insight - Scientific Computing - # Rashba-Holstein Model

The Impact of Rashba Spin-Orbit Coupling on Charge Density Wave and Superconducting Phases in the Two-Dimensional Rashba-Holstein Model at Half-Filling

Q: How would the inclusion of other types of spin-orbit coupling, such as Dresselhaus spin-orbit coupling, affect the competition between CDW and SC phases in this model?

Incorporating Dresselhaus spin-orbit coupling (DSOC), alongside Rashba SOC, would significantly enrich the competition between charge density wave (CDW) and superconducting (SC) phases in the Rashba-Holstein model. Here's a breakdown of the potential implications: Modified Band Structure: DSOC introduces an additional momentum-dependent spin splitting, distinct from the Rashba-induced splitting. The combined effect reshapes the Fermi surface, potentially altering nesting conditions crucial for CDW formation. The relative strengths and orientations of Rashba and Dresselhaus terms determine the intricate details of this modification. Anisotropic Superconductivity: The interplay of both SOC terms can lead to anisotropic superconducting pairings. While Rashba SOC generally favors unconventional pairing symmetries, the addition of DSOC can either enhance or suppress these tendencies depending on the specific form of the DSOC and the Fermi surface topology. Topological Phases: The combination of Rashba and Dresselhaus SOC, especially in the presence of strong electron-phonon coupling, might give rise to topological phases. The competition between CDW, SC, and these topological states would depend on the intricate details of the band structure and the interaction strengths. Enhanced Quantum Criticality: The presence of multiple tuning parameters (Rashba and Dresselhaus SOC strengths, electron-phonon coupling, etc.) opens up possibilities for richer quantum critical behavior. The system might exhibit multiple quantum critical points and potentially host exotic phases in the vicinity of these points. Investigating these effects would require extending the Quantum Monte Carlo simulations to include DSOC. Analyzing the resulting phase diagrams and the evolution of order parameters as a function of both SOC strengths would provide valuable insights into this complex interplay.

Q: Could the weak CDW regime observed at large RSOC values be a precursor to other exotic phases not captured in this study, such as unconventional superconductivity or topological states?

Yes, the weak CDW regime at large RSOC values could indeed harbor the potential for exotic phases not fully captured in the study, including unconventional superconductivity or topological states. Here's why: Suppressed CDW: The weakening of the CDW order parameter at large RSOC suggests a reduction in the dominant ordering tendency. This opens up a window for competing orders to emerge, especially at low temperatures where fluctuations become significant. Unconventional Superconductivity: Large RSOC often favors unconventional superconducting pairings, such as p-wave or d-wave symmetry, as opposed to the conventional s-wave pairing. These unconventional pairings might be masked by the dominant CDW order at lower RSOC but could become relevant as the CDW weakens. Topological Proximity: Even if the system itself doesn't directly transition into a topological state, the proximity to such phases in the parameter space could lead to unusual properties. For example, the system might exhibit edge states or unusual transport characteristics indicative of topological influences. Fluctuation-Driven Phases: The weak CDW regime implies enhanced quantum fluctuations. These fluctuations can, in principle, drive the system towards exotic phases not captured by mean-field theories or conventional order parameters. Exploring these possibilities would require: Lower Temperatures: Simulations at even lower temperatures are crucial to probe the competition between weak CDW and other potential orders. Alternative Order Parameters: Investigating order parameters associated with unconventional superconductivity or topological phases is essential to uncover these hidden orders. Advanced Numerical Techniques: Employing advanced numerical techniques, such as Dynamical Mean-Field Theory (DMFT) or Density Matrix Renormalization Group (DMRG), might be necessary to accurately capture the interplay of strong correlations and spin-orbit coupling in this regime.

Core Concepts

The inclusion of Rashba spin-orbit coupling (RSOC) in the two-dimensional Holstein model on a half-filled square lattice leads to the suppression of charge-density wave (CDW) order and does not favor superconductivity except in the extreme antiadiabatic limit where the model maps onto the attractive Hubbard model.

