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Journal of Statistical Mechanics Theory and Experiment

Thermal free entanglement of π-electronic spin and Landau-sublattice states in Rashba monolayer graphene

Rosa Safaiee, F. Aghel, Mohammad Mehdi Golshan

Published Feb 24, 2016• 6 citations
Publisher

Abstract

Free entanglement—the milestone of any quantum information processing scheme—among the π -electronic spin and its spatial states in graphene, as a function of temperature, is the main concern of the present report. It is assumed that a perpendicular magnetic field generates the Landau levels so that a coupling with the pseudo-spin (sublattice) states is enacted. Moreover, the pseudo-Rashba spin–orbit interaction (SOI), responsible for the coupling of spin and sublattice states, is also taken into account. From the structure of the total Hamiltonian, we introduce a Casimir operator which, in due turn, assists the development of a simple but efficient algorithm for our numerical computation. We then proceed by constructing the thermal density operator, its partially transposed one and, thereby, compute the negativity, the proper measure of free hybrid entanglement, at any temperature. Our results show that the negativity is nonvanishing at absolute zero temperature due to the fact that the ground state is an entangled one. Moreover, our results indicate that the negativity, at certain temperatures, exhibits maxima. The temperatures at which the entanglement (free) is maximal strongly depend on the magnetic field and pseudo-Rashba spin–orbit strength; decreasing the magnetic field and/or increasing the pseudo-Rashba parameter (PRP) enhances the maximal entanglement monotonically. As the temperature increases, however, it is shown that the negativity decreases asymptotically to zero. As a result, there exists distillable entanglement amid the π -electronic spin and its spatial states in graphene at any finite temperature .

