Material Switches Between Conducting and Insulating States

Researchers are investigating the complex interplay between superconductivity and strong electron correlations within Josephson junctions, a crucial area for advancing novel electronic devices. Don Rolih from the Jožef Stefan Institute and Faculty of Mathematics and Physics, University of Ljubljana, alongside Rok Žitko, present a detailed theoretical study of this proximity effect using the Hubbard model coupled to a BCS superconductor. Their collaborative work reveals the existence of two distinct phases, a Mott-like insulating phase and a proximitized superconducting phase, separated by a hysteretic first-order transition, demonstrating a controllable switch between conducting and insulating behaviours. By employing dynamical mean field theory with a numerical renormalization group impurity solver, the authors link these phases to fundamental properties of the underlying superconducting Anderson impurity problem and provide detailed insight into the resulting spectral structure, potentially offering new avenues for manipulating correlated electron systems.

Scientists are edging closer to realising practical quantum technologies with a better understanding of how superconductivity and strong electron interactions combine. This work illuminates a pathway to control electron behaviour within nanoscale circuits, potentially enabling more robust and switchable quantum components. The findings offer a novel means of tuning between conducting and insulating states at the quantum level.

Scientists have uncovered a surprising interplay between superconductivity and strong electron correlation within a novel Josephson junction system. Their work details how a single layer of strongly interacting electrons, when placed alongside conventional superconductors, can exhibit dramatically different behaviours, switching between an insulating and a metallic state.

This research centres on the proximity effect, where the properties of a superconductor induce behaviour in a neighbouring material, but here, the strong electron correlations within the layer introduce a complex and tunable response. The team has demonstrated that by manipulating external parameters, it is possible to control the flow of current through the junction, effectively creating a switch between conducting and insulating regimes.

This study focuses on a single-layer system described by the Hubbard model, a cornerstone of condensed matter physics used to understand materials where electrons strongly influence each other. By coupling this model to BCS superconductors, those exhibiting conventional superconductivity, researchers have identified two distinct phases: a Mott-like insulating phase and a proximitized superconducting phase.

These phases are separated by a first-order transition exhibiting hysteresis, meaning the system’s state depends on its history. In the Mott phase, the strong interactions suppress the critical current, while the superconducting phase behaves as a zero-junction, with an induced energy gap that closes at a specific phase difference, leading to a correlated metallic state.

Working within the framework of dynamical mean-field theory, a sophisticated computational technique, the researchers linked these phases to fundamental solutions of the underlying superconducting Anderson impurity problem. This connection provides detailed insight into the electronic structure at all energy scales. Specifically, the Mott phase exhibits unique sub-gap resonances, energy levels within the insulating gap, symmetrically arranged around the Fermi level, a characteristic feature arising from the splitting of a “mid-gap pole” commonly found in Mott insulators.

This structure explains the phase insensitivity observed in the system. The ability to tune between these phases using both the phase bias and junction transparency opens avenues for designing novel electronic devices and exploring fundamental physics at the interface between strongly correlated materials and superconductors.

Phase transitions and spectral evolution in a correlated system

Initial calculations reveal a clear distinction between two phases within the studied system. The critical values for the Bethe lattice at zero temperature were estimated as Uc1 = 2.39 and Uc2 = 2.92, establishing the parameter space for phase transitions. Spectral analysis at U = 3.2, exceeding Uc2, demonstrates a transition occurring at a critical hybridization strength of Γc = 0.13.

Below this value, the system exhibits characteristics of a Mott insulator, while above it, a proximitized superconducting phase emerges. As hybridization increases, spectral weight transfers towards energies near ∆, reducing the effective spectral gap from the Mott gap to a scale determined by the induced superconducting gap. A discontinuous change in the spectral function at Γc signals the emergence of superconducting coherence peaks, resembling a BCS superconductor with a gap ∆*.

The induced gap, initially finite at Γc, increases with hybridization following a power-law relationship, demonstrating a clear link between the bath coupling and the superconducting state. Detailed examination of the self-energy in the Mott phase reveals symmetrically located resonances around the Fermi level, originating from the splitting of the mid-gap pole characteristic of Mott insulators.

