Higher-Order Topological Dirac Superconductivity in C6-Symmetric Dirac Semimetals: An Analysis Using Magnetic Topological Quantum Chemistry

Core Concepts

This paper investigates the emergence of higher-order topological Dirac superconducting (HOTDSC) states in nodal Dirac semimetals with C6 symmetry, revealing that these states, characterized by Majorana corner modes, arise from the interplay of higher-order hinge Fermi-arc states in the normal state and the system's inherent particle-hole symmetry.

Abstract

Bibliographic Information:

Feng, G.-H. (2024). Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals. arXiv:2408.09541v3 [cond-mat.supr-con].

Research Objective:

This study aims to investigate the topological properties of nodal Dirac superconducting states arising from half-filled Dirac semimetals (DSMs) with C6 symmetry, specifically focusing on the emergence of higher-order topological Dirac superconducting (HOTDSC) states and their relationship to the underlying Dirac points and higher-order hinge Fermi-arc (HOFA) states present in the normal state.

Methodology:

The authors employ the theoretical framework of magnetic topological quantum chemistry (MTQC) to analyze the band structure and topological invariants of the system. They utilize compatibility relations to determine the occurrence of Dirac points and calculate symmetry indicators, filling anomalies, and relative topologies to characterize the topological properties of both the normal and superconducting states. The study focuses on systems respecting the non-magnetic (Type-II) Shubnikov space group (SSG) P6/mmm1′.

Key Findings:

• The study reveals that the BdG Dirac points in these systems can lead to HOTDSC states instead of the expected higher-order Majorana-arc (HOMA) states.
• HOTDSC states are shown to be a consequence of the crossing between HOFAs in the normal state and the BdG shadow states, indicating a bulk-hinge correspondence in these superconductors.
• The authors demonstrate that HOTDSC states can be identified by the relative topologies of BdG Dirac points, which are classified into symmetry-protected and accidental types.
• The study finds that 3D nodal Dirac superconductors respecting Type-II SSG P6/mmm1′ cannot host HOMA states.
• HOTDSC states are found to emerge at the time-reversal invariant planes only if the corresponding normal state exhibits HOFA states and the pairing channels are B1u or B2u.
• The analysis reveals that HOFA states in normal states are obstructed atomic limit states, while HOTDSC states are fragile topological states.

Main Conclusions:

The research demonstrates that the interplay of Dirac points, HOFA states, and specific pairing symmetries leads to the emergence of HOTDSC states in C6-symmetric Dirac semimetals. The study highlights the significance of relative topology in characterizing these states and provides a theoretical framework for understanding the intricate relationship between normal state topology and the emergence of higher-order topological superconductivity.

Significance:

This work contributes significantly to the field of topological condensed matter physics by providing a deeper understanding of the conditions under which HOTDSC states can arise in realistic materials. The findings have implications for the development of novel topological quantum materials and potential applications in fault-tolerant quantum computing.

Limitations and Future Research:

The study focuses on a specific symmetry class (Type-II SSG P6/mmm1′) and pairing channels (B1u/B2u). Exploring other symmetry classes and pairing mechanisms could reveal additional HOTDSC states and enrich the understanding of topological superconductivity. Further investigations into the experimental realization and manipulation of HOTDSC states in C6-symmetric Dirac semimetals are crucial for advancing their technological potential.

Stats

The symmetry group for the 2D planes with fixed kz ̸= 0, π in DSMs respecting the symmetries of Type-II double SSG P6/mmm1′ is Type-III MLG p6/m′mm.
The 2D planes with kz = 0, π respect the symmetries of Type-II SLG p6/mmm1′.
The SI group of G = p6/m′mm is XBS = Z1.
The SI group of G = p6/mmm1′ is XBS = Z6.
The refined symmetry group for B1u/B2u superconducting pairing representations is Z4.

Quotes

Key Insights Distilled From

Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals

by Guan-Hao Fen... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2408.09541.pdf

Deeper Inquiries

How could the findings of this research be applied to the development of novel materials for topological quantum computing?

