Jackiw-Rebbi fermions in a synthetic topological chain – STOIC
Engineering and detecting topological electronic states in synthetic carbon nanotube chains
By locally controlling a carbon nanotube with 15 electrodes, STOIC demonstrated that an electronic energy gap can be created and tuned over two orders of magnitude. This level of control opens the way to artificial quantum chains that could eventually host exotic and robust topological states.
Creating and controlling topological states in a one-dimensional quantum conductor through local and programmable engineering
Topological phases of matter are attracting strong interest because they can host electronic states with unusual properties that may be robust against certain perturbations. Such robustness is particularly appealing for the development of new approaches to quantum information. However, in real materials, these phases often rely on a complex combination of intrinsic properties that are difficult to control, while disorder can mask or even mimic their experimental signatures. The STOIC project explores a different strategy: artificially building a topological phase by locally controlling the parameters of a genuinely one-dimensional electronic conductor. The chosen platform is a suspended carbon nanotube positioned above an array of nanoscale electrodes. By applying different voltages to these electrodes, the electronic properties of the nanotube can be modulated along its length, creating a synthetic chain related to the Su-Schrieffer-Heeger model. The long-term objective is to generate Jackiw-Rebbi edge states, which are expected to carry a fractional electronic charge. The project addresses two main challenges. The first is to demonstrate that a large number of electrodes can collectively control the spectrum of a one-dimensional conductor and open a robust energy gap. The second is to develop a method for characterizing the localized states that may appear inside this gap. Because electrical transport measurements alone can produce ambiguous signatures, STOIC combines the chain with a microwave cavity, using photons as an independent and highly sensitive probe of its electronic properties. This approach therefore combines ultra-clean carbon nanotube nano-assembly, local multi-electrode control and microwave quantum measurement techniques. It aims to transform a simple quantum conductor into a programmable platform whose electronic properties can be spatially engineered. Beyond the fundamental study of topological phases and fractional charges, the techniques developed in STOIC are relevant more broadly to the engineering, readout and control of artificial quantum systems. In the longer term, such architectures could contribute to more robust quantum devices and to new quantum simulators for exploring phenomena that are difficult to isolate in natural materials.
The project is based on an experimental approach in which a one-dimensional quantum conductor is fabricated so that its properties can be adjusted locally, and its behaviour is then measured at very low temperature.
The system studied is a suspended carbon nanotube, chosen because it provides a conductor that is extremely close to the ideal one-dimensional case and can contain very few defects. It is positioned with high precision above an array of nanoscale electrodes fabricated on a chip. Each electrode can be controlled independently, allowing the electrical potential experienced by the electrons in the nanotube to be modified locally.
By applying alternating voltages to the different electrodes, we artificially create a periodic modulation along the nanotube. The aim is to shape its electronic spectrum in a controlled way, in particular by opening an energy gap. This first step is investigated using electrical transport measurements: a small current is sent through the nanotube and its response is measured while the voltages applied to the electrodes are varied. These measurements reveal how the spectrum evolves when the amplitude and shape of the modulation are changed.
The devices are studied at temperatures of only a few tens of thousandths of a kelvin, so that quantum effects dominate their electronic behaviour. Experimental results are compared with numerical models describing the potential generated by the electrodes and the resulting electronic states. This comparison helps distinguish the effects of the controlled modulation from those caused by disorder or charging effects in the device.
A second method complements the transport measurements. The nanotube is integrated into a microwave resonator, similar to a small cavity capable of storing photons. The electronic states of the nanotube slightly modify the response of this cavity. By precisely measuring the amplitude and phase of the transmitted microwaves, it is therefore possible to probe electronic properties without relying solely on the current flowing through the device.
The project also developed a method in which the electrodes are modulated at the frequency of the cavity. This modulation causes the electronic dipole to emit a controlled microwave field. By adjusting the phases and amplitudes of the different signals, this approach can strongly enhance the signature of the electronic states.
The overall methodology therefore combines nanoscale fabrication, local electrical control, transport measurements, microwave detection and numerical modelling. Their combination is essential both to create the desired electronic states and to identify them reliably.
