Hybrid Spin and Valley Quantum Computing with Singlet-Triplet Qubits

Rohling, Niklas; Russ, Maximilian; Burkard, Guido

doi:10.1103/physrevlett.113.176801

Cited by 36 publications

(41 citation statements)

References 80 publications

(103 reference statements)

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“…Figure 3 also shows that for screened impurities, τ v is decreasing with increasing effective Bohr radius, whereas for unscreened impurities τ v shows an opposite trend. As the only difference between the corresponding results (27) and (43) is the appearance of K in the latter, the different trends are explained by the relatively fast decay of K with increasing effective Bohr radius.…”

Section: Screened Impuritymentioning

confidence: 73%

“…The result was obtained by numerically computing the sum in Eq. (27), which converges due to the Gaussian decay of P 2 (k). The unit on the vertical axis of Fig.…”

Section: A Unscreened Impuritiesmentioning

confidence: 99%

“…3, where the valley relaxation time corresponding to the unscreened result (27), for grapheneimpurity distance d = 0, is shown as the blue line. The result was obtained by numerically computing the sum in Eq.…”

Section: A Unscreened Impuritiesmentioning

confidence: 99%

“…Importantly, the derivations of Eqs. (27) and (43) rely on our specific model for the electronic wave function (LCAO wave functions built from 2D Gaussian atomic wave functions) and the specific type of disorder (random, uncorrelated Coulomb impurities); therefore, it is possible that the notion of the effective intervalley dielectric constant is restricted to the present model only.…”

Section: Screened Impuritymentioning

confidence: 99%

“…Recently, ways to control and measure the valley degree of freedom (or valley index, for short) in these materials have been proposed [1][2][3][4][5][6][7][8] and tested experimentally [9][10][11][12][13][14][15][16]. The valley index is also being actively considered as a carrier of quantum information [14,[17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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Valley relaxation in graphene due to charged impurities

Boross

Pályi

2015

Phys. Rev. B

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Monolayer graphene is an example of materials with multivalley electronic structure. In such materials, the valley index is being considered as an information carrier. Consequently, relaxation mechanisms leading to loss of valley information are of interest. Here, we calculate the rate of valley relaxation induced by charged impurities in graphene. A special model of graphene is applied, where the p z orbitals are two-dimensional Gaussian functions, with a spatial extension characterized by an effective Bohr radius a eB . We obtain the valley relaxation rate by solving the Boltzmann equation, for the case of noninteracting electrons, as well as for the case when the impurity potential is screened due to electron-electron interaction. For the latter case, we take into account local-field effects and evaluate the dielectric matrix in the random phase approximation. Our main findings are as follows: (i) The valley relaxation rate is proportional to the electronic density of states at the Fermi energy. (ii) Charged impurities located in the close vicinity of the graphene plane, at distance d 0.3Å, are much more efficient in inducing valley relaxation than those farther away, the effect of the latter being suppressed exponentially with increasing graphene-impurity distance d. (iii) Both in the absence and in the presence of electron-electron interaction, the valley relaxation rate shows pronounced dependence on the effective Bohr radius a eB . The trends are different in the two cases: In the absence (presence) of screening, the valley relaxation rate decreases (increases) for increasing effective Bohr radius. This last result highlights that a quantitative calculation of the valley relaxation rate should incorporate electron-electron interactions as well as an accurate knowledge of the electronic wave functions on the atomic length scale.

