Dirac‐Like Quantum Dynamics and Tunable Non‐Markovian Effects in Bernal‐Stacked Bilayer Silicene

Abstract

ABSTRACT We investigate quantum entanglement, coherence, non‐Markovianity, and teleportation in Bernal‐stacked bilayer silicene (BBS) described by a tight‐binding Hamiltonian including mass and voltage terms. The noiseless dynamics is mapped onto a Dirac equation with pseudovector and tensor fields, while environmental noise is modeled as random fluctuations in the bias voltage and mass. Using open quantum system techniques, we demonstrate that the bias ratio, defined as the ratio between the bias voltage parameter and the interlayer coupling strength, serves as a powerful control parameter governing the quantum properties of the system. Entanglement entropy and quantum coherence exhibit a clear transition from pronounced oscillatory behavior at weak coupling to stable, maximally entangled and coherent states at strong coupling. The non‐Markovianity measure peaks at intermediate coupling, where memory effects and information backflow are maximally enhanced, marking a transition from non‐Markovian to Markovian dynamics as environmental memory diminishes. Under non‐Markovian noise, increasing the noise bandwidth parameter enhances the resilience of quantum correlations. When the noise bandwidth exceeds a certain threshold, the teleportation fidelity exhibits a significant enhancement, reflecting the improved robustness of the quantum state‐transfer dynamics. Our results demonstrate that BBS provides a versatile theoretical platform for investigating how the bias voltage and the noise bandwidth parameter influence entanglement, coherence, non‐Markovian dynamics, and teleportation fidelity.