insight - Condensed Matter Physics - # Topological Chiral Superconductivity

Topological Chiral Superconductivity Driven by Strong Repulsive Interactions in Fermi-Liquid Systems

Q: How do the properties of these topological chiral superconductors, such as the quantized ratios of electron densities and the charge-4 or higher condensation, affect their potential applications and experimental signatures?

The properties of topological chiral superconductors, particularly the quantized ratios of electron densities and the occurrence of charge-4 or higher condensation, have significant implications for their potential applications and experimental signatures. The quantized ratios of electron densities indicate that these superconductors can support a variety of distinct phases characterized by specific electron density configurations. This feature can be exploited in the development of novel electronic devices, such as topological qubits for quantum computing, where the robustness of topological states against local perturbations is crucial. Moreover, the presence of charge-4 or higher condensation suggests that these superconductors may exhibit exotic phenomena, such as fractional statistics and anyon excitations, which are of great interest in the field of topological quantum computing. The experimental signatures of these superconductors could include the detection of fractional charge excitations, non-abelian statistics in braiding experiments, and the observation of chiral edge modes that are robust against disorder. Additionally, the breaking of time-reversal and reflection symmetries can lead to unique magnetic properties, which can be probed through techniques such as scanning tunneling microscopy (STM) and transport measurements.

Q: What other types of strongly correlated electron systems, beyond graphene, could host similar topological chiral superconductivity driven by repulsive interactions?

Beyond graphene, several other strongly correlated electron systems could potentially host similar topological chiral superconductivity driven by repulsive interactions. One promising class of materials is transition metal oxides, particularly those exhibiting high-temperature superconductivity, such as cuprates. These materials often display strong electron correlations and can be tuned to explore different phases, including those that may support topological chiral superconductivity. Another candidate is the family of two-dimensional materials, such as transition metal dichalcogenides (TMDs), which can exhibit strong spin-orbit coupling and electron-electron interactions. The ability to manipulate their electronic properties through external fields or strain could facilitate the realization of topological chiral superconductivity. Furthermore, heterostructures composed of different materials, such as topological insulators combined with superconductors, may also provide a platform for exploring these exotic states. The interplay between the topological surface states and the superconducting order parameter could lead to novel chiral superconducting phases.

Q: How can the theoretical framework developed in this work be extended to study the interplay between topological chiral superconductivity, fractional quantum Hall states, and Wigner crystallization in more complex heterostructures or moiré materials?

The theoretical framework developed in this work can be extended to study the interplay between topological chiral superconductivity, fractional quantum Hall (FQH) states, and Wigner crystallization by incorporating additional degrees of freedom and interactions present in more complex heterostructures or moiré materials. One approach is to consider the effective field theories that describe the low-energy excitations of these systems, allowing for the inclusion of both topological and fractional excitations. In moiré materials, the emergence of flat bands due to the periodic potential can enhance electron correlations, making it possible to explore the coexistence of topological chiral superconductivity and FQH states. The framework can be adapted to account for the specific band structures and interaction strengths in these materials, leading to a richer phase diagram that includes various topological phases. Additionally, the study of Wigner crystallization can be integrated by examining the competition between the repulsive interactions that favor crystallization and the attractive interactions that may lead to superconductivity. This can be achieved through numerical simulations and analytical calculations that explore the stability of different phases as a function of electron density and interaction strength. By systematically varying parameters such as the strength of the periodic potential, the electron density, and the interaction types, researchers can gain insights into the conditions under which these exotic states emerge and their potential experimental signatures, paving the way for future discoveries in the realm of strongly correlated electron systems.

Core Concepts

Strong repulsive interactions can drive the formation of topological chiral superconductivity, which breaks time-reversal and reflection symmetries in the orbital motion of electrons, without relying on pairing instability in Fermi-liquids.

Abstract

The content explores a mechanism to produce superconductivity through strong purely repulsive interactions, without using pairing instability in Fermi-liquids. The resulting superconductors, referred to as topological chiral superconductors, break both time-reversal and reflection symmetries in the orbital motion of electrons, and exhibit non-trivial topological order.

The key insights are:

Topological chiral superconductivity is more likely to emerge near or between fully spin-valley polarized metallic phases (quarter Fermi-liquids) and Wigner crystal phases, as all these phases are driven by strong repulsive interactions.
Unlike conventional BCS superconductors in fully spin-valley polarized metals, these topological chiral superconductors are only partially spin-valley polarized, with the ratios of electron densities associated with different spin-valley quantum numbers quantized as simple rational numbers.
Many of these topological chiral superconductors exhibit charge-4 or higher condensation, and break time-reversal and space reflection symmetry, in addition to carrying gapless chiral edge modes.
One of the topological chiral superconductors (K2a) is in the same phase as the "spin"-triplet p+ip BCS superconductor, while others are in different phases than any BCS superconductors.
The same mechanism can also be used to produce anyon superconductivity between fractional anomalous quantum Hall states in the presence of a periodic potential.

