Advances towards graphene-based qubits

Hundreds, if not thousands of papers and talks in the past decade have started by stating that graphene and bilayer graphene are promising candidates for hosting spin qubits. Indeed, the small spin-orbit coupling and the low nuclear spin density, which characterize these materials, hold the promise of long spin-relaxation and -coherence times, which are essential qualities of good spin qubits.

The main reason why no spin-qubit has been demonstrated in graphene so far, is the novelty of the material, which has been isolated only in 2004. Furthermore, graphene poses the challenge of being a semimetal, i.e. it does not present a band gap that allows confining electrons by means of electrostatic gates. Initially, the most widely used approach to tackle this problem was to form the quantum dots by physically etching the graphene sheet. This etching approach was, however, mined by a fundamental problem: edge disorder, mostly introduced by the etching process itself, which prevented to reach clean quantum dots with a controlled number of electrons/holes and well tunable, spin-conserving tunneling barriers. A no-go for spin-qubits.

“The problem of edge disorder can be completely circumvented in bilayer graphene”, explains JARA-FIT Director Prof. Christoph Stampfer from the 2nd Institute of Physics at the RWTH Aachen University and the Peter Grünberg Institute (PGI-9) of the Forschungszentrum Jülich, “thanks to the fact that this material is essentially a tunable semiconductor”.  Indeed, the band-structure of bilayer graphene develops a gap in the presence of a perpendicularly applied electric field, a feature that allows using electrostatic gates to create quantum dots, similarly to what is done in silicon and gallium arsenide.

In the past decade, several groups have tried this route to create quantum dots in bilayer graphene. Until recently, however, essentially all devices were limited by leakage currents due to shortcomings in opening a clean and homogenous band gap through the whole devices. What really changed the field where two experiments from the group of Klaus Ensslin at ETH Zürich in 2018, who reported the first electrostatically induced quantum point contact [1] and the first gate-defined quantum dot in bilayer graphene [2]. “These experiments clearly set the direction one needs to go to explore quantum dots, and ultimately qubits, in bilayer graphene”, says Stampfer.

The Stampfer group was quick to follow these advancements, publishing its own first results on gate-defined quantum dots in bilayer graphene also in 2018 [3]. Since then, the progress has been fast, with more than a dozen of papers published by the Ensslin and the Stampfer groups – the two teams that are currently leading the field. Two of the last publications of the Stampfer group have been chosen as Editor’s Pick for the March 2021 edition of Applied Physics Letter, one of the two even gaining the cover page (see Fig. 1) [4,5]. “These two works reflect well the current effort in our lab”, says Stampfer.

One of two papers focuses on the excellent tunability obtained with the latest design of the quantum dot devices [5].  “In this work, we focused on the inter-dot coupling between two neighboring quantum dots”, explains Christian Volk, a post-doc in the Stampfer group and lead author of the paper. “Being able to tune this quantity over a wide range is an essential prerequisite for operating a so-called single-triplet qubit, which is one of the most versatile type of spin qubits. With the new design, we obtained a tuning range that is well comparable to what is typical for silicon and GaAs spin qubits.”

The same device allowed also exploring a unique and interesting aspect of bilayer graphene quantum-dots, namely the full valley-polarization of electrons and holes at moderate magnetic fields [6]. Electron and hole Bloch-states in bilayer graphene exhibit, in fact, a topological orbital moment with opposite signs for different valleys, as well as for electrons and holes. This causes a large and adjustable effective valley g-factor, which allows to achieve full valley polarization as a function of magnetic field and quasi particle index (electron or holes). This property makes bilayer-graphene quantum dots highly interesting for implementing spin-valley qubits – a type of qubit, which should be more resilient to noise than standard spin qubits [7].

