Periodic Reporting for period 1 - MaGnum (Majorana bound states in Ge/SiGe heterostructures)
Reporting period: 2019-04-01 to 2021-03-31
Problem/issue being addressed:
Each particle has its antiparticle, and upon bringing them in close vicinity, they annihilate (they disappear). An interesting question is therefore: what happens if a particle is its own antiparticle? Any such particle can only be created as a pair and whenever one disappears, the other must disappear as well. In this sense, a pair of such particles are very robust if they are brought far apart from each other: no local perturbation can destroy it since, due to its locality, it does not affect its pair. Although such particles have not been reported, certain excitations in semiconductors provide the same features: creating the excitation occurs through the same operator as annihilating the excitation. Therefore, these excitations can also only exist in pairs, and creating them spatially separated protects them from local perturbations. Such semiconductor excitations are called Majorana fermions.
Importance for society
Once created in low-dimensional semiconductors, moving these Majorana fermions with respect to each other follows different laws than the three-dimensional world suggests. For example moving one particle around the other, in a two-dimensional world, is related to a phase acquisition. While this feature is in itself intriguing, and even more, it is also useful: so-called braiding (i.e. moving around with respect to each other) of Majorana fermions can be used to perform simple quantum operations. Eventually, Majorana fermions may be important building blocks for quantum computers.
Overall objectives
Majorana fermions are predicted to emerge at the ends of a one-dimensional semiconductor proximitized to a superconductor if the semiconductor hosts a large spin-orbit field perpendicular to the wire and it is subject to a Zeeman magnetic field perpendicular to the spin-orbit field. While these conditions have been fulfilled and some evidence for Majorana bound states (MBS) have been provided, several open questions remain. Importantly, most studies have been performed in one kind of material system, namely InAs. However, holes in germanium are a promising alternative. The objectives of this project are demonstration of controlled confinement of hole states (which is used to build a one-dimensional wire), observation of large spin-orbit interaction, and development of high-transparency superconductor-germanium contacts.
Each particle has its antiparticle, and upon bringing them in close vicinity, they annihilate (they disappear). An interesting question is therefore: what happens if a particle is its own antiparticle? Any such particle can only be created as a pair and whenever one disappears, the other must disappear as well. In this sense, a pair of such particles are very robust if they are brought far apart from each other: no local perturbation can destroy it since, due to its locality, it does not affect its pair. Although such particles have not been reported, certain excitations in semiconductors provide the same features: creating the excitation occurs through the same operator as annihilating the excitation. Therefore, these excitations can also only exist in pairs, and creating them spatially separated protects them from local perturbations. Such semiconductor excitations are called Majorana fermions.
Importance for society
Once created in low-dimensional semiconductors, moving these Majorana fermions with respect to each other follows different laws than the three-dimensional world suggests. For example moving one particle around the other, in a two-dimensional world, is related to a phase acquisition. While this feature is in itself intriguing, and even more, it is also useful: so-called braiding (i.e. moving around with respect to each other) of Majorana fermions can be used to perform simple quantum operations. Eventually, Majorana fermions may be important building blocks for quantum computers.
Overall objectives
Majorana fermions are predicted to emerge at the ends of a one-dimensional semiconductor proximitized to a superconductor if the semiconductor hosts a large spin-orbit field perpendicular to the wire and it is subject to a Zeeman magnetic field perpendicular to the spin-orbit field. While these conditions have been fulfilled and some evidence for Majorana bound states (MBS) have been provided, several open questions remain. Importantly, most studies have been performed in one kind of material system, namely InAs. However, holes in germanium are a promising alternative. The objectives of this project are demonstration of controlled confinement of hole states (which is used to build a one-dimensional wire), observation of large spin-orbit interaction, and development of high-transparency superconductor-germanium contacts.
Step 1: device characterization
In collaboration with the group of G. Isella and D. Chrastina at Polytechnico Milano, we built a Ge/SiGe heterostructure with 70% Ge in the barriers and developed fabrication methods to access the two-dimensional hole gas. Characterization of both, the material and the fabrication, have been performed at 4 K in a liquid 4-He system as well as at 100 mK provided by a dilution refrigerator. The combination of successful growth and device manufacture allowed us to measure mobilities of 1e5 cm2/Vs at a hole density of 9.7e11cm-2. From that, we went on to demonstrate the confinement of states in zero dimensions (quantum dots), the presence of Pauli spin-blockade and successful observation of single-electron tunneling processes. These observations are summarized in a first publication: Assessing the potential of Ge/SiGe quantum dots as hosts for singlet-triplet qubits (arXiv:1910.05841).
Step 2: qubit and spin-orbit interaction
Continuing the path of quantum dots and aiming to demonstrate the presence and tunability of spin-orbit interaction, we built double quantum dots to be used as singlet-triplet qubits. We find that indeed, the spin-orbit interaction is large enough to allow for fast (up to 100 MHz) and coherent (up to almost 1 ps) qubit operation at magnetic fields below 5 mT. Moreover, the These results have been summarized in a second publication which is currently being peer reviewed in Nature Materials.
