The main characteristics of good qubits are long coherence times in combination with fast operating times. It is well known that carbon-based materials could increase the coherence times of spin qubits, which are among the most developed solid-state qubits. Here, we propose how to form spin qubits in graphene quantum dots. A crucial requirement to achieve this goal is to find quantum-dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with armchair boundaries. The most remarkable new feature of the proposed spin qubits is that, in an array of many qubits, it is possible to couple any two of them via Heisenberg exchange with the others being decoupled by detuning. This unique feature is a direct consequence of the quasi-relativistic spectrum of graphene.

Spin qubits in graphene quantum dots

Transport measurements through a few-electron circular quantum dot in bilayer graphene display bunching of the conductance resonances in groups of four, eight, and twelve. This is in accordance with the spin and valley degeneracies in bilayer graphene and an additional threefold ``minivalley degeneracy'' caused by trigonal warping. For small electron numbers, implying a small dot size and a small displacement field, a two-dimensional $s$ shell and then a $p$ shell are successively filled with four and eight electrons, respectively. For electron numbers larger than 12, as the dot size and the displacement field increase, the single-particle ground state evolves into a threefold degenerate minivalley ground state. A transition between these regimes is observed in our measurements and can be described by band-structure calculations. Measurements in the magnetic field confirm Hund's second rule for spin filling of the quantum dot levels, emphasizing the importance of exchange interaction effects.

Shell Filling and Trigonal Warping in Graphene Quantum Dots.

Quantum information science and engineering (QISE)—which entails the use of quantum mechanical states for information processing, communications, and sensing—and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid‐state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials‐based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next‐generation quantum devices for scalable and practical quantum applications.

Nanomaterials for Quantum Information Science and Engineering

The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Here we report on the interplay between spin–orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin–orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin–orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin–orbit interaction. The Kondo effect has been observed in a variety of systems, including carbon nanotube quantum dots and graphene in the presence of impurities. Here, the authors report the observation of the Kondo effect in bilayer graphene quantum dots and study its interplay with weak spin-orbit coupling.

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Kondo effect and spin-orbit coupling in graphene quantum dots.

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 $$K$$
 and $$K^{\prime}$$
 states below 20 μeV. Understanding the interaction between spin and valley degrees of freedom in graphene-based quantum dots underpins their applications in electronics and quantum information. Here, the authors study the low-energy spectrum and resolve the spin-valley coupling in single-electron quantum dots in bilayer graphene.

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

Quantum states in graphene are 2-fold degenerate in spins, and 2-fold in valleys. Both degrees of freedom can be utilized for qubit preparations. In our bilayer graphene quantum dots, we demonstrate that the valley g-factor gv, defined analogously to the spin g-factor gs for valley splitting in a perpendicular magnetic field, is tunable by over a factor of 4 from 20 to 90, by gate voltage adjustments only. Larger gv results from larger electronic dot sizes, determined from the charging energy. On our versatile device, bipolar operation, charging our quantum dot with charge carriers of the same or the opposite polarity as the leads, can be performed. Dots of both polarities are tunable to the first charge carrier, such that the transition from an electron to a hole dot by the action of the plunger gate can be observed. Addition of gates easily extends the system to host tunable double dots.

Agnese Sacchi

Papers

Tunable Valley Splitting and Bipolar Operation in Graphene Quantum Dots