Anomalous Hall Effect in Phase-Disordered Superconductors: A Theory Based on Screened Vortex Charge

Centrala begrepp

The anomalous Hall conductivity in a phase-disordered superconductor above the BKT transition is determined by the high-frequency AC Hall conductivity, which is closely related to the normal state anomalous Hall conductivity and Fermi surface Berry phase, despite the screening of vortex charge by many-body interactions.

Sammanfattning

Bibliographic Information:

Sau, J. D., & Wang, S. (2024). Theory of anomalous Hall effect from screened vortex charge in a phase disordered superconductor. arXiv preprint arXiv:2411.08969.

Research Objective:

This research paper investigates the relationship between the anomalous Hall effect in the normal state of a material and its manifestation in the phase-disordered state of a superconductor above the Berezinskii-Kosterlitz-Thouless (BKT) transition. The authors aim to understand how the anomalous Hall conductivity, originating from Berry curvature in the normal state, influences the behavior of the system in the superconducting phase.

Methodology:

The authors develop a theoretical framework based on a gauge-invariant effective action for a superconductor exhibiting an anomalous Hall response. They numerically calculate superconductivity in an anomalous Hall metal using a model based on a bilayer gapped Dirac model on a square lattice, incorporating px+ipy superconducting pairing. The charge difference between vortices and antivortices is analyzed as a function of chemical potential and compared to the normal state Hall conductivity.

Key Findings:

1. The study reveals that the difference in charge densities between the cores of vortices and antivortices in a chiral superconductor contributes to an anomalous Hall current in the phase-disordered state.
2. Numerical calculations demonstrate that the charge difference between vortices and antivortices is directly related to the Berry phase of the Fermi surface, indicating a connection between the anomalous Hall effect in the normal and superconducting states.
3. While many-body interactions screen the vortex charge, the dynamic screening cloud ensures that the resulting DC Hall conductivity in the BKT phase matches the AC Hall response, which remains similar to that of the normal state.

Main Conclusions:

The authors conclude that the DC anomalous Hall conductivity in a phase-disordered superconductor above the BKT transition is primarily determined by the high-frequency AC Hall conductivity. This finding suggests that despite the screening of vortex charge, the anomalous Hall response persists in the superconducting state and is closely tied to the normal state's Berry curvature.

Significance:

This research provides valuable insights into the behavior of anomalous Hall metals in their superconducting phases. The findings contribute to the understanding of how topological properties, such as Berry curvature, influence the transport properties of these materials.

Limitations and Future Research:

The study focuses on a simplified model system, and further research is needed to explore the applicability of these findings to more complex materials and experimental setups. Investigating the effects of disorder and other factors on the anomalous Hall response in phase-disordered superconductors could be promising avenues for future investigation.

Statistik

The charge difference between the vortex and the anti-vortex is defined as ΔQv = Q−−Q+.
The normal state Hall conductivity is σH = 1/2 [1 −m0/µ], where m0 is the Dirac mass.
The lattice model used has a size of N = 200, with parameters m0 = 0.1, ∆0 = 0.05, and coherence length ξ = 12.0.

Citat

"The occurrence of superconductivity in close proximity to correlated phases has led to many theoretical proposals for the mechanism of superconductivity, some based on strong correlation [17, 18] and others based on the proximity to correlated topological states [19, 20]."
"This chiral response has been conjectured to have a number of interesting consequences such as fractional charge and angular momentum of vortices [36]."
"The evidence for chiral superconductivity in a purely two dimensional anomalous Hall metal phase [19], where screening effects are reduced and phase disordered superconductivity is seen, motivates us to revisit the question of chiral response and vortex properties of such phases."

Viktiga insikter från

Theory of anomalous Hall effect from screened vortex charge in a phase disordered superconductor

by Jay D. Sau, ... på arxiv.org 11-15-2024

https://arxiv.org/pdf/2411.08969.pdf

Djupare frågor

How might the presence of disorder or impurities in the material affect the relationship between the anomalous Hall conductivity in the normal and phase-disordered superconducting states?

Answer:
The presence of disorder or impurities can significantly impact the relationship between the anomalous Hall conductivity (AHC) in the normal and phase-disordered superconducting states. Here's how:

Modification of Berry Curvature: Disorder can scatter electrons and alter their wavefunctions, leading to a modification of the Berry curvature. Since Berry curvature is intimately linked to the intrinsic AHC, any change in it will directly affect the AHC in both the normal and superconducting states. This effect can be particularly pronounced in systems with strong intrinsic AHC, where even small changes in Berry curvature can lead to measurable effects.

Enhanced Scattering: Impurities act as scattering centers for both electrons and vortices. Increased scattering in the normal state can reduce the AHC by disrupting the electron's trajectory and suppressing the skew-scattering contribution. In the phase-disordered state, impurity scattering can hinder vortex motion, affecting the flux-flow mechanism responsible for the Hall response.

Localization Effects: Strong disorder can lead to Anderson localization, where electron wavefunctions become spatially localized, leading to a suppression of conductivity. In the context of the AHC, localization can affect the relative contributions of intrinsic and extrinsic mechanisms. For instance, if localization predominantly affects the skew-scattering contribution, the intrinsic AHC might become more dominant.

Impact on Vortex Dynamics: Disorder can pin vortices, hindering their motion and affecting the flux-flow conductivity in the phase-disordered state. This pinning can lead to a discrepancy between the AHC inferred from vortex charge (C4) and the actual Hall response, which is determined by the high-frequency ac Hall conductivity (C5).

