Researchers find evidence of long-lived valley states in bilayer graphene quantum dots

Many research initiatives in physics and engineering laboratories center around the topic of what physical system and which degrees of freedom within that system may be utilized to encode quantum bits of information, or qubits, in the context of quantum computing.

Most people already agree that superconducting qubits, spin qubits, and qubits encoded in the motion of trapped ions are the best options for future real-world uses of quantum computing; however, other systems still require further understanding, which makes them interesting targets for basic research.

Rebekka Garreis, Chuyao Tong, Wister Huang, and their colleagues in the group of Professors Klaus Ensslin and Thomas Ihn from the Department of Physics at ETH Zurich have been investigating the possibility of encoding quantum information using another degree of freedom of bilayer graphene (BLG) quantum dots, which are known to be a potential platform for spin qubits.

Their most recent discoveries, which they co-authored with researchers from Japan's National Institute for Materials Science and recently published in Nature Physics, demonstrate that the so-called valley degree of freedom in BLG is linked to incredibly long-lived quantum states, making them worthy of further investigation as a potential resource for solid-state quantum computing.

The lattice structure contains everything.

A single layer of carbon atoms bonded together in a hexagonal lattice arrangement makes up the two-dimensional substance known as graphene. Graphene is one of the strongest materials on Earth, despite its sheet-like appearance; several industry sectors are very interested in its mechanical and electrical qualities.

The technology the researchers utilized, called bilayer graphene, consists of two layers of carbon atoms stacked on top of one another. Since they don't have the distinctive energy band gap seen in semiconductors and, most notably, insulators, graphene and BLG are both semimetals. Nevertheless, by applying an electric field perpendicular to the plane of the sheets, an adjustable band gap may be constructed in BLG.

In order to employ BLG as a host material for quantum dots—which are 'boxes' on the nanoscale that may confine one or more electrons—a band gap must be opened. Quantum dots, which are often created in semiconductor host materials, provide exceptional control over individual electrons. They are therefore a crucial platform for spin qubits, which are systems in which the degree of freedom of the electron spin contains quantum information.

Researchers studying various qubit candidates must characterize their coherence properties because, compared to classical information, quantum information is much more susceptible to environmental corruption, making it less suitable for computational tasks. These properties indicate how well and how long quantum information can survive in a qubit system.

The spin-orbit interaction, which creates an undesired coupling between the electron spin and the host lattice vibrations, and the hyperfine interaction between the electron spin and the nearby nuclear spins can both lead to electron spin decoherence in the majority of conventional quantum dots.

Because spin-orbit coupling and hyperfine interaction are poor in graphene and other carbon-based materials, graphene quantum dots are particularly attractive to spin qubits. The findings published by Garreis, Tong, and associates provide one additional encouraging aspect of the situation.

Certain microscopy methods can be used to observe the hexagonal lattice of BLG.

Momentum space has the same hexagonal symmetry as so-called real space, with the lattice's vertices representing the momentum values of the free electrons on the lattice rather than the actual positions of carbon atoms. The local minima and maxima of the energy landscape, or the locations where the conduction and valence bands converge, are where free electrons are located in momentum space.

We refer to these energy extremes as troughs. Two degenerate energy valleys, or regions with the same electron energy but opposing electron momentum values, are required to exist in BLG due to the hexagonal symmetry. Since valleys in graphene are sometimes referred to as pseudo-spins, this degree of freedom in the valley may be addressed in a manner similar to that of electron spin in BLG.

Although valley states in bilayer graphene were previously identified, it was not apparent if they could be used as useful qubits up to this point.

A lot of promise exists in the valley.

A double quantum dot, or two dots with adjustable coupling, was taken into consideration in BLG by Garreis, Tong, and colleagues, who studied the relaxation time for valley and spin states. The relaxation period determines the temporal scale during which the system changes from one spin state or valley state to another, loses energy throughout the relaxing process, and is no longer appropriate for performing more qubit operations.

The relaxation periods of valley states are found to be longer than half a second, which suggests that future valley qubits may exhibit coherence features.

The measurement of spin relaxation time in the BLG double quantum dot yields a value below 25 ms, which is in excellent agreement with spin relaxation periods observed in semiconductor quantum dots but significantly shorter than the relaxation time for valley states. Crucially, both values are suitable for excellent qubit reading and manipulation.

The researchers also point out areas in the study that require more theoretical and experimental exploration. They present data demonstrating how the relaxation periods for spin and valley states rely on two factors that are thought to be important for the relaxation dynamics of the states.

One parameter is the energy detuning, which is the difference in energy between the ground states of two different double quantum dot configurations. By adjusting the energy differential between the states participating in the relaxation process, the detuning may be changed. The other parameter, which is referred to as the inter-dot coupling, controls the ease with which an electron from one quantum dot can "trespass" into the domain of another dot.

The phenomena reported by the authors defy explanations based on the mechanics typically involved in quantum-dot spin qubits. It is demonstrated that the relaxation period increases with increasing energy detuning, in contrast to what has been observed in other systems. Surprisingly, the valley relaxation time remains constant when the inter-dot coupling is changed.

It is evident that in order to determine which parameters could be most useful for controlling future valley qubits, a deeper comprehension of the processes influencing valley and spin relaxation durations is required. In the meanwhile, the research of Garreis, Tong, and associates supports expanding the field of solid-state quantum computing by including valley states in BLG quantum dots.

Provided by ETH Zurich