## Project Details

### Description

Emergent phases in Kitaev spin-orbital magnets Emergent phases in Kitaev spin-orbital magnets Overview. Quantum spin liquids (QSLs) are remarked by the absence of magnetic order down to zero temperature. QSLs exhibit exotic properties such as long-range entanglement and fractionalized excitations due to their topological properties. Kitaev model on honeycomb lattice is of particular significance as it is the first exactly solvable model with a QSL ground state. Even though there has been an astounding progress in identifying materials with strong Kitaev interactions such as a number of iridates and a-RuCl3, direct application of Kitaev model to real materials is limited as the Kitaev QSL state is quite fragile to additional interactions present in real materials. The fragility of QSL is apparent from the destruction of the integrability of the Kitaev model upon most additional interactions. One way to remedy this challenge relies on extending the Kitaev model to its spin-orbital generalizations, commonly called Kitaev spin-orbital models (KSOMs). KSOMs allow for including a variety of perturbations that preserve the integrability of the model and keep the gauge structure intact. In addition to a-RuCl3, Kitaev interactions can also be strong in other van der Waals (vdW) materials such as CrI3. In recent years, it was realized that vdW materials can be arranged in different stacking patterns and be twisted to form moir superlattices. These advancements opened an unexplored venue of tunable quantum platforms for realization of emergent phases on every front including graphene, 2D magnets and superconductors. Therefore, the overarching goal of this proposal is to explore single- and bi-layer KSOMs as new platforms for realization of QSLs that are stable to additional perturbations. To this end, I devise two tasks. In task I, I propose to study vison crystals in KSOMs periodic arrangement of flux excitations that are stabilized by additional interactions. Vison crystals are unusual phases of matter where the topological order coexists with a Landau-type symmetry breaking. I will use variational analysis and Monte Carlo simulations to estimate the ground state phase diagram and transition temperature of the vison crystals. I will also calculate dynamical correlation functions to determine experimental signatures of KSOMs. In task II, I propose to study bilayer KSOMs and their moir superlattices. I will perform mean-field theory and perturbative analysis to estimate the phase diagram as a function of interlayer exchange and small angle twisting. I will also construct new bilayer KSOMs that can be solved exactly analytically. The proposed work is closely-tied with upcoming experiments and I am collaborating with experimentalists on the inelastic neutron scattering signatures of Kitaev spin-orbital magnets. Intellectual Merit. There are many up-to-date open questions in the field of spin-orbital generalizations of Kitaev magnets: In task I, what kind of vison crystals can be stabilized in KSOMs as a function of tuning parameters? What are the transition temperatures of the phases? Among the gapped states, what are the topological classifications? What are the key signatures of vison crystals in inelastic neutron scattering and resonant inelastic x-ray scattering experiments? In task II, what is the phase diagram of bilayer KSOMs for different stacking patterns? What are the effects of small angle twisting? Is it possible to construct exactly solvable KSOMs for bilayer systems and what are the properties of these models? Answers to these questions will provide key insights to upcoming experiments on QSLs while advancing our understanding of spin-orbital generalizations of Kitaev model. Broader Impacts. Quantum Leap is one of the NSFs 10 big ideas to guide the research and education in the U.S. and it aims to prepare future scientists in quantum sciences to discover the next quantum revolution. However, quantum physics is only introduced as an upper division course and generally perceived as complicated by the students. This hinders the development of a workforce in quantum sciences. Therefore, the main goal of my educational plan is to increase the quantum literacy - understanding the fundamentals of quantum physics - at high school level. To achieve this goal, I will participate in the Science and Engineering Experience and Clubes de Ciencia Arizona high school outreach programs. These programs are well-established and are supported by ASU.

Status | Active |
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Effective start/end date | 2/15/23 → 1/31/26 |

### Funding

- National Science Foundation (NSF): $292,283.00

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