These resonances broaden with increasing Γ, ultimately disappearing at the transition to the superconducting phase. In contrast, the imaginary part of the self-energy in the S-phase exhibits a near-zero value for low energies within the induced gap, confirming the establishment of superconducting coherence. This transition is marked by a discontinuous sign change in the anomalous spectral function, further solidifying the distinction between the two phases.

Dynamical Mean Field Theory and Numerical Renormalisation Group for Correlated Superconducting Junctions

A dynamical mean field theory (DMFT) framework, employing the numerical renormalization group (NRG) as an impurity solver, underpins this work investigating the interplay between strong electron correlations and proximity-induced superconductivity. This approach allows detailed examination of the local electronic structure and phase transitions within a single-layer correlated electron system coupled to superconducting reservoirs.

The choice of DMFT-NRG is crucial as it accurately captures the strong local interactions inherent in the Hubbard model, while the NRG method provides a precise determination of the impurity Green’s function, essential for understanding the low-energy physics. The study begins with a single-band Hubbard model defined on a Bethe lattice, characterised by a hopping parameter t and Coulomb repulsion U, representing the strongly-correlated material.

This model is then coupled to two superconductors, labelled L and R, via a tunneling Hamiltonian that describes electron transfer between the correlated region and the superconducting baths. Superconducting behaviour is incorporated through BCS Hamiltonians, each possessing a gap parameter ∆, effectively acting as reservoirs for electrons at each site of the Hubbard model.

This configuration mimics a phase-biased Josephson junction, enabling the exploration of transitions between insulating and conducting regimes. To calculate the effective hybridization function, a crucial step in the DMFT procedure, the self-energy arising from the proximity effect is included. This self-energy, denoted Σ BCS, is proportional to the square of the tunneling amplitude and the Green’s functions of the superconducting baths.

Calculations neglect the back-action of the correlated region on the superconducting baths, a reasonable approximation given the macroscopic size of the baths relative to the single correlated layer under investigation. All results are presented in units of half-bandwidth, D = 2t, with critical values *U c1 * = 2.39 and *U c2 * = 2.92 established for the Bethe lattice at zero temperature.

The effective impurity problem is solved using a full-density matrix NRG Ljubljana implementation, utilising a specific discretization scheme and improved self-energy estimators to ensure accurate results. Computations are performed at a low temperature of T = 10 -8 ≪ ∆, minimising thermal broadening effects and allowing for precise analysis of the spectral functions. Particular attention is paid to controlling residual in-gap spectral weight, a common artifact in NRG calculations, through careful benchmarking procedures detailed in the supplementary material.

Hubbard-BCS modelling elucidates correlated electron switching between superconductivity and insulation

Scientists have long sought to engineer materials that seamlessly transition between superconductivity and insulating behaviour, a feat crucial for advanced electronic devices and potentially revolutionary energy technologies. This work, detailing the behaviour of correlated electrons within a carefully constructed model system, represents a significant step towards that goal.

The ability to switch between conducting and insulating states isn’t simply about controlling current flow; it’s about creating adaptable materials that respond dynamically to external stimuli, opening doors to novel forms of computation and energy storage. For years, the challenge has been the inherent complexity of strong electron correlations, where electrons interact intensely with each other, defying simple descriptions.

This research bypasses some of that complexity by focusing on a specific, well-defined model, a Hubbard model coupled to a BCS superconductor, allowing for detailed theoretical analysis using sophisticated computational techniques. The discovery of distinct, switchable phases, governed by subtle changes in external parameters, demonstrates a level of control previously difficult to achieve.

However, the model itself is an idealisation. Real materials are far messier, with imperfections and competing interactions that could obscure these effects. The reliance on numerical methods also introduces limitations, particularly in accurately capturing the behaviour at very low temperatures or in systems with strong disorder. Future work must bridge the gap between these theoretical insights and experimental realisation, exploring how these principles manifest in actual materials and addressing the challenges of scalability and stability. The next logical step involves investigating similar phenomena in more complex geometries and exploring the potential for manipulating these phases with light or magnetic fields, potentially leading to entirely new functionalities.