Voltage-controlled Hubbard spin transistor

Yousefjani, Rozhin; Bose, Sougato; Bayat, Abolfazl

doi:10.1103/physrevresearch.3.043142

Cited by 5 publications

(4 citation statements)

References 89 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To obtain very high values of fidelity in many QST problems, the presence of localized eigenstates are instrumental [53][54][55][58][59][60][61][62].…”

Section: Eigenvectors and Localizationmentioning

confidence: 99%

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Serra¹,

Ferrón²,

Osenda³

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two diﬀerent values. We work out the exact solutions in the one- excitation sub-space. Regarding the problem of quantum state transfer, we use the solution and some theorems concerning the approximation of irrational numbers, to show the appearance of conclusive pretty good transmission for chains with particular lengths. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two. The set of spin chains that shows pretty good transmission is a subset of the family with an exact solution. Using perturbation theory, we thoroughly analyze the case when one of the exchange coupling strengths is orders of magnitude larger than the other. This strong coupling limit allows us to study, in a simple way, the appearance of pretty good transmission. The use of analytical closed expressions for the eigenvalues, eigenvectors, and transmission probabilities allows us to obtain the precise asymptotic behavior of the time where the pretty good transmission is observed. Moreover, we show that this time scales as a power law whose exponent is an increasing function of the chain length. We also discuss the crossover behavior obtained for the pretty good transmission time between the regimes of strong coupling limit and the one observed when the exchange couplings are of the same order of magnitude.

show abstract

“…To obtain very high values of fidelity in many QST problems, the presence of localized eigenstates are instrumental [53][54][55][58][59][60][61][62].…”

Section: Eigenvectors and Localizationmentioning

confidence: 99%

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Serra¹,

Ferrón²,

Osenda³

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…The SSH chains have increasingly attracted attention because they show localised states with topological properties [48]. The presence of topological, or non-topological, localised eigenstates on the extremes of the chain results in very high transmission fidelities [48][49][50][51][52][53]. Moreover, SSH chains are related to a number of experimental implementations, such as transmon chains [47] or quantum electrodynamics (QED) setups [54,55].…”

Section: Introductionmentioning

confidence: 99%

The scaling law of the arrival time of spin systems that present pretty good transmission

Serra,

Ferrón,

Osenda

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The pretty good transmission scenario implies that the probability of sending one excitation from one extreme of a spin chain to the other can reach values arbitrarily close to the unity just by waiting a time long enough. The conditions that ensure the appearance of this scenario are known for chains with different interactions and lengths. Sufficient conditions for the presence of pretty good transmission depend on the spectrum of the Hamiltonian of the spin chain. Some works suggest that the time $t_{\varepsilon}$ at which the pretty good transmission takes place scales as $1/(|\varepsilon|)^{f(N)}$, where $\varepsilon$ is the difference between the probability that a single excitation propagates from one extreme of the chain to the other and the unity, while $f(N)$ is an unknown function of the chain length. In this paper, we show that the exponent is not a simple function of the chain length but a power law of the number of linearly independent irrational eigenvalues of the one-excitation block of the Hamiltonian that enter into the expression of the probability of transmission of one excitation. We explicitly provide examples of a chain showing that the exponent changes when the couplings between the spins change while the length remains fixed. For centrosymmetric spin chains the exponent is at most $N/2$.

show abstract

“…The systems of low dimensionality (1D and 2D) [29,30], discussed above, have been widely used in the proposals for quantum transistors [6,18,[31][32][33][34][35][36][37][38][39][40], and studied using the approximation of the envelope function. In these systems, the confined regions are much larger than the atomic scale, and of the order of a few tens of the quasi-particle wavelength (the quasi-particle wavelength is around 400 Å in GaAs).…”

Section: Introductionmentioning

confidence: 99%

Calculation method for the conductance of mesoscopic systems: assembly of Tight Binding Hamiltonians with spin effects—revisited

Silva

Mendoza

2023

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

We discretize the Schr"odinger equation in the approximation of the effective mass for the 2DEG of GaAs, without magnetic field and on the other hand, with magnetic field. This discretization leads naturally to Tight Binding Hamiltonians in the approximation of the effective mass. An analysis of this discretization allows us to gain insight into the role of site and hopping energies, which allows us to model the Tight Binding Hamiltonian assembly with spin: Zeeman and spin-orbit coupling effects, especially the case Rashba.With this tool we can assemble Hamiltonians of quantum boxes, Aharanov-Bohm interferometers, anti-dots lattices and effects of imperfections, as well as disorder in the system. The extension to mount quantum billiards is natural. We also explain here how to adapt the recursive equations of Green's functions for the case of spin modes, apart from transverse modes, for the calculation of conductance in these mesoscopic systems. The assembled Hamiltonians allow to identify the matrix elements (depending on the different parameters of the system) associated with splitting or spin flipping, which gives a starting point to model specific systems of interest, manipulating certain parameters. In general, the approach of this work allows us to clearly see the relationship between the wave and matrix description of quantum mechanics. We discuss here also, the extension of the method for 1D and 3D systems, for the extension apart from the first neighbors and for the inclusion of other types of interaction. The way we approach the method, has the objective of showing how specifically the site and hopping energies change in the presence of new interactions. This is very important in the case of spin interactions, because by looking at the matrix elements (site or hopping) we can directly identify the conditions that can lead to splitting, flipping or a mixture of these effects. Which is essential for the design of devices based on spintronics. Finally, we discuss spin-conductance modulation (Rashba spin precession) for the states of an open quantum dot (resonant states). Unlike the case of a quantum wire, the spin-flipping observed in the conductance is not perfectly sinusoidal, there is an envelope that modulates the sinusoidal component, which depends on the discrete-continuous coupling of the resonant states.

show abstract

Voltage-controlled Hubbard spin transistor

Cited by 5 publications

References 89 publications

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

The scaling law of the arrival time of spin systems that present pretty good transmission

Calculation method for the conductance of mesoscopic systems: assembly of Tight Binding Hamiltonians with spin effects—revisited

Contact Info

Product

Resources

About