| Issue |
Europhysics News
Volume 56, Number 2, 2025
Quantum Science and Technologies
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|---|---|---|
| Page(s) | 32 - 34 | |
| Section | Features | |
| DOI | https://doi.org/10.1051/epn/2025213 | |
| Published online | 06 May 2025 | |
Semiconductor quantum devices: from GaAs to graphene
ETH Zurich
Qubits have been realized in a number of systems, ranging from ion traps to superconducting qubits, to Rydberg atoms, to spin qubits in semiconductors and many more. Spin qubits offer the advantage of long coherence times, small device size and the prospect of integration with existing Si technology. The first charge and spin qubits were realized in GaAs-AlGaAs heterostructures because of the ease of fabrication and electronic quality of this material system. Now the community has moved on to Si-based devices driven by industrial players and the need for ever more complex device fabrication. Here we will showcase some results obtained in graphene, a new exotic material in this context, but with the same fundamental advantages as other group IV materials such as Si and Ge.
© European Physical Society, EDP Sciences, 2025
Two-dimensional systems of exceptional electronic quality have been realized in GaAs-AlGaAs heterostructures as testified by the discovery of the fractional quantum Hall effect. Nano-patterned top gates lead to the discovery of quantized conductance in quantum point contacts as well as quantum dots with single charge occupancy [1]. These two basic quantum devices in semiconductors have remained the same for basically all material systems and enabled the development of spin qubits based on the original theory proposal [2]. By coupling a quantum point contact capacitively to a quantum dot, the charge occupancy of the dot could be monitored without measuring direct transport through the dot [3]. This kind of charge detector was used for single shot measurements in quantum dots which enabled the so-called Elzermann-readout [4] that lead to the first spin lifetime measurement, T1, in quantum dots. This measurement technique is still used today for Si-MOSFET-based qubits using a single spin as a qubit [2]. Another approach to use the spin degree of freedom is based on spin-triplet qubits that use spin-blockade for spin-charge conversion as a read-out mechanism [5]. This development has continued in industry with a 12 qubit architecture in Si fabricated by INTEL and now available for researchers [6].
Graphene is another group IV element, that has weak spin-orbit interactions because carbon is a light element. Furthermore, 99% of naturally abundant carbon consists of 12C, which has zero total nuclear spin. Carbon-based materials in general and therefore graphene in particular are therefore promising host materials for spin qubits given the prospect of long spin coherence times. Graphene consists of a hexagonal arrangement of carbon atoms with two atoms per primitive unit cell. This results in the socalled Dirac cones at K and K’ points in the bandstructure [7]. Since there is no bandgap, electronic transport in graphene cannot be switched off and therefore insulating barriers cannot be produced by gate voltages. Etching graphene into nanoscale islands has not resulted in useful quantum devices [8]. Bilayer graphene comes to the rescue, since a vertical electric field breaks the inversion symmetry of the layers [9] and bandgaps of the order of 100 meV can be achieved with electric field of the order of 1 V/nm. Bilayer graphene is electronically very clean and displays high carrier mobilities if encapsulated with hexagonal boron nitride. When tuning top and backgate voltages, the vertical electric field and therefore the magnitude of the bandgap is tuned by the difference between the voltages. The position of the Fermi energy in the gap (or in the valence or conduction band) results from the effective sum of the voltages. This way one can create highly insulating barriers that can be used to electrostatically define quantum point contacts [10] and quantum dots [11] with an electronic quality comparable to the best devices in standard semiconductors, such as GaAs or Si. Since the entire potential landscape in graphene quantum devices is tuned by gate voltages, one can achieve electron or hole population or define double quantum dots with an electron in one dot and a hole in the other dot [12]. Also the valley degree-of-freedom, which is absent in GaAs and difficult to control in Si, becomes a source of interesting physics in graphene [13] and possibly the basis for a novel kind of qubit, namely a valley qubit.
The valley degree of freedom can be described in a spin formalism but originates form orbital wavefunctions. The valley states display a linear dependence on perpendicular magnetic field. This arises from the Berry curvature, which effectively causes a magnetic moment and underlines the notion of a valley g-factor, in analogy to the Zeeman spin g-factor. The valley g-factor depends on the details of the quantum dot potential and can be tuned to be gV= 10 - 100, i.e. much larger than the spin g-factor gS=2. This has fundamental consequences for the energy spectrum of graphene quantum dots, their behavior in magnetic field, possible ground states and degeneracies.
 |
Fig. 1 Schematic layout for an electrically tuned quantum dot in bilayer graphene. The stack starts from a bottom graphite backgate (red), a layer of hexagonal boron nitride (hBN, not shown), a stripe of bilayer graphene (dashed pattern), a layer of hBN (not shown), metallic split gate electrodes (green), an insulating layer of an oxide (not shown) and metallic finger gates (blue). The voltages on the graphite back gate and the split gates is tuned to maximize the gap and position the Fermi energy in the middle of the gap, such that the current along the bilayer graphene stripe has to flow in the narrow channel between the split gates. The chemical potential in this channel is then tuned locally by the finger gates (blue), either used to tune the height of a tunneling barrier or to control the number of charges on a confined region. |
For a one carrier state in graphene one would expect a degeneracy of 4, 2 for spin and 2 for valley. Because of the small but finite spin-orbit interaction in graphene [14] of ESO≈70 μeV, this state is split into two doublets, each of which consists of a Kramers pair with two states of opposite spin and opposite valley quantum number. In a perpendicular magnetic field these states are split by the valley Zeeman energy and a transition between these states requires a valley and a spin flip. If two carriers occupy a graphene quantum dot, the additional valley degree-of-freedom leads to a Hilbert space with 16 dimensions, in contrast to a 4-dimensional Hilbert space for doubly occupied quantum dots in Si or GaAs (1 singlet and 3 triplets). In graphene one has found experimentally that the ground state is a valley-singlet and spin-triplet [15], again very different from standard semiconductors. It turns out that the valley-triplet is again split by spin-orbit interactions leading to a non-degenerate ground state for 2 carrier occupancy.
