March 20, 2024 | Manato Fujimoto, Daniel E. Parker, Junkai Dong, Eslam Khalaf, Ashvin Vishwanath, Patrick Ledwith
The paper introduces the concept of "first vortexability" to describe when a Chern band exhibits the essential characteristics of the first Landau level (1LL). This is achieved by defining a precise criterion for a band to be "first vortexable," which involves the existence of a partner band with zeroth vortexable structure, such that the two bands together form a vortexable system. The authors argue that this definition captures the quantum geometry of the 1LL more effectively than traditional single-band definitions based on the Fubini-Study metric.
The paper demonstrates that periodically strained Bernal graphene realizes a 1LL structure even in zero magnetic field, providing a concrete example of first vortexability. They also introduce a "maximality index" to quantify how closely a band approaches the ideal 1LL structure, with values close to 1 indicating maximal first vortexability.
The authors further explore the many-body physics of partially filled first vortexable bands, particularly at half filling where non-Abelian states are expected. They show that interactions can spectrally isolate the almost first-vortexable band, leading to the formation of isolated bands with non-Abelian topological orders.
Overall, the work advances the understanding of quantum geometry in Chern bands and opens up possibilities for realizing non-Abelian states in zero magnetic fields, which could have significant implications for fault-tolerant quantum computation.The paper introduces the concept of "first vortexability" to describe when a Chern band exhibits the essential characteristics of the first Landau level (1LL). This is achieved by defining a precise criterion for a band to be "first vortexable," which involves the existence of a partner band with zeroth vortexable structure, such that the two bands together form a vortexable system. The authors argue that this definition captures the quantum geometry of the 1LL more effectively than traditional single-band definitions based on the Fubini-Study metric.
The paper demonstrates that periodically strained Bernal graphene realizes a 1LL structure even in zero magnetic field, providing a concrete example of first vortexability. They also introduce a "maximality index" to quantify how closely a band approaches the ideal 1LL structure, with values close to 1 indicating maximal first vortexability.
The authors further explore the many-body physics of partially filled first vortexable bands, particularly at half filling where non-Abelian states are expected. They show that interactions can spectrally isolate the almost first-vortexable band, leading to the formation of isolated bands with non-Abelian topological orders.
Overall, the work advances the understanding of quantum geometry in Chern bands and opens up possibilities for realizing non-Abelian states in zero magnetic fields, which could have significant implications for fault-tolerant quantum computation.