Abstract

Bibliographic Information: Fa´undez, J., Fontenele, R. A., Sousa-J´unior, S. dos A., Assaad, F. F., & Costa, N. C. (2024). The two-dimensional Rashba-Holstein model. arXiv preprint arXiv:2411.07119v1.
Research Objective: This study investigates the impact of Rashba spin-orbit coupling (RSOC) on the formation of charge-density wave (CDW) and superconducting (SC) phases in the Holstein model on a half-filled square lattice.
Methodology: The researchers employed unbiased finite-temperature Quantum Monte Carlo (QMC) simulations to analyze the two-dimensional Rashba-Holstein model at half-filling. They examined charge and pairing correlations for various RSOC strengths and phonon frequencies.
Key Findings:
- The presence of RSOC weakens the CDW order in the system, leading to a crossover from a strong CDW regime to a weak CDW regime as RSOC increases.
- In the limit of pure Rashba hopping, the model exhibits four Weyl cones at half-filling, leading to a quantum phase transition from a semimetal to a CDW phase at a finite phonon frequency-dependent coupling strength.
- Only in the antiadiabatic limit, where the Holstein interaction reduces to an attractive Hubbard-U term, does a coexistence between CDW and SC order emerge due to an enhanced symmetry in the system.
Main Conclusions: The study reveals that the Rashba metal is unstable due to particle-hole instabilities, favoring the emergence of a CDW phase for any RSOC value. While RSOC generally suppresses CDW order, it does not promote superconductivity except in the extreme antiadiabatic limit.
Significance: This research advances the understanding of competing CDW and SC phases in systems with spin-orbit coupling, providing insights that may help clarify the behavior of related materials, such as transition-metal dichalcogenides.
Limitations and Future Research: Investigating the very weak CDW regime at large RSOC values using QMC is computationally challenging. Further studies could explore the effects of additional factors, such as thermal fluctuations or further-neighbor hopping terms, on the system's behavior.

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Stats

The critical temperature for the emergence of CDW order decreases as the strength of the RSOC increases.
For a fixed electron-phonon coupling strength of λ/t = 2 and phonon frequency of ω0/t = 1, the crossover from a strong CDW to a weak CDW regime occurs at an RSOC value of α/t ≈ 1.25 ± 0.05.
In the limit of pure Rashba hopping and a fixed phonon frequency of ω0/α = 2, the quantum critical point for the semimetal-CDW transition occurs at a coupling strength of λ/α ≈ 2.62.
In the attractive Hubbard model limit with pure Rashba hopping, the quantum critical point for both CDW and SC order occurs at an interaction strength of |Uc| ≈ 5.

Quotes

"As our main result, we provide finite temperature and ground state phase diagrams."
"These results advance our understanding of competing CDW and SC phases in systems with spin-orbit coupling, providing insights that may help clarify the behavior of related materials."

Key Insights Distilled From

The two-dimensional Rashba-Holstein model

by Juli... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.07119.pdf

The two-dimensional Rashba-Holstein model

Deeper Inquiries

How would the inclusion of other types of spin-orbit coupling, such as Dresselhaus spin-orbit coupling, affect the competition between CDW and SC phases in this model?

Incorporating Dresselhaus spin-orbit coupling (DSOC), alongside Rashba SOC, would significantly enrich the competition between charge density wave (CDW) and superconducting (SC) phases in the Rashba-Holstein model. Here's a breakdown of the potential implications:

Modified Band Structure: DSOC introduces an additional momentum-dependent spin splitting, distinct from the Rashba-induced splitting. The combined effect reshapes the Fermi surface, potentially altering nesting conditions crucial for CDW formation. The relative strengths and orientations of Rashba and Dresselhaus terms determine the intricate details of this modification.

Anisotropic Superconductivity: The interplay of both SOC terms can lead to anisotropic superconducting pairings. While Rashba SOC generally favors unconventional pairing symmetries, the addition of DSOC can either enhance or suppress these tendencies depending on the specific form of the DSOC and the Fermi surface topology.

Topological Phases:  The combination of Rashba and Dresselhaus SOC, especially in the presence of strong electron-phonon coupling, might give rise to topological phases. The competition between CDW, SC, and these topological states would depend on the intricate details of the band structure and the interaction strengths.

Enhanced Quantum Criticality: The presence of multiple tuning parameters (Rashba and Dresselhaus SOC strengths, electron-phonon coupling, etc.) opens up possibilities for richer quantum critical behavior. The system might exhibit multiple quantum critical points and potentially host exotic phases in the vicinity of these points.
Investigating these effects would require extending the Quantum Monte Carlo simulations to include DSOC. Analyzing the resulting phase diagrams and the evolution of order parameters as a function of both SOC strengths would provide valuable insights into this complex interplay.

