Spin-valley coupling in single-electron bilayer graphene quantum dots

Abstract

Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μeV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the $$K$$ K and $$K^{\prime}$$ K ′ states below 20 μeV.

Single-shot readout in graphene quantum dots

“…Typical values around g v = 30 [17] ensure that at electron temperatures below 100 mK, the two lowest energy levels are valley polarized already at perpendicular magnetic fields B ⊥ > 50 mT. As we operate our device at much higher fields, above B ⊥ = 1.75 T, we can consider our QD as an effective two-level spin system with the ground state (GS) |K ↑ and the excited state (ES) |K ↓ energetically split by ∆E = ∆ SO + g s µ B B with the zero-field spin orbit splitting ∆ SO with typical values on the order of 60 µeV [20,22,31,32].…”

“…Compared to the mature Si-based technology, the development of quantum devices in graphene is in its infancy. Recent advances in the controllability of individual states in single QDs [17][18][19][20] and double QDs [21,22], as well as the implementation of charge detection [23], enable the realization of spin qubits based on electrostatically defined QDs in bilayer graphene. Major milestones such as qubit manipulation and detection have yet to be achieved to unlock the qubit potential of graphene.…”

Spin relaxation in a single-electron graphene quantum dot

“…In contrast to silicon, the valley states in BLG are associated with topological outof-plane magnetic moments, which originate from the finite Berry curvature close to the K-points and has opposite sign for the K and K -valley [30]. At zero magnetic field, the Kane-Mele type spin-orbit interaction [31] splits the four degenerate states into two ∆ SO [4,24] (see inset of Fig. 1c).…”

“…Thanks to the low spin-orbit interaction and low hyperfine coupling, graphene and bilayer graphene (BLG) have long been considered promising platforms for spin qubits [1]. Only recently, it has become possible to control single-electrons in BLG quantum dots (QDs) and to understand their spin-valley texture [2][3][4], while the relaxation dynamics have remained mostly unexplored [5,6]. Here, we report spin relaxation times (T 1 ) of single-electron states in BLG QDs.…”

“…In contrast, flat graphene and BLG exhibit both low hyperfine coupling and small, Kane-Mele type, spin-orbit interaction on the order of 40-80 µeV [4,[21][22][23][24], promising long spin lifetimes. BLG is particularly suitable for realizing highly tunable QDs [2,25], and important steps towards the realization of spin qubits have already been achieved -such as the implementation of charge detection [26,27], the investigation of the electron-hole crossover [28] and the measurement of the spin-orbit gap in BLG [4,24,29]. However, electrical measurements of the spin relaxation time have remained elusive until now.…”