The main result of STOIC is the demonstration that the electronic behaviour of a carbon nanotube can be strongly shaped using an array of 15 independently controlled electrodes. By applying a spatial modulation of the electrical potential, we opened a robust electronic energy gap that can be continuously tuned over approximately two orders of magnitude, from about 200 microelectronvolts to nearly 30 millielectronvolts. The same nanotube can therefore be driven from an almost metallic regime to a strongly insulating one. This result is an essential step towards artificial quantum chains capable of hosting topological states localized at their ends.
The project also showed that conventional electrical transport measurements need to be complemented by other probes. In a related device, we observed that ordinary non-topological states can accumulate near zero energy and mimic some of the signatures usually sought when identifying topological states. This finding strengthens the motivation for using a microwave cavity to obtain independent information about the nature of the electronic states.
In this direction, STOIC enabled the development of a new readout method based on electrical modulation at the cavity frequency. The observed mechanism turned out to be different from the one initially expected: the signal mainly originates from radiation emitted by the electronic dipole into the cavity. This discovery nevertheless led to a particularly sensitive method, capable of strongly increasing the signal-to-noise ratio and producing phase differences of up to π.
Finally, we demonstrated that quantum states in a carbon nanotube integrated into a microwave cavity can be manipulated directly using photons while maintaining coherence times longer than one microsecond. This result validates the compatibility of ultra-clean nanotubes, local electrical control and microwave manipulation.
Overall, the project led to five scientific publications and established a complete experimental platform combining controlled gap creation, local engineering of electronic properties and sensitive microwave detection.
The first perspective is to use the existing 15-electrode chain to reach the topological regime originally targeted by the project. The experiments carried out during STOIC have clarified how the energy gap depends on the applied modulation, disorder and the position of the electronic levels. It is now possible to design more complex potential profiles in order to create states localized at the ends of the chain and study how they evolve between ordinary and topological configurations.
A second perspective concerns the direct measurement of the charge carried by these states. The parametric readout method developed during the project provides a highly sensitive signal linked to the electric dipole. After calibration, it could be used to determine the charge of a localized state and therefore search for the fractional charge expected for certain Jackiw-Rebbi topological states.
The project has also opened a direction that was not anticipated in this form at the outset. Rather than trying to generate the desired longitudinal interaction solely through electrostatic modulation, it may be more effective to directly modulate the electromagnetic properties of the resonator, for example its impedance. This approach could further improve the readout and control of quantum states.
In the longer term, the platform could be used to create chains containing several topological regions, to move or couple their edge states, and to investigate their exchange properties. It would then provide a highly controllable artificial system for exploring quantum phenomena that are difficult to isolate in natural materials.
More broadly, the techniques developed in STOIC (spatial control of a quantum conductor, sensitive microwave readout and photon-based manipulation) could contribute to the development of quantum simulators, new quantum nanoelectronic devices and, ultimately, architectures in which quantum properties are made more robust through topology.
Topological excitations emerge at the interface between phases of matter of different topological classes. As they inherit the mathematical resilience to disorder of their supporting topological phase, they are attractive for building highly coherent quantum bits robust to local disorder. Topological quasi-particles hosted in topologically non-trivial phases usually possess exotic properties underlying new physics, which makes them extremely interesting to investigate for purely fundamental prospects. Currently, the topological excitations most actively sought for are Majorana zero modes which should exhibit a particle/anti-particle duality and non-abelian exchange statistics. Despite years of effort, signatures of their presence in investigated devices remain more than elusive and no topological qubit has been realized de facto. Project STOIC proposes a radical shift in the experimental investigation of topological phases by changing the general approach.
Indeed, a chain whose local site parameters can be individually controlled constitutes the simplest system in which a topological phase can emerge. The modulation of the tunnel coupling in a 1D conductor emulates the SSH model where Jackiw-Rebbi fermions having a fractional charge and non-abelian exchange statistics should emerge. Project STOIC proposes to realize Jackiw-Rebbi fractional modes in an ultra-clean carbon nanotube, the closest to an ideal 1D conductor, deposited over an array of gate electrodes that can locally control the hopping term between neighbouring sites. The fractional charge will be measured by exploiting the capacitive coupling to a microwave cavity in a cQED architecture to reveal the existence of Jackiw-Rebbi fermions. Project STOIC will open a new route to the investigation of topological phases.
Project coordination
Matthieu Delbecq (Centre national de la recherche scientifique)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
Partnership
LPENS Centre national de la recherche scientifique
Help of the ANR 341,208 euros
Beginning and duration of the scientific project:
February 2023
- 36 Months
