Universal quantum computing with spin and valley states

Rohling, Niklas; Burkard, Guido

doi:10.1088/1367-2630/14/8/083008

Cited by 83 publications

(100 citation statements)

References 60 publications

(114 reference statements)

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“…We note that the projection operator over the whole antisymmetric subspace of the (1, 1)-sector can be written as [45] (see appendix B),…”

Section: Naming Basis States and Projection Operatorsmentioning

confidence: 99%

“…This case has been extensively treated in [45]. For later reference and readability we report the resulting effective Hamiltonian,…”

Section: Zero Spin-orbit Splitting (∆ = 0)mentioning

confidence: 99%

“…For simplicity we restrict each dot to the lowest orbital and we consider the system filled with two electrons. Starting from the model introduced in [45], we add the spin-orbit interaction and we find a low energy effec-tive Hamiltonian for the case where each dot is occupied by one electron. We also investigate the situations where the spin-orbit splitting is different for each dot and where we include the effects of a magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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Effective theory of monolayer TMDC double quantum dots

2018

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Monolayer Transition Metal Dichalcogenides (TMDCs) are promising candidates for quantum technologies, such as quantum dots, because they are truly two-dimensional semiconductors with a direct band gap. In this work, we analyse theoretically the behaviour of a double quantum dot (DQD) system created in the conduction band of these materials, with two electrons in the (1,1) charge configuration. Motivated by recent experimental progress, we consider several scenarios, including different spin-orbit splittings in the two dots and including the case when the valley degeneracy is lifted due to an insulating ferromagnetic substrate. Finally, we discuss in which cases it is possible to reduce the low energy subspace to the lowest Kramers pairs. We find that in this case the low energy model is formally identical to the Heisenberg exchange Hamiltonian.

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“…We note that the projection operator over the whole antisymmetric subspace of the (1, 1)-sector can be written as [45] (see appendix B),…”

Section: Naming Basis States and Projection Operatorsmentioning

confidence: 99%

“…This case has been extensively treated in [45]. For later reference and readability we report the resulting effective Hamiltonian,…”

Section: Zero Spin-orbit Splitting (∆ = 0)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effective theory of monolayer TMDC double quantum dots

2018

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“…In these materials, electrons can populate multiple low-energy states that are well separated in momentum space, known as valley. The electron's "valley address," or the valley degree of freedom, provides an additional quantum index which can be harnessed for new paradigm of classical and quantum information processing [12]. Valleytronics, alongside with spintronics [13], photonics, and plasmonics [14], has been proposed as a candidate system to replace the aging CMOS technology [15].…”

Section: Introductionmentioning

confidence: 99%

Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve, and universal reversible logic gate

et al. 2017

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Despite much anticipation of valleytronics as a candidate to replace the aging complementary metal-oxidesemiconductor (CMOS) based information processing, its progress is severely hindered by the lack of practical ways to manipulate valley polarization all electrically in an electrostatic setting. Here, we propose a class of all-electric-controlled valley filter, valve, and logic gate based on the valley-contrasting transport in a merging Dirac cones system. The central mechanism of these devices lies on the pseudospin-assisted quantum tunneling which effectively quenches the transport of one valley when its pseudospin configuration mismatches that of a gate-controlled scattering region. The valley polarization can be abruptly switched into different states and remains stable over semi-infinite gate-voltage windows. Colossal tunneling valleypseudomagnetoresistance ratio of over 10000% can be achieved in a valley-valve setup. We further propose a valleytronic-based logic gate capable of covering all 16 types of two-input Boolean logics. Remarkably, the valley degree of freedom can be harnessed to resurrect logical reversibility in two-input universal Boolean gate. The (2+1) polarization states (two distinct valleys plus a null polarization) reestablish one-to-one inputto-output mapping, a crucial requirement for logical reversibility, and significantly reduce the complexity of reversible circuits. Our results suggest that the synergy of valleytronics and digital logics may provide new paradigms for valleytronic-based information processing and reversible computing. Despite much anticipation of valleytronics as a candidate to replace the aging complementary metal-oxidesemiconductor (CMOS) based information processing, its progress is severely hindered by the lack of practical ways to manipulate valley polarization all electrically in an electrostatic setting. Here, we propose a class of all-electric-controlled valley filter, valve, and logic gate based on the valley-contrasting transport in a merging Dirac cones system. The central mechanism of these devices lies on the pseudospin-assisted quantum tunneling which effectively quenches the transport of one valley when its pseudospin configuration mismatches that of a gate-controlled scattering region. The valley polarization can be abruptly switched into different states and remains stable over semi-infinite gate-voltage windows. Colossal tunneling valley-pseudomagnetoresistance ratio of over 10 000% can be achieved in a valley-valve setup. We further propose a valleytronic-based logic gate capable of covering all 16 types of two-input Boolean logics. Remarkably, the valley degree of freedom can be harnessed to resurrect logical reversibility in two-input universal Boolean gate. The (2 + 1) polarization states (two distinct valleys plus a null polarization) reestablish one-to-one input-to-output mapping, a crucial requirement for logical reversibility, and significantly reduce the complexity of reversible circuits. Our results suggest that the synergy of va...

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“…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%

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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Universal quantum computing with spin and valley states

Cited by 83 publications

References 60 publications

Effective theory of monolayer TMDC double quantum dots

Effective theory of monolayer TMDC double quantum dots

Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve, and universal reversible logic gate

Valley relaxation in graphene due to charged impurities

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