DOI
10.1088/1742-5468/2016/02/023101

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Free entanglement—the milestone of any quantum information processing scheme—among the π -electronic spin and its spatial states in graphene, as a function of temperature, is the main concern of the present report. It is assumed that a perpendicular magnetic field generates the Landau levels so that a coupling with the pseudo-spin (sublattice) states is enacted. Moreover, the pseudo-Rashba spin–orbit interaction (SOI), responsible for the coupling of spin and sublattice states, is also taken into account. From the structure of the total Hamiltonian, we introduce a Casimir operator which, in due turn, assists the development of a simple but efficient algorithm for our numerical computation. We then proceed by constructing the thermal density operator, its partially transposed one and, thereby, compute the negativity, the proper measure of free hybrid entanglement, at any temperature. Our results show that the negativity is nonvanishing at absolute zero temperature due to the fact that the ground state is an entangled one. Moreover, our results indicate that the negativity, at certain temperatures, exhibits maxima. The temperatures at which the entanglement (free) is maximal strongly depend on the magnetic field and pseudo-Rashba spin–orbit strength; decreasing the magnetic field and/or increasing the pseudo-Rashba parameter (PRP) enhances the maximal entanglement monotonically. As the temperature increases, however, it is shown that the negativity decreases asymptotically to zero. As a result, there exists distillable entanglement amid the π -electronic spin and its spatial states in graphene at any finite temperature .
In this paper, the mechanism of entanglement between electronic spin states and their spatial degrees of freedom in graphene is reported. From a calculation of the time evolution of von Neumann entropy, as a measure of entanglement, we show that the general behavior is oscillatory with characteristics depending on the external magnetic field, the Rashba spin–orbit coupling and the Landau states. The effect of these agents on the degree of entanglement is also discussed. It is shown that an increase in the magnetic field decreases the degree of entanglement, while an increase in Rashba spin–orbit coupling enhances the entanglement. Furthermore, for higher Landau levels the electronic states become more entangled. The material presented in this paper offers new means of controlling the entanglement of electronic states.
In this paper we study the entanglement dynamics of spin–subband states for an electron in a quasi-one-dimensional Rashba quantum loop, in a strong perpendicular magnetic field, explicitly including the confining potential and the Rashba spin–orbit coupling into the entropy, which is a measure of entanglement, as a function of time. Our results indicate that the entanglement between the spin states and the structural subbands undergoes periodic oscillations. Furthermore, it is shown that the period of oscillations strongly depends upon the Rashba coupling, while the amplitudes may be optimized by making proper choices of the external magnetic field. It is also shown that the maxima of entanglement, in the long run, oscillate under periodic envelopes, whose characteristics depend upon the magnetic field. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these agents.
A static deformation of graphene can act on its Dirac electrons as a valley-odd magnetic field. In sublattice-gapped graphene this field makes the two valleys add in the parity-odd response rather than cancel. We derive the equilibrium thermodynamics of this effect and separate it from the finite-frequency transport response. At fixed electrochemical potential, reversing the pseudomagnetic field removes every nonzero pseudo-Landau level in the continuum theory. The remaining grand-potential difference is fixed by the spectrally asymmetric zeroth level. The static charge response is a thermally broadened plateau confined to the gap and has no metallic m/∣μ∣m/|μ|m/∣μ∣ tail. Near a band edge, pseudofield reversal transfers Bln⁡2\mathrm{B}\ln2Bln2 of entropy per unsplit zero-mode state in the low-temperature window. The fixed-μμμ heat capacity has two side lobes per edge and a universal peak 0.439229 DBkB0.439229\,D_B k_{\mathrm B}0.439229DB​kB​. We then formulate a definite constant-gate-voltage circuit and show that the measured sheet heat capacity depends on the electrical boundary condition. The full massive-Dirac density of states and an exact finite-field pseudo-Landau-level calculation give the same gate crossover in their common limit. At fixed carrier number, the low-temperature edge value is −2(ln⁡2)2DBkB-2(\ln2)^2 D_B k_{\mathrm B}−2(ln2)2DB​kB​, rather than a node. A finite geometric capacitance gives a continuous and experimentally tunable interpolation. Finally, we give a trace-free triaxial strain geometry, a disorder--interaction window, and realistic calorimetric and quantum-capacitance scales. The field-reversal protocol isolates an equilibrium electromechanical anomaly without a real magnetic field.
Abstract We investigate the dynamics of entanglement and quantum coherence between the pseudospin and valley indices of individual electrons in two-dimensional graphene, thermalized at an equilibrium temperature T . The system is modeled by an effective Dirac-like Hamiltonian describing a graphene valley-pseudospin qubit under polarized laser driving, including sublattice-dependent scattering process, while the thermal fluctuations are accounted through the standard Gibbs thermal state. Entanglement between the two degrees of liberty of electrons is quantified using concurrence, and coherence with the system is measured employing the relative entropy of coherence. The findings demonstrate that the behavior of entanglement and coherence under thermal noise strongly depends on the scattering strength, wavevector components, and electromagnetic field. Additionally, our results indicate that the strong polarized fields ( ξ 0 = 8 meV 2 ) with low-frequency ( ω = 0.06 eV ) can be employed to enhance the robustness of thermal entanglement and coherence of the system at intermediate temperatures. We also explore the impact of the other system parameters, like scattering strength and wavevector components, in enhancing and preserving quantum resources within graphene-based systems, noting particularly that the relative entropy of coherence is more resilient than concurrence against thermal decoherence.
In this article, we investigate how various parameters such as the nanoribbon length, temperature, external magnetic field, and Coulomb interactions affect fundamental quantum correlations in zigzag graphene nanoribbons. Using an effective Heisenberg model derived from the Hubbard Hamiltonian, we analyze three essential quantifiers: thermal entanglement, correlated quantum coherence, and local quantum uncertainty. Our results reveal that increasing the ribbon length leads to an exponential reduction of the exchange interaction between edge‐localized electronic states, which causes a gradual decrease of thermal entanglement. Both temperature and Coulomb repulsion significantly reduce the concurrence, while quantum coherence and local quantum uncertainty exhibit greater robustness, maintaining nonclassical correlations even at elevated temperatures. Furthermore, the application of an external magnetic field strongly influences these quantum correlations and enhances their sensitivity to thermal and geometric effects. These findings provide a comprehensive understanding of how structural and environmental parameters govern quantum correlations in graphene‐based nanostructures, offering valuable insights for the design of stable platforms for quantum information processing and spintronic applications.
We explore the quantum-memory assisted entropic uncertainty (QMA-EU), Jensen-Shannon coherence and entanglement dynamics in a Graphene sheet of disordered electrons in the presence of the intrinsic decoherence. The Graphene sheet containing two sublattices in a two-dimensional honeycomb lattice, which results due to the impurity-potentials interaction of two Dirac points. Entropic uncertainty and logarithmic negativity are used to investigate the generation and preservation of QMA-EU and entanglement under the major factors of Graphene material, including the band structure parameter, the wave numbers as well as the decoherence effect. For the initial uncorrelated two-lattice-point-qubit state, it is found that the lattice-point interactions have high capacity to generated partially/maximally two-lattice-point-qubit entangled and hence the partial/perfect Bob’s ability to guessing the outcome of Alice’s measurement. The increase of the graphite band structure parameter, the wave numbers enhance the generated lattice-point entanglement and Jensen-Shannon coherence, and hence the quantum memory game has a high prediction accuracy. For the intrinsic decoherence, the ability to generate entanglement, Jensen-Shannon coherence. and guessing the Alice’s measurement outcomes weakens. The sudden death-birth phenomenon in the logarithmic-negativity dynamics appears. The increase of the graphite band structure parameter weakens the robustness dynamics against the decoherence effect, while the increase of the wave number operators enhances this robustness. For initial maximally correlated state, the robustness dynamics of the QMA-EU, Jensen-Shannon coherence, and logarithmic-negativity entanglement is very sensitive to the increase of the band structure, wave numbers, and intrinsic decoherence.