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Thermotronics aims to process information with Thermal networks and heat flows

The control of electric currents in solids is at the origin of modern electronics which has revolutionised our daily life. The diode and the transistor introduced by Braun  and Bardeen and Brattain  are undoubtedly the corner stones of modern information technologies. Such devices allow for rectifying, switching, modulating, and even amplifying the electric current.


Researchers have experimented with similar devices which would control the  heat flow. An important step forward in this direction has been carried out in 2006 by Li et al. by introducing phononic counterpart of a field-effect transistor. In their device, composed as its electronic analogue, of three interconnected solid elements, the temperature bias plays the role of the voltage bias and the heat currents carried by phonons play the role of the electric currents. Later, several prototypes of phononic thermal logic gates  and thermal memories have been developed in order to process information by phononic heat currents rather than by electric currents. Beside these results, different phononic thermal rectifiers have been proposed  to introduce an asymmetry in the heat transport with respect to the sign of the temperature gradient  opening so the way to the development of thermal diodes.


However, this transport of heat with phonons in solid networks suffers from some weaknesses of fundamental nature which intrinsically limit its performances. One of these limitations is linked to the speed of acoustic phonons itself which is limited by the speed of sound in solids. Another intrinsic limitation of phononic devices is the presence of local Kapitza resistances which come from the mismatch of vibrational modes supported by the different solid elements in the network. This resistance can drastically reduce the heat flux transported across the system.


Solid-state thermotronics research investigates the possibility of controlling heat flows through temperature gradients in a similar way to that in which electrical currents and voltages are controlled in existing devices. Recently many researchers have proposed thermal analogues of electronic fundamental building blocks such as thermal transistor, thermal memory and thermal logic gates for controlling the flow of heat by radiation, storing thermal energy, and even making logical operations using thermal photons instead of electrons.


Thermal Transistor

Electronic transistor made of three terminals, the source (S), the gate (G), and the drain (D). The gate is used to actively control (by applying a voltage bias V on it) the apparent electric conductivity of the channel between the source and the drain. The radiative analogue of an electronic transistor  is depicted in Figure b. It basically consists in a source and a drain, labelled by the indices S and D, which are maintained at temperatures TS and TD (which play an analogue role as the voltage) using thermostats where TS>TD so that a net heat flux is transferred from the source towards the drain. A thin layer of a metal-isulator transition material (MIT) labelled by G of width δ is placed between the source and the drain at a distance d from both media and operates as a gate.


This configuration coincides with two heat-radiation diodes  which are connected in series, so that the heat radiation transistor corresponds to a bipolar transistor. In an MIT material, a small change in the temperature around its critical temperature Tc causes a sudden qualitative and quantitative changes in its optical properties. Vanadium dioxide (VO2) is one of such materials which undergoes a first-order transition (Mott transition [24]) from a high-temperature metallic phase to a low-temperature insulating phase  close to room-temperature (Tc=340 K)


(b) Radiative thermal transistor. A membrane of an MIT material (VO2) acts as the gate between two silica (SiO2) thermal reservoirs (source and drain). The temperature (TG) of the gate is chosen between the temperatures of the source and the drain (TS and TD). ΦD and ΦS are the radiative heat fluxes received by the drain and emitted by the source, respectively.


Figure 1:


Different works have shown  that the heat-flux exchanged at close separation distances (i.e. in the near-field regime) between an MIT material and another medium can be modulated by several orders of magnitude across the phase transition of MIT materials.


Researchers have also investigated the possibility offered by this system to amplify the heat flux received by the drain. This effect is the thermal analogue of the classical transitor effect. As shown in Figure,  operating mode in the region of phase transition around Tc where a small increase in TG leads to a drastic reduction of flux received by the drain. This behaviour can be associated in far-field to a reduction of the thermal emission. This anomalous behaviour corresponds to the so-called negative differential thermal conductance. The presence of a negative differential thermal conductance is a necessairy condition (but not sufficient) for observing a transistor effect.


Figure 3:


This drastic change in the transfer of energy can be used to modulate the heat flux received by the drain by changing the gate temperature around its critical value. The thermal inertia of the gate as well as its phase transition delay defines the timescale at which the switch can operate. Usually, the thermal inertia limits the speed to some microseconds or even less.


Thermal memory

In 1946, Williams and Kilburn developed a memory to store data electronically using a cathode ray tube. The basic idea of their invention is summarised in Figure. A small electrostatic charge appears on the surface of a screen lighted up by an electron beam and this charge remains for a short period of time before leaking away. This invention constitutes the first volatile memory. Information is stored as long as the charge is not dissipated.

