Strained Superconductors Generate Unusual Magnetism Perpendicular to Applied Fields

[Crystalline symmetry lowering in elemental superconductors, such as vanadium and niobium, enables the formation of spin-singlet orbitally polarized Cooper pairs with identical orbital moments. Gabor Csire of Wigner Research Centre for Physics, University of Salerno and colleagues used superconducting density functional theory to reveal that reducing trigonal symmetry to $C_s$ activates interorbital pairing in both bulk and surface regions, with a notable enhancement occurring on surfaces. The resulting orbitally polarized superconducting state exhibits a new transverse magnetic response, generating a sizable orbital magnetization perpendicular to an applied in-plane magnetic field. This effect directly links to equal-orbital-moment Cooper pairing, offering a clear experimental signature. These positions strained elemental superconductors as a promising minimal platform for superconducting orbitronics

Modelling electron pairing in vanadium and niobium using superconducting density functional theory

Superconducting density functional theory served as a powerful computational microscope to explore electron behaviour within vanadium and niobium. The technique solves the complex Dirac, Bogoliubov, de Gennes equation, a cornerstone of many-body physics, mapping electron energy, momentum, spin, and orbital characteristics to understand how they pair to form superconducting states. This equation describes the quantum mechanical behaviour of interacting electrons in a superconducting material, accounting for both particle and hole excitations. This approach allows for modelling realistic materials, incorporating the three-dimensional Fermi surface, the boundary in momentum space separating occupied and unoccupied electron states, electron spin-orbit interaction, which couples an electron’s spin to its orbital motion, and specific electron interactions, such as Coulomb repulsion. Crucially, the method also simulates exposed material surfaces, essential for understanding surface-enhanced effects. Calculations incorporated bulk samples comprising 111 layers, alongside surface modelling employing slab geometries with vacuum layers, to accurately predict orbital pairing amplitudes; this framework enables detailed analysis of electron pairing mechanisms and the resulting superconducting properties. The choice of 111 layers ensures sufficient bulk-like behaviour is maintained within the simulated structure, minimising surface effects in the bulk calculations. Furthermore, the inclusion of surface modelling allows for a direct comparison of bulk and surface pairing strengths, revealing the pronounced surface enhancement observed.

Enhanced orbital magnetisation via symmetry reduction activates interorbital Cooper pairing

Strained vanadium and niobium exhibit a sizable orbital magnetization, reaching 0.17m℄b per unit cell, a magnitude previously unattainable in elemental superconductors without symmetry lowering. This value surpasses the sensitivity of current magneto-optical Kerr effect measurements, a technique sensitive to surface magnetism, opening a direct pathway to detect orbitally polarized Cooper pairs. These pairings feature electrons with aligned orbital movements, differing fundamentally from conventional superconductivity where pairing typically occurs between electrons with opposite spins and momenta. The orbital magnetization arises from the net orbital angular momentum of the Cooper pairs, a consequence of the specific orbital character of the electrons involved in the pairing process.

Reducing trigonal crystalline symmetry to Cs activates interorbital pairing, particularly enhancing the effect on material surfaces. This symmetry reduction fundamentally alters the electronic structure, lifting orbital degeneracies and modifying the electronic band structure, enabling the formation of these unique electron pairings and a corresponding transverse magnetic response. The Cs symmetry, retaining a single mirror plane, allows for a specific mixing of orbitals that promotes interorbital pairing, a process where electrons from different atomic orbitals combine to form the Cooper pair. Calculations reveal that this symmetry lowering maintains a single mirror plane in both bulk and surface regions of vanadium and niobium, vital for potential device applications as it dictates the allowed electronic states and pairing symmetries. The preservation of this mirror plane is crucial for the observed transverse magnetic response, ensuring the orbital magnetization aligns perpendicularly to the applied magnetic field.

Applying an in-plane magnetic field to these strained materials induces a sizable orbital magnetization perpendicular to the field, a direct consequence of equal-orbital-moment Cooper pairs forming. This orbital magnetization represents a novel transverse magnetic response, offering a clear experimental signature for detecting these unique pairings, predicted to be particularly strong at material surfaces due to the increased density of states and reduced screening effects. The perpendicular alignment of the magnetization and the applied field is a hallmark of this orbitally polarized superconducting state, distinguishing it from conventional superconducting responses. Despite predicting a substantial effect, the calculations do not yet quantify the strain required for practical implementation, nor do they address the impact of material imperfections, such as defects or impurities, on sustaining this delicate symmetry-broken state. Understanding the tolerance of this state to imperfections is crucial for realising robust devices.

Strained vanadium demonstrates potential for orbitronic devices through theoretical modelling

Superconducting orbitronics, electronics based on the spin and orbital states of electrons, promises devices beyond the limitations of conventional semiconductors, potentially enabling faster and more energy-efficient computation and data storage. Realising this potential demands materials exhibiting strong orbitally polarised superconductivity, where electrons pair with aligned orbital movements, and a clear signal to detect it. This work demonstrates a pathway using strained elemental superconductors, but relies heavily on theoretical modelling using density functional theory; experimentally verifying these predictions and quantifying the precise strain needed for practical devices remains a key hurdle. The magnitude of strain required to induce the necessary symmetry lowering and achieve optimal orbital polarization needs to be determined through experimental investigation.

Lowering the symmetry of crystalline structures in vanadium and niobium unlocks a unique superconducting state, enabling the formation of orbitally polarised Cooper pairs. Calculations utilising superconducting density functional theory reveal this symmetry reduction activates electron pairing, particularly at material surfaces, resulting in a transverse magnetic response. Specifically, an orbital magnetisation emerges perpendicularly to an applied magnetic field, offering a novel pathway to explore superconducting orbitronics and unlock novel device functionalities exceeding current semiconductor limits, justifying further investigation despite modelling challenges. The potential for manipulating orbital magnetization with electric fields, a key feature of orbitronic devices, remains to be explored theoretically and experimentally. Further research should focus on exploring different strain configurations and their impact on the superconducting properties, as well as investigating the stability of the symmetry-broken state under various environmental conditions.

This research demonstrated that reducing the symmetry of crystalline vanadium and niobium induces a unique superconducting state with orbitally polarised Cooper pairs. This is significant because it provides a minimal material platform for superconducting orbitronics, potentially enabling devices beyond the limitations of conventional semiconductors. The study revealed a transverse magnetic response and the emergence of orbital magnetisation, offering an experimentally accessible signature of this state. Researchers suggest further investigation is needed to quantify the precise strain required and explore the stability of this symmetry-broken state.