“Improving the tunability of the devices is only part of our current effort”, says Luca Banszerus, who is leading the quantum-dot team in the Stampfer group. “To be able to implement spin and spin-valley qubits, we also need to be able to accurately manipulate and detect the states of dots”. For what concerns the manipulation of the dot states, Banszerus and colleagues have already reached an important milestone demonstrating high-frequency gate manipulation in a single-electron quantum dot in bilayer graphene [8]. This is not only a key requirement for qubit operations, but it also provides information on the lifetimes of the excited states in the dot. Applying a megahertz square-pulse to one of the finger gates, they have been able to extract a lower bound for the relaxation time of single-electron spin states in bilayer graphene of 0.5 ms. “This value is in line with what has been measured in similar experiments in quantum dots in semiconductors or in carbon nanotubes”, says Stampfer. “It tells us that there are no unexpected spin relaxation mechanisms – which is a good, even if unsurprising news. Unfortunately, with the current detection scheme we cannot investigate the true nature of spin relaxation in bilayer graphene. For this, we first need to achieve fast, if not single-shot, readout.”

Single-shot readout means the ability of detecting the occupation of the dot in real time, and is the one requirement that is still missing for realizing a spin qubit in bilayer graphene. In most of the current experiments, the information on the state of the dot is, in fact, inferred via transport spectroscopy, i.e. by measuring the current that is flowing through the dot itself, an approach that can only provide information on the average occupation of the dot.  Recently, Banszerus and colleagues have been able to demonstrate a different detection scheme, based on the dispersive read-out of a resonant circuit attached to one of the Ohmic contacts of the dot [4]. The technique turned out to be sensitive enough to accurately resolve the excited-state spectrum of the dot, but not for single-shot measurements. 

“There is still a lot of room for improvement”, says Banszerus. “It should be possible to gain a lot in sensitivity by improving the resonant circuit, possibly reaching the level needed for single-shot read-out. In parallel, we are going to pursue also the more conventional approach of using a charge sensor capacitively coupled to the dot, as it is done in semiconductor qubits. Charge detection in bilayer graphene quantum dot has already been demonstrated by the Ensslin group – even if still with limited bandwidth. I’m pretty confident that, in one way or the other, we are going to reach the single-shot limit.”  

This research is to large extent financed by Stampfer’s ERC Consolidator Grant “2D Materials for Quantum Technologies (2D4QT)”. “The goal of 2D4QT is to assess experimentally the potential of graphene-based heterostructures for quantum technology applications”, explains Stampfer. “In other words, we want to give quantitative answers to open questions such as what are the relaxation and coherence times of spin and valley qubits in bilayer graphene, and what can be gained by using isotopically purified carbon. Answering these questions requires continuous technological advancements. The progresses achieved in our lab and at ETH show that we are on the right track. I’m sure that the next years will be full of exciting developments.”

The original publications on the subject can be found in the journal Applied Physics Letters and Nano Letters:

Tunable interdot coupling in few-electron bilayer graphene double quantum dots
Electron-hole crossover in gate-controlled bilayer graphene quantum dots

References

• [1] H. Overweg et al., Electrostatically Induced Quantum Point Contacts in Bilayer Graphene, Nano Lett. 18, 553 (2018).
• [2] M. Eich et al., Spin and Valley States in Gate-defined Bilayer Graphene Quantum Dots, Phys. Rev. X 8, 031023 (2018).
• [3] L. Banszerus et al., Gate-defined electron-hole double dots in bilayer graphene, Nano Lett. 18, 4785 (2018).
• [4] L. Banszerus et al., Dispersive sensing of charge states in a bilayer graphene quantum dot, Appl. Phys. Lett. 118, 093104 (2021).
• [5] L. Banszerus et al., Tunable interdot coupling in few-electron bilayer graphene double quantum dots, Appl. Phys. Lett. 118, 103101 (2021)
• [6] L. Banszerus et al., Electron-hole crossover in gate-controlled bilayer graphene quantum dots, Nano Lett. 10, 7709 (2020).
• [7] D. Culcer et al, Valley-Based Noise-Resistant Quantum Computation Using Si Quantum Dots, Phys. Rev. Lett. 108, 126804 (2012); N. Rohling, and G. Burkard, Universal quantum computing with spin and valley states, New J. Phys. 14, 083008 (2012).
• [8] L. Banszerus et al., Pulsed-gate spectroscopy of single-electron spin states in bilayer graphene quantum dots, Phys. Rev. B 103, L081404 (2021).