Researchers have demonstrated a pathway towards enhancing topological superconductivity within a non-Hermitian Kitaev chain exhibiting staggered pairing imbalance. Xiao-Jue Zhang, Rong Lü, and Qi-Bo Zeng from the Department of Physics, Capital Normal University, et al. detail how manipulating chemical potential and pairing imbalance induces transitions in the eigenenergy spectrum, potentially shifting from real to complex gaps. This work is significant because it reveals that a topologically nontrivial phase, capable of hosting zero modes, can emerge even with strong chemical potential through careful control of pairing imbalance, effectively broadening the scope for realising topological superconductivity in non-Hermitian systems and offering a novel platform for exploration.
Pairing imbalance expands topological superconductivity in a non-Hermitian Kitaev chain by promoting Andreev bound state localization
Researchers have unveiled a novel topological superconducting phase within a one-dimensional non-Hermitian Kitaev chain exhibiting staggered imbalance in its superconducting pairing. This work demonstrates how manipulating the chemical potential and pairing imbalance induces transitions in the system’s eigenenergy spectrum, shifting the spectral gap from a real to an imaginary configuration.
Crucially, the introduction of pairing imbalance significantly expands the range of parameters supporting a topological superconducting phase, offering enhanced control over this quantum state of matter. The study reveals that a topologically nontrivial phase, capable of hosting Majorana zero modes, can be induced solely by adjusting the pairing imbalance, even when a strong chemical potential is present.
Analytical determination of gap-closing points and phase boundaries allows for precise characterization of the resulting phase diagrams through a nonzero topological invariant. These calculations confirm the existence of both zero modes and finite-energy edge modes within the system, indicating a rich and complex interplay of quantum phenomena.
This research establishes a new platform for investigating topological superconductivity in non-Hermitian systems, moving beyond traditional Hermitian constraints. By exploring imbalanced pairing, scientists have discovered exotic behaviours and opened avenues for potential applications in fault-tolerant quantum computation.
The ability to induce and control topological phases with greater flexibility promises advancements in the development of robust quantum technologies. The findings demonstrate that non-Hermitian pairing imbalance can constructively stabilize topological superconductivity, offering a versatile approach to exploring topological phases in superconducting systems.
Hamiltonian formulation of the imbalanced Kitaev chain model reveals interesting topological properties
A one-dimensional Kitaev chain incorporating staggered imbalance in the p-wave superconducting pairing serves as the foundation for this work. The system is modelled as a lattice comprising N unit cells, each containing sublattice sites A and B, with a total chain length of 2N. The Hamiltonian describes a network where electrons can hop between adjacent sites and experience superconducting pairing with spatially varying strengths.
Specifically, the Hamiltonian incorporates a chemical potential μ, a hopping amplitude t set to 1, and a pairing amplitude ∆, alongside imbalance parameters γ1 and γ2. These imbalance parameters modulate the superconducting pairing on both intra- and inter-cell bonds, effectively introducing gain and loss processes related to pair creation and annihilation.
The Hamiltonian explicitly details the annihilation and creation operators for spinless fermions on each sublattice site, accounting for both nearest-neighbor hopping and p-wave pairing interactions. Hopping between sites is represented by terms involving c†j,Bcj,A and its Hermitian conjugate, while pairing interactions are described by terms such as c†j,Bc†j,A and cj,Acj,B, modified by the imbalance parameters γ1 and γ2.
Analytical determination of gap-closing conditions and transition points within the momentum-space spectrum was performed to characterise the resulting phase diagrams. This analysis reveals that the inclusion of pairing imbalance significantly expands the parameter region supporting a topologically nontrivial superconducting phase compared to the Hermitian limit.
Furthermore, the research demonstrates that a topologically nontrivial phase hosting Majorana zero modes can be sustained even with arbitrarily large chemical potential, provided the imbalances are introduced in an alternating manner across the lattice. The study identifies regimes where Majorana zero modes coexist with finite-energy Majorana edge modes, highlighting the constructive role of non-Hermitian pairing imbalance in stabilising topological superconductivity.
Pairing imbalance induces and stabilises topological superconductivity and Majorana zero modes in a non-Hermitian Kitaev chain, offering potential for robust quantum computation
Eigenenergy spectra in a one-dimensional non-Hermitian Kitaev chain exhibit real-to-complex transitions dependent on chemical potential and pairing imbalance. Spectral gaps transition from real to imaginary line gaps as parameters are tuned, demonstrating a shift in the system’s fundamental energetic properties.
The pairing imbalance significantly enlarges the parameter region supporting a topological superconducting phase compared to Hermitian limits, indicating enhanced stability of this phase. Remarkably, a topologically nontrivial phase hosting Majorana zero modes emerges through variation of the pairing imbalance, even with strong chemical potential present.
Gap-closing points and phase boundaries were determined analytically, resulting in phase diagrams characterised by a nonzero topological invariant, confirming the robustness of the topological state. The analysis reveals that the topological phase and Majorana zero modes can persist even with arbitrarily large chemical potential when imbalances are introduced in an alternating manner.
Furthermore, the research identifies the existence of both Majorana zero modes and finite-energy Majorana edge modes within the system. These modes coexist in a specific parameter regime, expanding the potential for manipulating and observing topological phenomena. The work demonstrates that non-Hermitian pairing imbalance constructively stabilises topological superconductivity, offering a versatile platform for exploring topological phases in non-Hermitian superconducting systems.
The model Hamiltonian considers a one-dimensional lattice with staggered imbalance in p-wave superconducting pairing, comprising N unit cells and a chain length of 2N. The chemical potential, μ, is uniform, while the nearest-neighbor hopping amplitude, t, is set to 1 throughout the study.
Enhanced topological superconductivity via non-Hermitian pairing imbalance and chemical potential tuning offers novel routes to robust quantum computation
A one-dimensional non-Hermitian Kitaev chain exhibiting staggered imbalance in superconducting pairing has been investigated, revealing novel spectral features and an expanded topological superconducting phase. Tuning the chemical potential alongside the pairing imbalance induces transitions between real and complex energy spectra, altering the nature of the spectral gap from real to imaginary.
This manipulation significantly broadens the parameter range supporting a topological phase, enabling the emergence of topologically nontrivial states even with substantial chemical potential. Analytical determination of gap-closing points and phase boundaries, corroborated by numerical results, provides a comprehensive understanding of the system’s behaviour.
The introduction of pairing imbalance notably enhances the topological superconducting phase compared to Hermitian counterparts, allowing for robust Majorana zero modes across a wider range of parameters. Furthermore, the system exhibits both zero-energy and finite-energy Majorana edge modes, originating from the staggered non-Hermitian pairing and observable even within the bulk spectrum.
The authors acknowledge that in certain parameter regimes, a negative topological invariant does not necessarily indicate the presence of Majorana zero modes, highlighting a limitation in relying solely on the Pfaffian evaluation. Future research could explore experimental realisation through proximitizing semiconductors with periodic superconducting arrays or utilising quantum-dot platforms, potentially enabling the study of non-Hermitian effects on spectral and transport properties within topological superconductors. These findings demonstrate the constructive role of non-Hermitian pairing imbalance in stabilising and augmenting topological superconducting phases.
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🗞 Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
🧠ArXiv: https://arxiv.org/abs/2602.02059