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Spin and valley control in semiconductor and carbon quantum dots

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Coherent control of single electron spins in quantum dots has been implemented in a variety of experimental demonstrations. However, to use electron spins as qubits, the spin coherence time should significantly exceed the time for elementary operations. In typical semiconductor materials, the hyperfine coupling to a large ensemble of nuclear spins limits the electron coherence. This brings up interesting theoretical questions, e.g., regarding the possibility of preparing a nuclear spin state that allows for prolonged electron coherence [1]. It turns out that the nuclear spin ensemble in a can even be taken advantage of for spin qubit manipulation using Landau-Zener transitions, by using the so-called singlet-triplet T+ qubit [2]. An alternative strategy to achieve long spin coherence is to use materials with lower nuclear spin content, such as silicon or carbon. Carbon has emerged as an interesting alternative material for spin qubits, due to both the low concentration of nuclear spins and relatively weak spin-orbit coupling. However, the formation of quantum dots in graphene is a non-trivial task due to the absence of a band gap and the related effect of Klein tunneling [3]. Interestingly, electrons in some carbon-based quantum dots comprise a degree of freedom in addition to spin: The existence of two Dirac cones in the graphene band structure leads to the valley degree of freedom which can be coherently manipulated with oscillatory fields in a similar way as the spin [4]. The valley degeneracy also enters the hyperfine interactions with remaining 13C nuclear spins and is manifestated in the spin-valley blockade effect [5]. Finally, spin-orbit coupling in graphene and (more importantly) carbon nanotubes affects the spin blockade as well as the spin lifetime [6].

[1] H. Ribeiro and G. Burkard, Phys. Rev. Lett. 102, 216802 (2009). [2] H. Ribeiro, J. R. Petta, and G. Burkard, Phys. Rev. B 82 , 115445 (2010). [3] B. Trauzettel, D. Bulaev, D. Loss, and G. Burkard, Nature Phys. 3, 192 (2007). [4] A. Pályi and G. Burkard, Phys. Rev. Lett. 106, 086801 (2011). [5] A. Pályi and G. Burkard, Phys. Rev. B 80 , 201404 (2009); ibid. 82, 155424 (2010). [6] P. R. Struck and G. Burkard, Phys. Rev. B 82 , 125401 (2010).

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