelity predictions, but we can also learn new facts about the underlying physical system, detect symmetries, and measure relative importance of the contributing physical processes.
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