Quantum Geometry Impacts Superconductor Impurity Sensitivity, Influencing Critical Temperature Via Broken Time-reversal Symmetry

The sensitivity of superconductors to impurities represents a long-standing challenge in condensed matter physics, and recent work by Denis Sedov, Mathias S. Scheurer, and colleagues at the University of Stuttgart reveals a crucial role for quantum geometry in determining this vulnerability. The team demonstrates that the momentum-dependence of electron behaviour, specifically its quantum geometry, significantly impacts how impurities disrupt superconductivity, particularly in materials lacking time-reversal symmetry. This research establishes a connection between quantum geometry and a novel mechanism, termed ‘quantum geometric pair breaking’, which renders even conventionally robust superconductors susceptible to non-magnetic impurities, and further predicts a complex, non-monotonic relationship between impurity concentration and superconducting strength. These findings have direct implications for understanding superconductivity in materials such as rhombohedral graphene, twisted molybdenum ditelluride, and a newly emerging class of materials known as altermagnets.

Quantum Geometry’s Role in Superconductivity

Scientists are investigating how quantum geometry influences superconductivity, exploring mechanisms that can either strengthen or disrupt this remarkable state of matter. This research moves beyond traditional understandings of superconductivity, highlighting the importance of the geometric properties of electron behavior. Quantum geometry describes how the energy of electrons varies with their momentum, and crucially, how different momentum states connect to one another, a concept linked to the Berry phase. Disrupting the formation of Cooper pairs, the fundamental building blocks of superconductivity, is known as pair breaking, and can occur through various mechanisms.

This research explores a new pathway for pair breaking, driven by the geometric properties of electron behavior. Scientists employ a mathematical technique called gauge fixing to identify the most stable superconducting state by optimizing the arrangement of Cooper pairs, maximizing the localization of the Cooper pair wavefunction. Researchers detailed a specific model system to study the effects of quantum geometry, focusing on a checkerboard lattice with spin-orbit coupling and altermagnetic order. They demonstrate that, under certain conditions, quantum geometry can stabilize superconductivity, enhancing its robustness.

Extending this analysis to scenarios where Cooper pairs possess a non-zero total momentum, scientists confirm that quantum geometry continues to play a crucial role in either strengthening or disrupting superconductivity. This research demonstrates that quantum geometry is a fundamental aspect of superconductivity, capable of either enhancing or breaking it depending on the material and conditions. By carefully choosing the mathematical gauge, scientists can identify the most stable superconducting state and understand the role of quantum geometry. This work also generalizes Anderson’s theorem, demonstrating that superconductivity can be protected by quantum geometry even in materials lacking traditional time-reversal symmetry.

Disorder Impacts Superconductivity in Broken Symmetry Materials

Scientists have developed a theoretical framework to understand how imperfections, or disorder, affect superconductivity, particularly in materials where time-reversal symmetry is broken. The research models the effects of impurities using a mathematical description of electron scattering, incorporating a random disorder potential. Researchers simplify calculations by focusing on the most relevant energy states at the Fermi level. This approach allows the team to analyze how impurities impact the superconducting order parameter, expressed mathematically through a matrix. They formulate a general expression for the critical temperature at which superconductivity emerges, considering different scenarios regarding spin polarization.

A key innovation involves defining a measure of “quantum geometric pair breaking”, which quantifies how impurities disrupt Cooper pair formation. The team demonstrates that, in the absence of time-reversal symmetry, even non-magnetic impurities can disrupt Cooper pairs due to contributions from quantum geometry. This optimization problem also provides a natural way to fix the gauge, ensuring consistency in the calculations. By applying this framework to models relevant to rhombohedral graphene, twisted MoTe₂, and altermagnets, scientists illustrate the interplay between disorder, quantum geometry, and superconductivity.

Quantum Geometry Breaks Superconducting Pair Formation

This work presents a comprehensive theory detailing how broken time-reversal symmetry impacts superconductivity, revealing a novel mechanism for pair breaking induced by quantum geometry. Scientists demonstrate that even nominally non-magnetic impurities can disrupt superconductivity when time-reversal symmetry is absent, a consequence of the interplay between the momentum dependence of electron states and the impurity potential. The research establishes a direct link between the localization of Cooper pairs and the degree of quantum geometric pair breaking, formulating this as an optimization problem. The team developed a general expression for impurity effects on the critical temperature, incorporating both wave-function effects and kinetic pair breaking arising from the broken time-reversal symmetry in the electronic dispersion.

Analysis reveals that this quantum geometric pair breaking occurs because the absence of a relationship between electron states at different momenta allows impurities to disrupt Cooper pairs, regardless of the superconductor. This is fundamentally different from the behavior predicted by Anderson’s theorem. The results are directly applicable to several materials, including rhombohedral graphene, twisted MoTe₂, and systems exhibiting altermagnetism, providing a theoretical framework for understanding and potentially manipulating superconductivity in these materials. The team’s work establishes a new understanding of disorder sensitivity in superconductors, highlighting the crucial role of quantum geometry when time-reversal symmetry is broken.

Quantum Geometry Drives Superconductor Disorder Sensitivity

This research demonstrates that quantum geometry, arising from the momentum-dependence of electron states, significantly influences the sensitivity of superconductors to disorder, particularly when time-reversal symmetry is broken. The team developed a general expression describing how the critical temperature of a superconductor is affected by impurities, revealing that even non-magnetic impurities can disrupt superconductivity due to contributions from quantum geometry. This effect, termed “quantum geometric pair breaking”, stems from the way electron states at different momenta are related. Furthermore, the study shows that broken time-reversal symmetry can lead to complex behavior in the critical temperature as impurity concentration changes, with impurities potentially enhancing pairing under certain conditions. The researchers also investigated the implications for finite-momentum pairing, a phenomenon relevant to several materials.