Mesoscopic Effects: In mesoscopic systems, where the system size is comparable to the electron mean free path, disorder can lead to universal conductance fluctuations and other interference effects. These effects can influence the AHC in both the normal and superconducting states, making the relationship between them more complex.
In summary, disorder can significantly complicate the relationship between the AHC in the normal and phase-disordered states. The specific impact depends on the nature and strength of the disorder, as well as the material's intrinsic properties. Experimental investigations into the role of controlled disorder would be valuable to further understand these effects.

Could the theoretical framework presented in this paper be extended to understand the anomalous Hall effect in other topological phases of matter, such as topological insulators or Weyl semimetals?

Answer:
Yes, the theoretical framework presented in the paper, which links the anomalous Hall conductivity (AHC) to the Berry curvature and vortex charge, can potentially be extended to understand the AHC in other topological phases of matter, such as topological insulators and Weyl semimetals. However, some modifications and considerations are necessary:
Topological Insulators:

Surface States: Topological insulators are characterized by insulating bulk states but conducting surface states with a non-trivial Berry curvature. The framework would need to be adapted to account for the contribution of these surface states to the AHC.
Absence of Vortex Charge: Unlike superconductors, topological insulators do not exhibit vortex excitations. Therefore, the relationship between vortex charge and AHC wouldn't directly apply. Instead, the focus should be on relating the Berry curvature of the surface states to the observed AHC.
Quantum Hall Analogy: The AHC in topological insulators is closely related to the Quantum Hall effect, where quantized Hall plateaus arise from the topological properties of the system. The effective action approach could be modified to incorporate the Chern-Simons term, which captures the topological nature of the AHC in these systems.
Weyl Semimetals:

Weyl Nodes: Weyl semimetals host Weyl nodes, points in momentum space where the valence and conduction bands touch linearly. These nodes act as sources and sinks of Berry curvature, leading to a non-trivial AHC. The framework would need to account for the contribution of these Weyl nodes to the overall Berry curvature and AHC.
Chiral Anomaly: Weyl semimetals exhibit the chiral anomaly, a quantum phenomenon where the application of parallel electric and magnetic fields leads to a non-conservation of chiral charge. This anomaly can manifest as a negative magnetoresistance and could potentially be incorporated into the effective action approach.
Fermi Arcs: The surface states of Weyl semimetals form Fermi arcs, open curves connecting the projections of Weyl nodes with opposite chirality. These Fermi arcs can also contribute to the AHC and should be considered in the theoretical framework.
General Considerations:

Role of Interactions: The paper primarily focuses on a mean-field description of superconductivity. Extending the framework to strongly correlated topological phases would require incorporating the effects of electron-electron interactions more rigorously.
Disorder Effects: As discussed in the previous question, disorder can significantly impact the AHC. Any extension of the framework to other topological phases should carefully consider the role of disorder.
In conclusion, while the core principles of relating Berry curvature and AHC are applicable to other topological phases, specific adaptations are needed to account for the unique properties of each phase. Further theoretical and experimental investigations are crucial to fully explore these connections.

If the Berry curvature could be dynamically manipulated, what implications would this have for controlling the anomalous Hall conductivity and other transport properties in these materials?

Answer:
The ability to dynamically manipulate Berry curvature would open up fascinating possibilities for controlling the anomalous Hall conductivity (AHC) and other transport properties in topological materials, leading to novel device applications and a deeper understanding of topological phases. Here are some potential implications:
Anomalous Hall Effect Control:

AHC Switching: By dynamically changing the Berry curvature, one could achieve on-demand switching of the AHC between high and low conductivity states. This could be realized by applying external stimuli like electric fields, strain, or light, which can modify the band structure and hence the Berry curvature.
AHC Modulation: Instead of just switching, a more finely tuned manipulation of Berry curvature could enable continuous modulation of the AHC. This could be valuable for analog applications and for studying the intricate relationship between Berry curvature and AHC in detail.
Spatial Control: If the manipulation of Berry curvature could be localized to specific regions within the material, it would allow for the creation of AHC channels or junctions. This could pave the way for designing novel electronic devices based on the AHC.
Beyond Anomalous Hall Effect:

Topological Transistor: The concept of an AHC switch could be extended to create a "topological transistor," where the Berry curvature manipulation acts as a gate, controlling the flow of charge current through the AHC channel.
Optical Applications: Dynamically manipulating Berry curvature could lead to novel optical responses. For instance, by modulating the Berry curvature with light, one could control the material's refractive index or achieve ultrafast optical switching.
Thermoelectric Properties: Berry curvature also plays a role in thermoelectric effects, such as the anomalous Nernst effect. Dynamic manipulation of Berry curvature could lead to enhanced thermoelectric efficiency and the development of new energy harvesting technologies.
Exploring Topological Phase Transitions: By dynamically driving the Berry curvature, one could potentially induce topological phase transitions in a controlled manner. This would provide a powerful tool for studying the properties of different topological phases and the transitions between them.
Challenges and Opportunities:
Realizing dynamic Berry curvature manipulation poses significant experimental challenges. It requires identifying suitable materials and developing techniques to control the Berry curvature with high precision and speed. However, the potential rewards in terms of novel device functionalities and fundamental insights into topological matter make it a highly promising avenue for future research.