Figure 6:

Researchers have also investigated the possibility to store information or energy for arbitrary long time using thermal photons. The concept of thermal memory is closely related to the thermal bistability of a system, that is, the presence of at least two equilibrium temperatures


To illustrate this, let us consider the system as depicted in Figure  composed by two parallel homogeneous membranes made of VO2 and SiO2. These slabs have finite thicknesses δ1 and δ2 and are separated by a vacuum gap of distance d. The left (right) membrane is illuminated by the field radiated by a blackbody of temperature TL (TR), where TL≠TR. The membranes themselves interact on the one hand through the intracavity fields and on the other with the field radiated by the two black bodies. The system possesses three equilibrium temperatures while only two of three equilibrium points are stable.


The two stable thermal states can naturally be identified to the ‘0’ and ‘1’ of one bit of information. As long as the temperatures of the two reservoirs are held constant, the system remains in the same stable thermal state. By perturbating the system (for instance by adding or extracting a certain power to one membrane), it is possible to switch from one thermal state to the other state.


These results show that many-body radiative systems could be used as volatile thermal memory. The radiative bistability which exists in some of these media can be exploited for energy storage at both macroscale (far-field regime) and subwavelength scale (near-field regime). This thermal energy could in principle release heat upon request in its environment making these systems active building blocks for a smart management of heat exchanges between different objects without any contact.


Logic Gates with Thermal Photons

The next-generation of internet of things infrastructures has the potential to change the way people and systems live in a world of massive and disparate data sources and to provide opportunities for connectivity at different scales. Instead of using electrical signals, purely thermal signals could be used. However, the development of such a technology requires the existence of thermal logic gates being able to perform a boolean information treatment as their electronic counterpart do.


Magnetic Control of Heat Flux

Recently strong tunability of heat transfers in magneto-optical networks has been demonstrated with an external magnetic field. This magnetic control of heat flux is associated to the presence of a photon thermal Hall effect in these systems.


The classical Hall effect discovered by Edwin Hall at the end of the 19th century results in the appearance of a transverse electric current inside a conductor under the action of an external magnetic field applied in the direction orthogonal to the primary voltage gradient. This effect comes from the Lorentz force that acts transversally on the electric charges in motion through the magnetic field curving so their trajectories. Very shortly after this discovery, a thermal analogue of this effect has been observed by Righi and Leduc  when a temperature gradient is applied throughout an electric conductor. As for the classical Hall effect, this effect is intrinsically related to the presence of free electric charges. So, one cannot expect a thermal Hall effect with neutral particles. Nevertheless, during the last decade, researchers have highlighted such an effect in nonconducting materials due to phonons or magnons (spin waves)


These results could find broad applications in MEMS/NEMS technologies to generate mechanical work by using microresonators coupled to a transistor as well as in energy storage technology, for instance, to store and release thermal energy upon request. They could also be used to develop purely thermal wireless sensors that work by implementing logic functions with heat instead of electricity.


The realization of a single-quantum-dot heat valve reported in Jan 2021

A team of researchers at University Grenoble Alpes in France and Centre of Excellence—Quantum Technology in Finland has recently developed a single-quantum-dot heat valve, a device that can help to control the flow of heat in single-quantum-dot junctions. This heat valve, presented in a paper published in Physical Review Letters, could help to prevent quantum computers from overheating.



The realization of a single-quantum-dot heat valve

“With the miniaturization of electronic components handling of excess heat at nanoscales has become an increasingly important issue to be addressed,” Nicola Lo Gullo, one of the researchers who carried out the study, told “This is especially true when one wants to preserve the quantum nature of a device; the increase in temperature does typically result in the degradation of the quantum properties. The recent realization of a photonic heat-valve by another research group ultimately inspired us to create a heat valve based on a solid-state quantum dot.”


One of the key objectives of the recent study carried out by Lo Gullo and his colleagues was to demonstrate the feasibility of controlling the amount of heat that flows across a quantum dot junction, while also enabling the flow of a set amount of electric current. To design their single-quantum-dot heat valve, the researchers placed a gold nanoparticle between two metallic contacts, using it as a junction. This nanoparticle is so small that it can be used to intervene on a single energy level, acting as a bigger artificial atom would with several accessible energy levels.


“By properly tuning the external parameters it is possible to allow the electrons in one of the contacts to flow through only one of the levels of this artificial atom and reach the other contact,” Lo Gullo explained. “The single-level quantum dot therefore acts as a bridge between the two metallic contacts.”


In normal circumstances, the exchange of energy is only possible when the energy level of a quantum dot is in resonance with the energy of the electrons in the contacts. In the device developed by Lo Gullo and his colleagues, however, the presence of the contacts changes the properties of the artificial atom, by broadening its energy levels.