 |
Fig. 2 Conductance through a graphene quantum dot as a function of one of the finger gate voltages from Fig. 1. Two situations are shown. Top: quantum dot is loaded with electrons starting from one electron. Bottom: quantum dot is loaded with holes. |
The findings about the energy spectrum of graphene have led to measurements of lifetimes for a number of states. Experimentally one finds values for the T1 time T1(spin)≈400 ms and for Kramers pairs (spin-valley) of T1(Kramers)≈40 s [16].
A number of other physical phenomena have been investigated using graphene quantum dots. This includes the Kondo effect both in the spin and valley domain [14]. Different blockade situations have been investigated, such as the conventional spin blockade, valley blockade as well as electron-hole blockade [15]. The valley degree-of-freedom leads to substantially modified and enriched physics situation that leave their mark in effects known from experiments in standard semiconductor quantum devices.
 |
Fig. 3 Schematic level diagram for a bilayer graphene quantum dot as a function of magnetic field B. At B=0, the quadruplet expected from spin and valley degeneracy is split into two doublets because of spin-orbit interactions. In a perpendicular magnetic field each doublet is split because of the valley Zeeman effect. A parallel magnetic field aligns the spins with the magnetic field and does not lift the degeneracy of the doublets. |
Twisting of graphene layers has led to the discovery of a number of phases, including superconductivity, ferromagnetism and correlated insulators. Using these tunable phases quantum devices such as Josephson junctions [17] and SQUIDs have been realized. It remains to be seen, whether it will be possible to realize more complex quantum devices such as e.g. transmon qubits based on twisted graphene layers. The possibility to realize quantum devices from different qubit platforms involving quantum dots on the one hand and Josephson junctions on the other hand in one and the same material platform opens new possibilities which usually require several materials.
Transition-metal-dichacogenides (TMDs) are another family of materials that can be exfoliated and enable transport measurements. Again first electronic constrictions and quantum dots [18] have been realized but their quality needs to be improved. The elastic mean free path in TMDs is typically 10 nm or less because of residual impurities. Efforts are under way to make cleaner TMD layers by chemical vapor deposition and other techniques. So far excellent results have been obtained by optical experiments covering small areas, but the quality of the material is not good enough yet for quantum transport devices.The strong spin-orbit interactions of TMDs or the ferromagnetic behavior of other 2D insulators can be used when these materials are van-der Waals bonded for example with bilayer graphene. This offers even more tunable degrees of freedom in hybrid graphene quantum devices and exciting perspectives for the utilization of electronic phases with device functionality.
This article summarizes work done by a large number of talented colleagues: Christoph Adam, Dominick Bischoff, Artem Denisov, Fokko De Vries, Hadrien Duprez, Marius Eich, Rebekka Garreis, Lisa Gächter, Jonas Gerber, Carolin Gold, Annika Kurzmann, Chuyao Tong, Wister Huang, Michele Masseroni, Elias Portoles, Riccardo Pisoni, Peter Rickhaus, Giulia Zheng and Thomas Ihn.
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All Figures
|
Fig. 1 Schematic layout for an electrically tuned quantum dot in bilayer graphene. The stack starts from a bottom graphite backgate (red), a layer of hexagonal boron nitride (hBN, not shown), a stripe of bilayer graphene (dashed pattern), a layer of hBN (not shown), metallic split gate electrodes (green), an insulating layer of an oxide (not shown) and metallic finger gates (blue). The voltages on the graphite back gate and the split gates is tuned to maximize the gap and position the Fermi energy in the middle of the gap, such that the current along the bilayer graphene stripe has to flow in the narrow channel between the split gates. The chemical potential in this channel is then tuned locally by the finger gates (blue), either used to tune the height of a tunneling barrier or to control the number of charges on a confined region. |
| In the text | |
|
Fig. 2 Conductance through a graphene quantum dot as a function of one of the finger gate voltages from Fig. 1. Two situations are shown. Top: quantum dot is loaded with electrons starting from one electron. Bottom: quantum dot is loaded with holes. |
| In the text | |
|
Fig. 3 Schematic level diagram for a bilayer graphene quantum dot as a function of magnetic field B. At B=0, the quadruplet expected from spin and valley degeneracy is split into two doublets because of spin-orbit interactions. In a perpendicular magnetic field each doublet is split because of the valley Zeeman effect. A parallel magnetic field aligns the spins with the magnetic field and does not lift the degeneracy of the doublets. |
| In the text | |
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