RCQM/FCMP: Yu-Ping Lin: Rich electronic phase diagram in kagome flat band

The speaker introduces Dr. Lin from UC Berkeley, who is giving a talk on his postdoctoral research. Dr. Lin obtained his PhD from the University of Colorado and is now working at UC Berkeley. The talk focuses on the discovery of unique electronic phases in kagome lattice materials, particularly focusing on the repulsive electrons on the flatband. The speaker also acknowledges the support from the Birley group and the CMT group at the University of Bristol, where the work was conducted under the supervision of advisor Joe Mo.

This paragraph delves into the behavior of interacting electrons in a crystal lattice. It explains how electrons form bands due to dispersion energy and how interactions can lead to symmetry breaking and the emergence of different ground states. The speaker discusses the concept of an order parameter and how it can be used to characterize symmetry breaking in systems such as ferromagnetism, charge density waves, and superconductivity. The strength of the interaction phase is estimated by the number of electronic states within the interaction window, which is defined by the interaction strength and the band width.

The speaker explores the concept of flatbands and their significance in frustrated lattice systems. Flatbands occur when the bandwidth vanishes, leading to a very strong interaction electron phase. The interest in flatbands has grown due to their potential to host strongly correlated electron phases and their high tunability through doping or magnetic fields. The speaker highlights the kagome lattice as a prime example of a frustrated system that can host flatbands due to destructive interference in electron hopping.

This section focuses on kagome materials and their properties, particularly the presence of flatbands close to the Fermi level. The speaker discusses the binary materials TX, where T could be iron, molybdenum, or cobalt, and X could be germanium or silicon. These materials exhibit intralayer ferromagnetism and charge density waves. The speaker also mentions the tunability of the Fermi level in these materials through elemental substitution, which can lead to the observation of various electron phases in experiments.

The speaker introduces the mean-field theory (MFT) as a method to analyze the behavior of repulsive electrons on the flatband. The Hartree-Fock approximation is used to map the interacting electron problem onto an effective single-particle problem. The speaker discusses the limitations of previous MFT analyses and presents a more comprehensive approach that does not impose constraints on the wave function, allowing for a more accurate determination of the ground state and symmetry breaking orders.

In this paragraph, the speaker presents the results of their comprehensive Hartree-Fock analysis, which reveals a variety of new magnetic orders across the flatband. These include stripe and non-collinear spin orders that have not been previously reported in the literature. The speaker also discusses the importance of the 120-degree spin order in the face diagram and how their analysis differs from previous studies.

The speaker discusses the phase diagram resulting from their analysis and attempts to relate their theoretical findings to practical materials like iron and iron germanium. They propose that by reducing the Coulomb repulsion in these materials, it might be possible to observe non-collinear and stripe orders. The speaker also suggests that current materials may be in a strongly repulsive regime, which could be why certain orders are not observed experimentally.

In the final part of the talk, the speaker speculates on what could be observed beyond the mean-field level, such as quantum spin liquids, fractional excitations, and unconventional superconductivity. They mention ongoing work using techniques like the density matrix renormalization group (DMRG) to explore these possibilities and express hope for future discoveries.

The final paragraph consists of a Q&A session where the audience asks questions about the ordering vectors of different phases, the topological aspects of the bands, and the experimental relevance of the findings. The speaker addresses these questions, providing insights into the stability of the states, the potential impact of considering band topology, and the expected changes in the band structure for different materials.