Entangled end states with fractionalized spin projection in a time-reversal-invariant topological superconducting wire

Aligia, A. A.; Arrachea, Liliana

doi:10.1103/physrevb.98.174507

Cited by 21 publications

(21 citation statements)

References 48 publications

(107 reference statements)

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“…For each spin, the operators Γ o kσ and Γ e kσ are related with the local ones Γ jσ by a unitary matrix U σ with coefficients given by Eqs. (30) and (31) and similarly for spin down. Using this transformation and Eq.…”

Section: B Effect Of a Magnetic Field At One Endmentioning

confidence: 98%

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Exact analytical solution of a time-reversal-invariant topological superconducting wire

Aligia

Camjayi

2019

Phys. Rev. B

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We consider a model proposed before for a time-reversal-invariant topological superconductor (TRITOPS) which contains a hopping term t, a chemical potential µ, an extended s-wave pairing ∆ and spin-orbit coupling λ. We show that for |∆| = |λ|, µ = t = 0, the model can be solved exactly defining new fermion operators involving nearest-neighbor sites. The many-body ground state is four-fold degenerate due to the existence of two zero-energy modes localized exactly at the first and the last site of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results we correct some statements related with the so called "time-reversal anomaly". Addition of a small hopping term for a chain with an even number of sites breaks the degeneracy and the ground state becomes unique with an even number of particles. We also consider a small magnetic field applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains with numerical results obtaining good agreement.

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Section: B Effect Of a Magnetic Field At One Endmentioning

confidence: 98%

“…where the annihilation operators are given above [see Eqs. (29), (30), (31)]. It is important to note that for small t as we assume, the energies corresponding to all these operators are positive [Eqs.…”

Section: B Effect Of a Magnetic Field At One Endmentioning

confidence: 99%

Exact analytical solution of a time-reversal-invariant topological superconducting wire

Aligia

Camjayi

2019

Phys. Rev. B

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“…The system in ( 7) displays a damped oscillatory response, which is typical of many feedback-controlled transduction processes encountered in cantilever positioning in atomic force microscopy, 93 optical force feedback microphones, [94][95][96] or the control of complex deexcitation lifetimes encountered in many types of spectroscopies, e.g., nuclear magnetic, 97 electron-spin, 98,99 microwave, [100][101][102] and multiphoton fluorescence, e.g., Förster resonance, 103 and in lock-in applications 104 or in other control and identification schemes. 105 The desired closed-loop dynamics are specified in the form (6) with aD = bD = 0.5, which corresponds to a first-order transfer function with a time constant of 2 s. All the simulations were carried out by using the Matlab ® /Simulink ® software and the FOTF code 106 for fractional-order systems available within the FOMCON toolbox (www.fomcon.net).…”

Section: Preliminary Examplementioning

confidence: 99%

Measurement and control of emergent phenomena emulated by resistive-capacitive networks, using fractional-order internal model control and external adaptive control

Galvão

Hadjiloucas

2019

Review of Scientific Instruments

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A fractional-order internal model control technique is applied to a three-dimensional resistive-capacitive network to enforce desired closedloop dynamics of first order. In order to handle model mismatch issues resulting from the random allocation of the components within the network, the control law is augmented with a model-reference adaptive strategy in an external loop. By imposing a control law on the system to obey first order dynamics, a calibrated transient response is ensured. The methodology enables feedback control of complex systems with emergent responses and is robust in the presence of measurement noise or under conditions of poor model identification. Furthermore, it is also applicable to systems that exhibit higher order fractional dynamics. Examples of feedback-controlled transduction include cantilever positioning in atomic force microscopy or the control of complex de-excitation lifetimes encountered in many types of spectroscopies, e.g., nuclear magnetic, electron-spin, microwave, multiphoton fluorescence, Förster resonance, etc. The proposed solution should also find important applications in more complex electronic, microwave, and photonic lock-in problems. Finally, there are further applications across the broader measurement science and instrumentation community when designing complex feedback systems at the system level, e.g., ensuring the adaptive control of distributed physiological processes through the use of biomedical implants.

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“…PC: particleconserving, DOS: density of states, SC: superconductor (or superconducting, depending on context). Additional models that are amenable to solution by our approach include Majorana chains with twisted BCs 20 or longer-range (e.g., next-nearestneighbor) couplings 21 , dimerized Kitaev chains 22 , period-three hopping models 23 , as well as time-reversal-invariant TSC wires with spin-orbit coupling 24 , to name a few.…”

Section: Tailoring the Generalized Bloch Theorem To Surface Physimentioning

confidence: 99%

Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure

et al. 2018

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We describe a method for exactly diagonalizing clean D-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface. The specification of boundary conditions and interfaces can be easily adjusted to describe relaxation, reconstruction, or disorder away from the clean bulk regions of the system. Our diagonalization method builds on the generalized Bloch theorem [A. Alase et al., Phys. Rev. B 96, 195133 (2017)] and the fact that the bulk-boundary separation of the Schrödinger equation is compatible with a partial Fourier transform operation. Bulk equations may display unusual features because they are relative eigenvalue problems for non-Hermitian, bulk-projected Hamiltonians. Nonetheless, they admit a rich symmetry analysis that can simplify considerably the structure of energy eigenstates, often allowing a solution in fully analytical form. We illustrate our extension of the generalized Bloch theorem to multicomponent systems by determining the exact Andreev bound states for a simple SNS junction. We then analyze the Creutz ladder model, by way of a conceptual bridge from one to higher dimensions. Upon introducing a new Gaussian duality transformation that maps the Creutz ladder to a system of two Majorana chains, we show how the model provides a first example of a short-range chiral topological insulators hosting topological zero modes with a power-law profile. Additional applications include the complete analytical diagonalization of graphene ribbons with both zigzag-bearded and armchair boundary conditions, and the analytical determination of the edge modes in a chiral p + ip twodimensional topological superconductor. Lastly, we revisit the phenomenon of Majorana flat bands and anomalous bulk-boundary correspondence in a two-band gapless s-wave topological superconductor. Beside obtaining sharp indicators for the presence of Majorana modes through the use of the boundary matrix, we analyze the equilibrium Josephson response of the system, showing how the presence of Majorana flat bands implies a substantial enhancement in the 4π-periodic supercurrent. arXiv:1808.07555v1 [cond-mat.stat-mech]

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Entangled end states with fractionalized spin projection in a time-reversal-invariant topological superconducting wire

Cited by 21 publications

References 48 publications

Exact analytical solution of a time-reversal-invariant topological superconducting wire

Exact analytical solution of a time-reversal-invariant topological superconducting wire

Measurement and control of emergent phenomena emulated by resistive-capacitive networks, using fractional-order internal model control and external adaptive control

Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure

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