[Paper Review] A Phenomenological Theory of Superconductor Diodes in Presence of Magnetochiral Anisotropy

James Jun He, Yukio Tanaka+1 more|arXiv (Cornell University)|Jun 7, 2021

Physics of Superconductivity and Magnetism4 citations

TL;DR

This paper develops a Ginzburg-Landau-based phenomenological theory to explain superconductor diodes exhibiting nonreciprocal critical current responses under magnetic fields, particularly in noncentrosymmetric systems with magnetochiral anisotropy. It derives analytical relations for critical current asymmetry and provides a unified design framework for superconductor diodes across various parameter regimes, including long Josephson junctions near Tc and broader field conditions via numerical analysis.

ABSTRACT

Nonreciprocal responses in noncentrosymmetric systems contain a broad range of phenomena. Especially, non-dissipative and coherent nonreciprocal transport in solids is an important fundamental issue. The recent discovery of superconductor diodes under external magnetic fields, where the critical current changes as the direction is reversed, significantly boosted this research area. However, a theoretical understanding of such phenomena is lacking. Here, we provide theoretical descriptions of superconductor and Josephson junction diodes with the Ginzburg-Landau method. The theory is applied to a few typical systems, where the analytical relations between the nonreciprocal critical currents and the system parameters are obtained. Long Josephson junctions near the superconducting transition temperature under weak fields are studied analytically, while broader parameter regimes are investigated numerically. These results offer a unified description and design principle of superconductor diodes.

Motivation & Objective

• To address the lack of theoretical understanding of nonreciprocal critical current responses in superconductor diodes under magnetic fields.
• To provide a unified theoretical framework for superconductor and Josephson junction diodes in systems with magnetochiral anisotropy.
• To derive analytical relations between nonreciprocal critical currents and system parameters such as magnetic field and material symmetry.
• To extend the analysis beyond weak fields and near-Tc conditions using numerical methods for broader parameter regimes.

Proposed method

• Application of the Ginzburg-Landau formalism to model superconducting order parameters in noncentrosymmetric systems with magnetochiral anisotropy.
• Derivation of analytical expressions for nonreciprocal critical currents in long Josephson junctions near the superconducting transition temperature.
• Incorporation of magnetochiral anisotropy terms into the Ginzburg-Landau free energy to capture field-direction-dependent superconducting responses.
• Use of numerical simulations to explore the nonreciprocal critical current behavior in broader parameter regimes beyond the analytical limit.
• Systematic analysis of the interplay between magnetic field direction, symmetry breaking, and critical current asymmetry.
• Development of a unified phenomenological description applicable to diverse superconductor diode systems.

Experimental results

Research questions

• RQ1 How does magnetochiral anisotropy induce nonreciprocal critical current responses in superconductors under external magnetic fields?
• RQ2 What analytical relationships exist between the nonreciprocal critical current and system parameters such as magnetic field strength and symmetry breaking?
• RQ3 How do the critical current asymmetries in long Josephson junctions behave near the superconducting transition temperature?
• RQ4 To what extent can the Ginzburg-Landau framework describe nonreciprocal transport in noncentrosymmetric superconductors?
• RQ5 What design principles emerge from the theoretical description of superconductor diodes across varying magnetic field and material conditions?

Key findings

• Analytical expressions are derived for the nonreciprocal critical current in long Josephson junctions near Tc, linking it directly to the magnetochiral anisotropy and magnetic field direction.
• The theory predicts a clear dependence of critical current asymmetry on the sign and magnitude of the applied magnetic field in noncentrosymmetric systems.
• Numerical results confirm the robustness of nonreciprocal behavior across a wide range of magnetic fields and system parameters beyond the analytical regime.
• The Ginzburg-Landau framework successfully captures the essential physics of nonreciprocal transport in superconductor diodes without requiring microscopic details.
• A unified phenomenological description is established that applies to both intrinsic and engineered superconductor diodes with magnetochiral anisotropy.
• The results provide a design-oriented framework for engineering superconductor diodes with tailored nonreciprocal responses through symmetry control and field tuning.