Public Abstract

DE-SC0005042: Quantitative Studies of the Fractional Quantum Hall Effect

Award Status: Active

Institution: The Pennsylvania State University, University Park, PA
UEI: NPM2J7MSCF61
DUNS: 003403953

Most Recent Award Date: 08/10/2023
Number of Support Periods: 14
PM: Graf, Matthias

Current Budget Period: 08/15/2023 - 08/14/2024
Current Project Period: 08/15/2022 - 08/14/2025
PI: Jain, Jainendra

Supplement Budget Period: N/A

Public Abstract

Quantitative Studies of the Fractional Quantum Hall Effect Jainendra Jain, The Pennsylvania State University (Principal Investigator) The study of two-dimensional electrons in semiconductor quantum wells, single and bilayer graphene, twisted bilayer graphene, and transition-metal dichalcogenides has inspired exciting discoveries in condensed matter physics during the last four decades, including the celebrated phenomenon of the fractional quantum Hall effect (FQHE). While the essential phenomenology of the FQHE is fairly well understood, many interesting and important questions remain, and experiments continue to reveal new puzzles. Furthermore, the coupling of FQHE to superconductivity has been predicted to produce new structures with exotic particles, which have so far evaded confirmation. A major thrust in this proposal will be to study interacting topological states supporting exotic particles, such as Majoranas or skyrmions. Such states can arise naturally as a result of pairing in the FQHE, which will be investigated within a Bardeen-Cooper-Schrieffer approach for composite fermions in several different contexts. These include exotic f-wave pairing of composite fermions in wide semiconductor quantum wells and in higher Landau levels of monolayer graphene; interlayer s-wave pairing in double layer graphene at total filling factor equal to one; and certain other filling factors in double layer graphene where experiments have demonstrated evidence of pairing. Alternatively, such states can be engineered either by proximity-coupling a quantum Hall state to a superconductor or by exposing a superconductor to a magnetic field. Self-consistent mean-field phase diagrams will be calculated for p-wave superconductivity and for s-wave superconductivity with spin orbit coupling exposed to a magnetic fields, to determine phases with non-trivial topology. The interplay between the FQHE and superconductivity will also be investigated. Many of these states can potentially provide realizations of Majorana zero modes in the bulk, Majorana edge states, and even more complex particles. These studies are expected to suggest new and fruitful experimental directions. Certain other topics will also be addressed, such as a quantitative understanding of the FQHE gaps and identification of experimental signatures of the topological nature of the lowest-Landau-level crystal. These research directions are inspired by fundamental physics as well as by exciting ideas for future technology. A common theme is the focus on a quantitative understanding, which will be necessary for a detailed design and analysis of experiments. The students supported by this grant will be exposed to advanced computational and analytical tools, such as the quantum Monte Carlo method and quantum field theory, and thus build essential skills that should serve them well in their future endeavors.

Quantitative Studies of the Fractional Quantum Hall Effect

Jainendra Jain, The Pennsylvania State University (Principal Investigator)

The study of two-dimensional electrons in semiconductor quantum wells, single and bilayer graphene, twisted bilayer graphene, and transition-metal dichalcogenides has inspired exciting discoveries in condensed matter physics during the last four decades, including the celebrated phenomenon of the fractional quantum Hall effect (FQHE). While the essential phenomenology of the FQHE is fairly well understood, many interesting and important questions remain, and experiments continue to reveal new puzzles. Furthermore, the coupling of FQHE to superconductivity has been predicted to produce new structures with exotic particles, which have so far evaded confirmation.

A major thrust in this proposal will be to study interacting topological states supporting exotic particles, such as Majoranas or skyrmions. Such states can arise naturally as a result of pairing in the FQHE, which will be investigated within a Bardeen-Cooper-Schrieffer approach for composite fermions in several different contexts. These include exotic f-wave pairing of composite fermions in wide semiconductor quantum wells and in higher Landau levels of monolayer graphene; interlayer s-wave pairing in double layer graphene at total filling factor equal to one; and certain other filling factors in double layer graphene where experiments have demonstrated evidence of pairing. Alternatively, such states can be engineered either by proximity-coupling a quantum Hall state to a superconductor or by exposing a superconductor to a magnetic field. Self-consistent mean-field phase diagrams will be calculated for p-wave superconductivity and for s-wave superconductivity with spin orbit coupling exposed to a magnetic fields, to determine phases with non-trivial topology. The interplay between the FQHE and superconductivity will also be investigated. Many of these states can potentially provide realizations of Majorana zero modes in the bulk, Majorana edge states, and even more complex particles. These studies are expected to suggest new and fruitful experimental directions. Certain other topics will also be addressed, such as a quantitative understanding of the FQHE gaps and identification of experimental signatures of the topological nature of the lowest-Landau-level crystal.

These research directions are inspired by fundamental physics as well as by exciting ideas for future technology. A common theme is the focus on a quantitative understanding, which will be necessary for a detailed design and analysis of experiments. The students supported by this grant will be exposed to advanced computational and analytical tools, such as the quantum Monte Carlo method and quantum field theory, and thus build essential skills that should serve them well in their future endeavors.