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arXiv:2303.17656 · Physical review. B./Physical review. B

Quasiperiodicity-induced enhancement of superconductivity in one-dimensional critical systems

Ricardo C. L. F. Oliveira, Miguel Gonçalves, Pedro Ribeiro, Eduardo V. Castro, Bruno Amorim

Published Apr 27, 2026• 2 citations
arXivHTMLPDF

Abstract

We show that quasiperiodicity can enhance superconductivity in one-dimensional narrow-band systems with s-wave pairing. Using a generalized Aubry-André-Harper model featuring quasiperiodic modulations in both the on-site potential and the hoppings, we study superconductivity across the extended, critical, and localized phases present in the noninteracting limit. Our results show that within the critical and localized phases, the superconducting critical temperature exhibits an algebraic scaling with the interaction strength, in contrast to the conventional BCS scaling observed in periodic approximants with a similar density of states. This direct comparison establishes that the enhancement originates from the nature of the single-particle eigenstates, rather than from band flattening alone. Furthermore, we find that the superfluid weight remains finite across all phases, including the localized regime, highlighting that superconducting phase coherence is retained throughout. The effects of quasiperiodicity on the superfluid weight are most pronounced in the weak-coupling regime, indicating the nontrivial role of the localization properties of the parent eigenstates in shaping the superconducting phases.

DOI
10.1103/dq2r-6gxd

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We show that quasiperiodicity can enhance superconductivity in one-dimensional narrow-band systems with s-wave pairing. Using a generalized Aubry-André-Harper model featuring quasiperiodic modulations in both the on-site potential and the hoppings, we study superconductivity across the extended, critical, and localized phases present in the noninteracting limit. Our results show that within the critical and localized phases, the superconducting critical temperature exhibits an algebraic scaling with the interaction strength, in contrast to the conventional BCS scaling observed in periodic approximants with a similar density of states. This direct comparison establishes that the enhancement originates from the nature of the single-particle eigenstates, rather than from band flattening alone. Furthermore, we find that the superfluid weight remains finite across all phases, including the localized regime, highlighting that superconducting phase coherence is retained throughout. The effects of quasiperiodicity on the superfluid weight are most pronounced in the weak-coupling regime, indicating the nontrivial role of the localization properties of the parent eigenstates in shaping the superconducting phases.
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Abstract Quantum simulation enables study of many-body systems in non-equilibrium by mapping to a controllable quantum system, providing a powerful tool for computational intractable problems. Here, using a programmable quantum processor with a chain of 10 superconducting qubits interacted through tunable couplers, we simulate the one-dimensional generalized Aubry-André-Harper model for three different phases, i.e., extended, localized and critical phases. The properties of phase transitions and many-body dynamics are studied in the presence of quasi-periodic modulations for both off-diagonal hopping coefficients and on-site potentials of the model controlled respectively by adjusting strength of couplings and qubit frequencies. We observe the spin transport for initial single- and multi-excitation states in different phases, and characterize phase transitions by experimentally measuring dynamics of participation entropies. Our experimental results demonstrate that the recently developed tunable coupling architecture of superconducting processor extends greatly the simulation realms for a wide variety of Hamiltonians, and can be used to study various quantum and topological phenomena.
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In a recent experiment, Anderson localization was observed directly for non-interacting Bose-Einstein Condensate in one dimension. The experiment was performed using quasiperiodic optical lattice. Their system can be described by the one-dimensional noninteracting Aubry-Andr�e model. This model which simulates disorder with its quasiperiodic potential shows transition from extended to localised states at a critical disorder strength. The ground state gets localised around a single point for disorder larger than the critical value. We find that while inverse participation ratio increases as we increase disorder and rises to one in insulator phase, super uid fraction decreases as we increase disorder and goes to zero sharply in the insulator phase . When we introduce weak repulsive interaction for Bose gas in the model at the mean field level, we see that the ground-state shows multiple-site localization for certain disorder range, which lies above the critical value. For given interaction strength, we find that the inverse participation ratio increases slowly and super uid fraction decreases slowly as we increase disorder. Moreover, by representing our model as a classical two-dimensional nonlinear Hamiltonian map, we distinguish between localised and extended states by studying the trajectories in phase-space. Using this, we find out the localization length of eigenstates as a function of disorder for non-interacting model. Further, we study the time-evolution of a wave-packet in different regimes of disorder and see the effect of interaction on it.