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Stats

The electron density ne is of order 1012 cm-2.
The electron dispersion has a form ε = c2k2 + c4k4.
The interaction is modeled by a screened Coulomb potential e2/ϵr.

Quotes

"The supercon-ductivity from our mechanism is very different from BCS superconductivity."
"We stress that, in our chiral superconductors, the ratio of different species of electrons are quantized as simple rational numbers."
"Thus, in contrast to BCS superconductors of quarter Fermi liquid, the transition from spin-valley partially-polarized chiral superconductors to quarter Fermi liquid cannot be continuous at zero temperature in the clean limit."

Key Insights Distilled From

Topological chiral superconductivity beyond paring in Fermi-liquid

by Minho Kim, A... at arxiv.org 10-03-2024

https://arxiv.org/pdf/2409.18067.pdf

Topological chiral superconductivity beyond paring in Fermi-liquid

Deeper Inquiries

How do the properties of these topological chiral superconductors, such as the quantized ratios of electron densities and the charge-4 or higher condensation, affect their potential applications and experimental signatures?

The properties of topological chiral superconductors, particularly the quantized ratios of electron densities and the occurrence of charge-4 or higher condensation, have significant implications for their potential applications and experimental signatures. The quantized ratios of electron densities indicate that these superconductors can support a variety of distinct phases characterized by specific electron density configurations. This feature can be exploited in the development of novel electronic devices, such as topological qubits for quantum computing, where the robustness of topological states against local perturbations is crucial.
Moreover, the presence of charge-4 or higher condensation suggests that these superconductors may exhibit exotic phenomena, such as fractional statistics and anyon excitations, which are of great interest in the field of topological quantum computing. The experimental signatures of these superconductors could include the detection of fractional charge excitations, non-abelian statistics in braiding experiments, and the observation of chiral edge modes that are robust against disorder. Additionally, the breaking of time-reversal and reflection symmetries can lead to unique magnetic properties, which can be probed through techniques such as scanning tunneling microscopy (STM) and transport measurements.

What other types of strongly correlated electron systems, beyond graphene, could host similar topological chiral superconductivity driven by repulsive interactions?

Beyond graphene, several other strongly correlated electron systems could potentially host similar topological chiral superconductivity driven by repulsive interactions. One promising class of materials is transition metal oxides, particularly those exhibiting high-temperature superconductivity, such as cuprates. These materials often display strong electron correlations and can be tuned to explore different phases, including those that may support topological chiral superconductivity.
Another candidate is the family of two-dimensional materials, such as transition metal dichalcogenides (TMDs), which can exhibit strong spin-orbit coupling and electron-electron interactions. The ability to manipulate their electronic properties through external fields or strain could facilitate the realization of topological chiral superconductivity.
Furthermore, heterostructures composed of different materials, such as topological insulators combined with superconductors, may also provide a platform for exploring these exotic states. The interplay between the topological surface states and the superconducting order parameter could lead to novel chiral superconducting phases.

How can the theoretical framework developed in this work be extended to study the interplay between topological chiral superconductivity, fractional quantum Hall states, and Wigner crystallization in more complex heterostructures or moiré materials?

The theoretical framework developed in this work can be extended to study the interplay between topological chiral superconductivity, fractional quantum Hall (FQH) states, and Wigner crystallization by incorporating additional degrees of freedom and interactions present in more complex heterostructures or moiré materials. One approach is to consider the effective field theories that describe the low-energy excitations of these systems, allowing for the inclusion of both topological and fractional excitations.
In moiré materials, the emergence of flat bands due to the periodic potential can enhance electron correlations, making it possible to explore the coexistence of topological chiral superconductivity and FQH states. The framework can be adapted to account for the specific band structures and interaction strengths in these materials, leading to a richer phase diagram that includes various topological phases.
Additionally, the study of Wigner crystallization can be integrated by examining the competition between the repulsive interactions that favor crystallization and the attractive interactions that may lead to superconductivity. This can be achieved through numerical simulations and analytical calculations that explore the stability of different phases as a function of electron density and interaction strength.
By systematically varying parameters such as the strength of the periodic potential, the electron density, and the interaction types, researchers can gain insights into the conditions under which these exotic states emerge and their potential experimental signatures, paving the way for future discoveries in the realm of strongly correlated electron systems.