Fractional Quantum Hall-Superconductor Heterostructures Exhibit Non-Abelian Zero Modes at Fixed Filling

The search for robust quantum states capable of supporting topological quantum computation receives a significant boost from new research into the behaviour of electrons at the interface between fractional quantum Hall systems and superconductors. Gustavo M. Yoshitome and Pedro R. S. Gomes, both from Universidade Estadual de Londrina, investigate the emergence of unusual quantum states, known as non-Abelian zero modes, arising from imperfections in these carefully constructed materials. Their work demonstrates how these zero modes, which possess unique exchange statistics, can be created and controlled within a heterostructure, effectively inducing new types of anyonic symmetries. This achievement represents a crucial step towards realising more stable and versatile quantum bits, potentially unlocking powerful new approaches to quantum information processing.

Anyons and Robust Quantum Computation

Scientists are exploring the creation and detection of unusual quantum states, called non-Abelian anyons, within specially designed materials. These anyons hold promise for building more reliable quantum computers because their quantum information is naturally protected from environmental disturbances. This research focuses on engineering these states by combining a fractional quantum Hall state with a superconductor, and then identifying their presence through measurable electrical effects, specifically the Josephson current. This work investigates the possibility of realizing non-Abelian anyons at the interface between a fractional quantum Hall (FQH) state and a superconductor.

FQH states exhibit exotic excitations with fractional charge and unusual particle statistics. Bringing this state close to a superconductor can induce superconductivity, potentially leading to the formation of Majorana zero modes, a type of non-Abelian anyon. A key challenge is distinguishing these modes from other possible states and demonstrating their unique quantum properties. The researchers propose a method to engineer the interface and eliminate unwanted effects that could obscure the desired results. They then predict how the Josephson current will behave if these Majorana zero modes are present, providing a measurable signature for their detection. This research builds on the idea that these hybrid structures can host topological quantum computation, where information is encoded in the way anyons interact, making it inherently resistant to errors. The ultimate goal is to create a robust platform for quantum information processing.

Fractional Quantum Hall and Superconducting Heterostructure Fabrication

Scientists engineered a novel material combining a fractional quantum Hall (FQH) system with a conventional superconductor, creating a platform to investigate non-Abelian anyonic excitations. Building on previous work, this setup induces interactions between the FQH phase and the superconductor, modifying the anyonic spectrum and introducing new symmetries. The team specifically focused on a system with a particular filling fraction, which exhibits three distinct symmetries related to charge and particle statistics. To create defects hosting non-Abelian zero modes, the team arranged two identical FQH phases side by side, inducing alternating superconducting and insulating potentials at the interface.

This created domain walls that act as locations for the defects, effectively implementing charge conjugation as electrons experience a change in charge when crossing the superconducting regions. This configuration allows for the trapping of non-Abelian zero modes associated with charge conjugation, particle statistics, and a composite symmetry, all at a fixed filling fraction. The study then developed models to isolate the contributions of anyonic symmetries from other effects, a critical step in understanding the origin of observed zero modes. These models enabled the team to predict physical signatures of the zero modes, specifically in the periodicity of the Josephson tunneling current, offering a potential pathway for experimental detection. This approach enables the investigation of non-Abelian zero modes in a controllable physical setup, addressing a significant challenge in the field and paving the way for future explorations of exotic excitations.

Fractional Quantum Hall Anyons and Zero Modes

This work details the emergence of non-Abelian zero modes within defects in an Abelian topological system, created by combining a fractional quantum Hall (FQH) phase with a superconductor. Researchers constructed a material inducing a topological phase characterized by new anyonic symmetries and supporting distinct types of zero modes at a specific filling fraction. These defects, modeled at the interface between two identical materials, generate modes that can be influenced by interactions, realizing the anyonic symmetries. The study focuses on a system with a particular filling fraction in proximity with a conventional superconductor, demonstrating that the superconductor introduces additional fractionalization of quantum Hall anyons, making Cooper pairs the fundamental excitation.

This reconfiguration introduces several anyonic symmetries, enabling the realization of different non-Abelian zero modes. Scientists carefully considered the contribution of boundary effects to ground state degeneracy, emphasizing that the entire Laughlin phase, including both bulk and edge, is in proximity with the superconducting potential. For a specific filling fraction, the research reveals three anyonic symmetries: charge conjugation, particle statistics, and a composite symmetry. The physical setup supports defects trapping non-Abelian zero modes for charge conjugation, particle statistics, and the composite symmetry.

Models were constructed to isolate intrinsic boundary contributions, allowing researchers to derive physical signatures of the zero modes in the periodicity of Josephson tunneling current. The team describes the topological phase using a mathematical formulation, revealing a bosonic sector with a specific level and two fermionic sectors. The analysis demonstrates that the anyonic symmetries act on the fields, preserving the fusion algebra and braiding statistics, and are described by symmetry matrices. Researchers found that the fermionic sectors do not carry nontrivial anyonic symmetries, residing exclusively in the bosonic sector. The work establishes a framework for understanding and characterizing these zero modes, paving the way for potential applications in topological quantum computation and novel electronic devices.

Non-Abelian Modes from FQH Superconductors

This research demonstrates the emergence of non-Abelian zero modes arising from defects within an Abelian topological system, specifically a fractional quantum Hall (FQH) state coupled with a superconductor. By considering a material combining the FQH effect at a specific filling fraction with a conventional superconductor, the team engineered a system exhibiting new anyonic symmetries, and consequently, distinct types of zero modes. These zero modes appear as a result of defects created at the interface between two such materials, effectively implementing charge conjugation and generating localized, non-Abelian excitations. The study characterizes the parafermions associated with these anyonic symmetries and details how their presence influences the periodicity of Josephson tunneling current, offering a potential pathway for experimental detection. The team successfully modeled the system and predicted specific signatures of the zero modes, enabling future experimental verification.