Could the weak CDW regime observed at large RSOC values be a precursor to other exotic phases not captured in this study, such as unconventional superconductivity or topological states?

Yes, the weak CDW regime at large RSOC values could indeed harbor the potential for exotic phases not fully captured in the study, including unconventional superconductivity or topological states. Here's why:

Suppressed CDW:  The weakening of the CDW order parameter at large RSOC suggests a reduction in the dominant ordering tendency. This opens up a window for competing orders to emerge, especially at low temperatures where fluctuations become significant.

Unconventional Superconductivity:  Large RSOC often favors unconventional superconducting pairings, such as p-wave or d-wave symmetry, as opposed to the conventional s-wave pairing. These unconventional pairings might be masked by the dominant CDW order at lower RSOC but could become relevant as the CDW weakens.

Topological Proximity:  Even if the system itself doesn't directly transition into a topological state, the proximity to such phases in the parameter space could lead to unusual properties. For example, the system might exhibit edge states or unusual transport characteristics indicative of topological influences.

Fluctuation-Driven Phases: The weak CDW regime implies enhanced quantum fluctuations. These fluctuations can, in principle, drive the system towards exotic phases not captured by mean-field theories or conventional order parameters.
Exploring these possibilities would require:

Lower Temperatures:  Simulations at even lower temperatures are crucial to probe the competition between weak CDW and other potential orders.
Alternative Order Parameters:  Investigating order parameters associated with unconventional superconductivity or topological phases is essential to uncover these hidden orders.
Advanced Numerical Techniques:  Employing advanced numerical techniques, such as Dynamical Mean-Field Theory (DMFT) or Density Matrix Renormalization Group (DMRG), might be necessary to accurately capture the interplay of strong correlations and spin-orbit coupling in this regime.

If we consider the Rashba-Holstein model as a simplified representation of a real material, how can we experimentally manipulate the RSOC strength and observe the predicted transition between different electronic phases?

While the Rashba-Holstein model provides a simplified framework, experimentally manipulating RSOC strength in real materials to observe the predicted electronic phase transitions presents significant challenges and opportunities:
Manipulating RSOC Strength:

Gating in 2D Materials: In two-dimensional materials like transition metal dichalcogenides (TMDs), applying an external electric field through gating techniques can effectively tune the RSOC strength. This arises from the breaking of inversion symmetry at the interface.

Strain Engineering: Applying strain to materials can modify the crystal lattice symmetry, directly influencing the RSOC strength. This approach offers a way to dynamically control the spin-orbit interaction.

Interfacial Engineering: Creating interfaces between materials with different spin-orbit coupling properties can lead to emergent RSOC at the interface. This provides a platform for exploring the interplay of different SOC types.

Observing Electronic Phase Transitions:

Transport Measurements:  Changes in electronic phases often manifest as distinct signatures in transport properties. For instance, the onset of CDW order typically leads to an increase in resistivity, while the emergence of superconductivity results in zero resistance below a critical temperature.

Spectroscopic Techniques: Techniques like Angle-Resolved Photoemission Spectroscopy (ARPES) can directly probe the electronic band structure, revealing changes in Fermi surface topology and the emergence of gaps associated with different electronic orders.

Scattering Experiments: Neutron scattering and X-ray scattering experiments can detect the periodic modulations in charge density associated with CDW order. These techniques provide information about the ordering wavevector and the temperature dependence of the order parameter.

Scanning Tunneling Microscopy (STM): STM offers atomic-scale resolution of the electronic density of states, allowing for the direct visualization of CDW modulations and potentially even the spatial variations in superconducting order parameters.

Challenges and Considerations:

Material Selection: Identifying suitable materials with strong electron-phonon coupling and tunable RSOC remains a key challenge.
Disorder Effects:  Disorder inherent in real materials can obscure the signatures of these phase transitions and complicate the interpretation of experimental data.
Competing Orders:  The presence of other competing orders not explicitly included in the simplified model can complicate the experimental observation and interpretation.
Despite these challenges, the combination of advanced material synthesis, sophisticated experimental techniques, and close collaboration between theorists and experimentalists holds promise for uncovering the rich physics associated with the interplay of electron-phonon coupling and spin-orbit coupling in real materials.