Step 3: superconducting contacts
The challenge of building semiconductor-superconductor hybrid hosts for Majorana bound states is twofold: the contact between the two material systems needs to be highly transparent, and the superconductor is required to sustain magnetic fields up to few hundred millitesla (depending on the specific approach and g-factor of the semiconductor). Aluminium as a superconductor facilitates high-transparency contacts, while it is not magnetic-field resilient. Niobium, on the other hand, is resilient but does not support high-transparency contacts. Via surface passivation and combination of the two said materials, we achieve 88% transparency and measure superconducting properties up to magnetic fields of 1.5 T. This study has been performed using material grown by the group of G. Scappucci. The results have been summarized in a third publication which is currently being peer reviewed in Physical Review Research.
In collaboration with the group of G. Isella and D. Chrastina at Polytechnico Milano, we built a Ge/SiGe heterostructure with 70% Ge in the barriers and developed fabrication methods to access the two-dimensional hole gas. Characterization of both, the material and the fabrication, have been performed at 4 K in a liquid 4-He system as well as at 100 mK provided by a dilution refrigerator. The combination of successful growth and device manufacture allowed us to measure mobilities of 1e5 cm2/Vs at a hole density of 9.7e11cm-2. From that, we went on to demonstrate the confinement of states in zero dimensions (quantum dots), the presence of Pauli spin-blockade and successful observation of single-electron tunneling processes. These observations are summarized in a first publication: Assessing the potential of Ge/SiGe quantum dots as hosts for singlet-triplet qubits (arXiv:1910.05841).
Step 2: qubit and spin-orbit interaction
Continuing the path of quantum dots and aiming to demonstrate the presence and tunability of spin-orbit interaction, we built double quantum dots to be used as singlet-triplet qubits. We find that indeed, the spin-orbit interaction is large enough to allow for fast (up to 100 MHz) and coherent (up to almost 1 ps) qubit operation at magnetic fields below 5 mT. Moreover, the These results have been summarized in a second publication which is currently being peer reviewed in Nature Materials.
Step 3: superconducting contacts
The challenge of building semiconductor-superconductor hybrid hosts for Majorana bound states is twofold: the contact between the two material systems needs to be highly transparent, and the superconductor is required to sustain magnetic fields up to few hundred millitesla (depending on the specific approach and g-factor of the semiconductor). Aluminium as a superconductor facilitates high-transparency contacts, while it is not magnetic-field resilient. Niobium, on the other hand, is resilient but does not support high-transparency contacts. Via surface passivation and combination of the two said materials, we achieve 88% transparency and measure superconducting properties up to magnetic fields of 1.5 T. This study has been performed using material grown by the group of G. Scappucci. The results have been summarized in a third publication which is currently being peer reviewed in Physical Review Research.
Progress beyond the state of the art
The progress beyond state of the art includes the demonstration of a coherent operation of a singlet-triplet Ge hole spin qubit at magnetic fields below a millitesla. The low magnetic field required enables combining quantum dot spin qubits with the superconducting platform. In this direction, we demonstrate contacts of a Ge heterostructure with superconducting contacts which are beyond state-of the art in terms of contact transparency and magnetic field resilience.
Socio-economic impact and wider societal implications
The advancement of germanium semiconductor increases the choices of semiconductor material as building blocks for advanced devices. For example, the qubit built under this action may act as a building block for a large quantum computer. Moreover, the possibility for it to interact with the superconducting platform shows the large range of its applicability. On the other hand, the demonstration of high-quality superconductor-semiconductor interfaces enlarges the range of the germanium platform for applications depending on superconducting technology.
Within the scope of this research, action has been taken to disseminate results to a broad public. For example, we participated at the Open Campus day organized by IST Austria to demonstrate superconductivity to the public. Moreover, a small movie explaining the concept of quantum computers has been recorded and made publicly available.
The progress beyond state of the art includes the demonstration of a coherent operation of a singlet-triplet Ge hole spin qubit at magnetic fields below a millitesla. The low magnetic field required enables combining quantum dot spin qubits with the superconducting platform. In this direction, we demonstrate contacts of a Ge heterostructure with superconducting contacts which are beyond state-of the art in terms of contact transparency and magnetic field resilience.
Socio-economic impact and wider societal implications
The advancement of germanium semiconductor increases the choices of semiconductor material as building blocks for advanced devices. For example, the qubit built under this action may act as a building block for a large quantum computer. Moreover, the possibility for it to interact with the superconducting platform shows the large range of its applicability. On the other hand, the demonstration of high-quality superconductor-semiconductor interfaces enlarges the range of the germanium platform for applications depending on superconducting technology.
Within the scope of this research, action has been taken to disseminate results to a broad public. For example, we participated at the Open Campus day organized by IST Austria to demonstrate superconductivity to the public. Moreover, a small movie explaining the concept of quantum computers has been recorded and made publicly available.