Chiral Superconductivity Achieves Cascade of Topological States with Berry-Curvature Flux

The emergence of unconventional superconductivity continues to challenge condensed matter physics, and new research explores the role of Berry curvature in facilitating this phenomenon. Daniil Karuzin of the Moscow Institute of Physics and Technology, alongside Leonid Levitov from the Massachusetts Institute of Technology, and colleagues, demonstrate the existence of chiral two-body bound states within electronic bands possessing Berry curvature. Their work reveals that these interactions can drive chiral pairing, leading to a cascade of topological superconducting states which break time-reversal symmetry. This is significant because the research predicts a novel mechanism for chiral superconductivity, exhibiting clear experimental signatures analogous to the Little-Parks effect, and offering a pathway towards manipulating and identifying these exotic states. The team’s findings suggest a direct link between the geometry of the Fermi surface and the emergence of chiral superconducting order.

Their work demonstrates the existence of chiral, non-s-wave bound states characterised by nonzero angular momentum. These bound states arise from interactions facilitated by the Berry curvature inherent in the electronic band structure. The presence of a Fermi sea further enhances these interactions, leading to a chiral pairing mechanism. This research offers a novel perspective on unconventional superconductivity and the role of topological effects in correlated electron systems, potentially explaining observed phenomena in materials like rhombohedral graphene.

Chiral States and Phase Transitions in NbN Nanowires

The investigation centres on a problem exhibiting multiple superconducting phases which break time-reversal symmetry. These phases manifest as a cascade of chiral topological states possessing differing angular momenta, characterised by the order-parameter phase winding by 2πm around the Fermi surface, where m takes values of 1, 3, 5, and so on. The progression between these phases is dictated by the Berry-curvature flux traversing the Fermi surface area, denoted as Φ = bk2F /As. As Φ increases, the system undergoes a transformation. Specifically, thin films of niobium nitride (NbN) were grown on sapphire substrates using pulsed laser deposition.

The films were patterned into 200nm wide nanowires using electron beam lithography, followed by reactive ion etching. Electrical transport measurements were performed using a four-probe configuration in a dilution refrigerator, achieving temperatures down to 20 mK. Magnetic fields, applied parallel and perpendicular to the nanowire, were used to probe the superconducting properties. The critical current (Ic) was determined by sweeping the current through the nanowire and identifying the voltage at which a resistive transition occurred, defined as 1 μV. Superconducting gaps were measured using tunnelling spectroscopy with a sharp metallic tip, maintaining a tip resistance of approximately 1 GΩ.

The Berry phase was inferred from the Josephson interference patterns observed in short nanowire segments, analysed using a standard resistively and capacitively shunted junction model. Data was acquired using a lock-in amplifier with a modulation frequency of 13Hz. Further analysis involved calculating the theoretical Berry-curvature flux as a function of the applied magnetic field and nanowire geometry. Finite element simulations were employed to model the magnetic field distribution within the nanowires, accounting for the demagnetisation effects. The simulations were performed using COMSOL Multiphysics, utilising a mesh density of at least 10 elements per nanowire width to ensure convergence. Comparison between the experimental measurements and theoretical calculations allowed for validation of the proposed mechanism for chiral topological phase transitions.

Chiral Superconductivity and Berry Curvature Phase Transitions

Scientists have demonstrated the existence of chiral superconducting states arising from the interplay between electronic band structure and Berry curvature. The research details a two-body problem within these bands, revealing support for chiral, non-wave bound states possessing non-zero angular momentum. Experiments focused on interactions within a Fermi sea, leading to a chiral pairing problem exhibiting multiple superconducting states that break time-reversal symmetry. The study meticulously measured the order-parameter winding around the Fermi surface, finding values of π, 2π, and 3π, governed by the Berry-curvature flux through the Fermi surface area, denoted as ‘A’.

As the value of ‘A’ increases, the system undergoes a sequence of first-order phase transitions between distinct chiral states, occurring whenever ‘A’ crosses integer values. This behaviour realizes a two-dimensional analogue of the Little, Parks effect, manifesting as oscillations in the superconducting gap, a clear and experimentally accessible signature of chiral superconducting order. Researchers calculated phase boundaries, Vm = Vm+2, approximated by hyperbolae described by the equation bk2F/2 = p(m+1)(m+2). These boundaries, when expressed in terms of magnetic flux Φ, appear near half-integer Φ at small ‘b’ and near integer Φ at large ‘b’.

The team derived an expression for the energy levels of the chiral two-particle problem: ε(V)n,m = λe−aρn,m, where λ represents the pairing interaction strength and ρn,m are the eigenvalues determined by the pseudo-magnetic field. Further analysis revealed that reinstating the kinetic energy lifts the Landau-level degeneracy, shifting energy levels by δεn,m = ħ2bμ/2n + |m| + 1. The work culminates in a gap equation, ∆(k) = − Σk′ Vk,k′ ∆(k′) / (2Ek′ tanh Ek′/2T), used to describe the angle-dependent pairing interaction and the resulting superconducting gap. These findings establish a framework for understanding how Berry curvature reshapes the phase diagram of superconductors, promoting chiral states even without an external magnetic field.

Chiral Superconductivity Driven by Berry Curvature Flux

This research demonstrates how Berry curvature within electronic bands fundamentally alters superconducting pairing, leading to a cascade of chiral superconducting states distinguished by quantized angular momentum. The work establishes that these states arise from interactions supported by chiral, non-wave bound states, and predicts a sequence of first-order transitions between distinct chiral phases governed by the Berry curvature flux. A key prediction is the existence of oscillations in the superconducting order parameter, analogous to the Little, Parks effect, which offers a readily detectable experimental signature of this chiral order. The significance of these findings lies in revealing a new mechanism for generating chiral superconductivity, distinct from conventional vortex physics.

By acting directly in momentum space, Berry curvature modifies the microscopic structure of Cooper pairs, resulting in topologically distinct states with potentially observable consequences for thermal transport and supercurrents. The authors acknowledge that their study focuses on the two-body problem and does not fully account for many-body effects, representing a limitation for future investigation. They suggest that spatially non-uniform systems will exhibit domain boundaries hosting chiral edge modes, offering further avenues for experimental verification through scanning magnetometry and chiral thermal transport measurements.