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Section: Screened Impuritymentioning

confidence: 73%

“…The result was obtained by numerically computing the sum in Eq. (27), which converges due to the Gaussian decay of P 2 (k). The unit on the vertical axis of Fig.…”

Section: A Unscreened Impuritiesmentioning

confidence: 99%

Section: A Unscreened Impuritiesmentioning

confidence: 99%

Section: Screened Impuritymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Valley relaxation in graphene due to charged impurities

Boross

Pályi

2015

Phys. Rev. B

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Quantum Computing with Solid‐State Systems

Burkard

Loss

2016

Quantum Information

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Ferroelectricity Tailored Valley Splitting in Monolayer WTe₂/YMnO₃ Heterostructures: A Route toward Electrically Controlled Valleytronics

Song

Wang

2017

Adv Elect Materials

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polarized quantum states, (2) controllably switching between different states, and (3) detecting the states themselves. Many strategies have been proposed to lift the valley degeneracy, such as optical pumping, [10,11] magnetic doping, [12,13] and proximity. [14,15] Previous results show that the valley splitting can be switched by a magnetic field. [16][17][18][19] Recently, a remarkable progress has been made in utilizing the interfacial exchange field to enhance the magnetic control on valley splitting. [20] A valley splitting of 2.5 meV T −1 has been achieved in monolayer WSe 2 deposited on a ferromagnetic EuS substrate. [20] The modulation is an order of magnitude higher than the traditional 0.2 meV T −1 . [20] However, the electrical control on the spin and valley transport is more desirable and practical for valleytronic applications. Multiferroic materials provide a fertile background to control one degree of freedom through the other. [21] Since it is still an open question whether the coupling between valley and ferroelectricity is realizable in a specific system, the electronic properties of monolayer WTe 2 on multiferroic YMnO 3 are investigated. It is found that the coupling appears between valley and ferroelectricity. For a valley-polarized monolayer, a valley splitting of 36 meV is altered when the polarization of the multiferroic substrate is reversed. The spontaneous ferroelectric polarization that can be switched by an electric field shows potential in the electrical control on valley degree of freedom. Considering different multiferroic materials and the artificial design of improper ferroelectrics, [22,23] we further argue that the multiferroic intermediate is an innovating approach toward the electrical control on valley degree, which is a superior approach than the traditional magnetic one.According to previous results, [24] the depolarization field in proper ferroelectric films, for example, BaTiO 3 or PbTiO 3 , strongly suppresses the tendency toward single-domain ferroelectric state, especially in its ultrathin case. Contrary to the proper ones, the improper ferroelectrics like YMnO 3 do not present a critical thickness below which the ferroelectricity disappears. The spontaneous polarization persists in an isolated slab of YMnO 3 . Its value is comparable to that in bulk. So it would be advantageous to consider YMnO 3 substrate and investigate the coupling between valley and ferroelectricity.Hexagonal YMnO 3 with a space group of P6 3 cm has an improper ferroelectricity. [25] Its ferroelectric Curie temperature is about 880 K, [26] much higher than its Néel temperature Control of valley degree of freedom in monolayer transition-metal dichalcogenide (TMDC) has been realized by using optical pumping and magnetic fields. However, an electrical approach is missing and has potential for practical applications. In this paper, valley/ferroelectricity coupling is demonstrated for the first time in a monolayer WTe 2 /YMnO 3 heterostructure. Tunable valley splitting by an electric field is predict...

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Hybrid Spin and Valley Quantum Computing with Singlet-Triplet Qubits

Cited by 36 publications

References 80 publications

Valley relaxation in graphene due to charged impurities

Valley relaxation in graphene due to charged impurities

Quantum Computing with Solid‐State Systems

Ferroelectricity Tailored Valley Splitting in Monolayer WTe₂/YMnO₃ Heterostructures: A Route toward Electrically Controlled Valleytronics

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Hybrid Spin and Valley Quantum Computing with Singlet-Triplet Qubits

Cited by 36 publications

References 80 publications

Valley relaxation in graphene due to charged impurities

Valley relaxation in graphene due to charged impurities

Quantum Computing with Solid‐State Systems

Ferroelectricity Tailored Valley Splitting in Monolayer WTe2/YMnO3 Heterostructures: A Route toward Electrically Controlled Valleytronics

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Product

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Ferroelectricity Tailored Valley Splitting in Monolayer WTe₂/YMnO₃ Heterostructures: A Route toward Electrically Controlled Valleytronics