This research significantly advances the search for materials suitable for topological quantum computing by providing a deeper understanding of Higher-Order Topological Dirac Superconducting (HOTDSC) states. Here's how:

Identifying promising materials: The study establishes a clear connection between the presence of HOTDSC states and specific material properties. This includes the crystallographic symmetries (specifically, systems respecting Type-II Shubnikov space group P6/mmm1'), the existence of Dirac points in their electronic structure, and the nature of superconducting pairing (B1u/B2u pairing channels). This knowledge acts as a guide for experimentalists to focus on materials exhibiting these characteristics, potentially leading to the discovery of new HOTDSC candidates.
Predicting HOTDSC states: The concept of relative topology, as applied to both normal and BdG Dirac points, offers a powerful tool for predicting the emergence of HOTDSC states. By analyzing the change in topological invariants, such as filling anomaly (η) and symmetry indicators, across these Dirac points, researchers can predict the presence of Majorana zero modes (MZMs) localized at the corners of the material in specific 2D planes.
Engineering MZMs: The study highlights the crucial role of symmetry-protected BdG Dirac points in giving rise to HOTDSC states. This understanding paves the way for potential engineering of these states in materials. By manipulating the electronic structure and pairing symmetries, for instance, through strain engineering or external fields, it might be possible to induce or control the emergence of MZMs.
The ability to reliably predict and potentially engineer MZMs in HOTDSC materials is a crucial step towards their utilization in topological quantum computing. These exotic quasiparticles are promising candidates for building topologically protected qubits, which are inherently robust against environmental noise and decoherence, a major obstacle in conventional qubit designs.

Could there be alternative mechanisms, beyond the specific symmetries and pairing channels discussed, that could also give rise to HOTDSC states in other materials?

While the research focuses on specific symmetries and pairing channels, it's highly plausible that alternative mechanisms could lead to HOTDSC states in other materials. Here are some possibilities:

Different symmetry classes: The study concentrates on systems with Type-II SSG P6/mmm1′ symmetry. Exploring other symmetry classes, particularly those allowing for nonsymmorphic symmetries, could unveil new avenues for HOTDSC states. Nonsymmorphic symmetries, which involve fractional lattice translations, are known to enrich topological classifications and could stabilize exotic states.
Alternative pairing mechanisms: The research primarily considers conventional Bardeen-Cooper-Schrieffer (BCS) type superconductivity. However, unconventional pairing mechanisms, such as those mediated by spin fluctuations or other bosonic modes, could lead to different pairing symmetries beyond the discussed B1u/B2u channels, potentially supporting HOTDSC states.
Interplay with other ordered states: Combining superconductivity with other ordered states, like magnetism or charge density waves, could create complex electronic structures that host HOTDSC states. The interplay of multiple order parameters can lead to emergent topological behavior not present in the individual phases.
Artificial lattices and heterostructures: Engineering artificial lattices, such as optical lattices for cold atoms or photonic crystals, provides a platform to design specific symmetries and band structures. This approach could be employed to realize HOTDSC states in systems with tailored properties. Similarly, heterostructures combining different materials with complementary properties could also provide a route to engineer these states.
The search for HOTDSC states is still in its early stages. Exploring these alternative mechanisms will be crucial in broadening the range of materials and platforms for realizing topological superconductivity and its associated applications in quantum computing.

What are the potential connections between the concept of relative topology in condensed matter physics and the emergence of complexity in other scientific disciplines?

The concept of relative topology, while rooted in condensed matter physics, resonates with the emergence of complexity in other scientific disciplines. Here are some potential connections:

Network theory: In complex networks, such as social networks or biological systems, relative topology could be used to understand how local changes in connectivity or node properties affect the overall network structure and function. For example, analyzing the change in topological invariants like centrality or modularity across different network regions could reveal critical nodes or pathways that influence information flow or system robustness.
Brain research: The brain exhibits a hierarchical organization with interconnected regions exhibiting distinct functionalities. Relative topology could provide insights into how changes in local neural activity or connectivity patterns within specific brain regions influence the global brain dynamics and cognitive processes.
Evolutionary biology: Evolutionary processes involve changes in the genetic makeup of populations over time. Relative topology could be applied to analyze how mutations or genetic variations, viewed as local changes in the "topology" of the genome, lead to the emergence of new traits and drive the diversification of species.
Climate science: Climate models often involve complex interactions between various components of the Earth system. Relative topology could be employed to study how local changes in factors like temperature, precipitation, or ice cover in specific geographic regions can propagate through the system, leading to global climate shifts and extreme weather events.
The common thread across these disciplines is the focus on understanding how local changes in a complex system can have far-reaching consequences on its global behavior. Relative topology, with its emphasis on comparing topological properties across different regions or states, offers a powerful framework for quantifying and potentially predicting such emergent complexity. By drawing analogies and transferring knowledge from condensed matter physics, researchers in these diverse fields can gain new perspectives and tools to tackle complex systems.