“This effect is at the heart of the heat-valve effect we have studied,” Lo Gullo added. “The broadening amounts to the creation of virtual states, which are not classically accessible and allow electrons to flow from one contact to another, by carrying energy and giving rise to the heat-valve effect we reported.” In larger (macroscopic) conductors, researchers have identified a simple and universal relationship between their ability to conduct electrical charge and their ability to conduct heat. This relationship is outlined by a theoretical construct known as the Wiedemann-Franz law.


In quantum devices such as the one developed by Lo Gullo and his colleagues, however, things are not as straightforward. This is due to the quantization of charge and energy, which leads to deviations from the Wiedemann-Franz law. “Using the most basic quantum mechanical picture (called semi-classical), one would expect a quantum dot junction not to conduct heat at all,” Clemens Winkelmann, another researcher involved in the study, told “Our measurements, however, show that this is not true, and the theoretical explanation is related to quantum fluctuations, exactly as in the Heisenberg uncertainty principle, which partly restore the energy and thus the heat flow.”


When they were developing their device, the researchers had to overcome a number of technical challenges. For instance, they had to identify a strategy to measure the temperature (and temperature differences) locally inside a quantum device. Ultimately, one of the greatest achievements of their study is that they were able to collect these measurements and thus gain a better understanding of how heat is managed inside quantum devices.


“Electronic devices produce dissipation when they treat information, and this leads to the well-known overheating issues observed in classical processors, which also occur the quantum world,” Winkelmann said. “Overheating can perturb the logical operation of the device, leading to errors. Our work provides a better understanding of how heat is generated and can be drained in such a device.”


By introducing a strategy to achieve control over the heat flowing through the smallest junctions in quantum devices, the recent paper by Lo Gullo, Winkelmann and their colleagues could open up interesting new possibilities related to an emerging field of study known as solid-state thermotronics. Solid-state thermotronics research investigates the possibility of controlling heat flows through temperature gradients in a similar way to that in which electrical currents and voltages are controlled in existing devices.


“Solid-state thermotronics is a relatively new field, but important progress has been made, such as the realization of heat valves, thermal diodes and transistors, energy harvesters and even the proposals of thermal logic gates,” Lo Gullo said. “We provided yet another example of the feasibility of controlling and measuring heat currents and temperatures in solid-state devices.”


In the future, the heat valve developed by this team of researchers could improve the reliability and safety of quantum devices, reducing the risk of overheating. In their next studies, Lo Gullo and Winkelmann would like to devise strategies to measure dissipation over time. In other words, instead of focusing on a quantum device’s steady-state heating, they plan to examine single, elementary quantum-dissipative processes, such as the tunneling of a single electron or a single 2π slip of the quantum mechanical phase.


“There are many possible directions for future research,” Lo Gullo added. “We are currently looking at junctions with a more complex structure to see if they offer some advantages in terms of range of operability. Another appealing possibility is to achieve time-resolved control over the heat flow, thus allowing real time operations in view of applications to thermotronics.”


French Researchers investigating Thermotronics: processing information with heat (ComputHeat)

This project aims to develop a new technology for information processing, active thermal management and wireless sensing using heat carried by thermal photons and phonons. The infrared emission from systems (people, machines…) and the dissipated power in industrial processes can be captured by active thermal blocks (thermal analogs of transistor) to launch a sequence of logic operations in order to directly control the heat flow propagation or to store this heat and release it as requested, process this thermal information (Boolean treatment of heat) and trigger specific actions. This technology also called “thermotronics” could allow for a quasi-infinite liftetime of monitoring which is not possible today with traditional electronics without costly battery replacement or wired installations.


What makes this new paradigm possible is the recent invention of radiative thermal components, such as the thermal transistor, thermal diode and thermal memory introduced by many of project participants. These building blocks are based on the drastic non-linear change of physical properties of materials with respect to their temperature.


The project includes modeling, nanofabrication, material characterization and proof of operating principle of building blocks. Also we will develop elementary circuits to process basic logical operations (OR, NOT and AND gates) and more complex thermal networks to implement arbitrary logical operations. It will not only allow the first experimental demonstration of logical operations with thermal photons but will push also forward the development of the thermotronics by introducing new functionality to manipulate heat flow (heat flux splitters, thermal valves, neural networks for thermal learning….) to manipulate heat flow and thermal information. Finally, in an effort to get rid of thermal inertia problem which intrinsically limit the operating speed of thermal circuits we will also explore news solutions with thermal circuits made with either magneto-optical systems submitted to external magnetic fields or 2 dimensional materials with low heat capacity.


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