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Description
The goal of this project is to describe the hydrodynamic properties of electrons inside certain recently discovered materials, usually called topological semimetals. What is peculiar about the flow of electrons inside these materials, is the fact that exotic quantum effects allows to transport electrons inside a wire made of this material without loosing energy. The understanding of such properties will settle the ground for the design of more efficient devices to store energy, and might serve for the construction of quantum computers. The origin of such exotic properties relies on certain similarities of the mathematical models describing the physical properties of the electrons inside the material and the ones describing the interaction of highly energetic particles. In some sense, learning about the properties of such materials will provide us not only with important technological advances, but will help us acquire a deeper understanding of the fundamental laws of physics responsible for the structure of our universe. Based on the similarities to the relativistic subatomic particles, we propose in this project to apply these techniques in the description of those apparently disconnected systems, like electrons inside a material. Within these tools we will use the holographic principle which relates black holes with the dynamics of quantum particles in hydrodynamic regime. The holographic principle, usually called gauge/gravity duality, surprisingly relates the dynamics of the events horizon of a black hole with the theories of fluid dynamics. In other words, black holes behaves as a fluid. In particular, holography becomes a useful tool when the interaction between particles is so strong, that all the standard computational techniques fail. Finally, with this project we expect to predict the existence of new electronic transport properties in topological materials, and settle the ground for important technological advances in electronics.
Summary of project results
Liquid water is made of a large number of microscopic particles ( molecules). However, from our perspective, it is nothing else than a continuum entity with the properties of what we usually call a fluid. Within its properties, for example, we find the propagation of waves. The physical theory describing the fluid dynamics is called hydrodynamics. The success of hydrodynamics to describe liquid water relies on the fact that is not necessary to know the microscopic details of the system. Instead, it is enough to assume that all the microscopic particles behave in a collective way. Therefore, the problem of finding the velocity of all these particles, is reduced to solving for the local velocity of the fluid, and thermodynamic variables as local temperature and density.
The goal of this project was to describe the hydrodynamic properties of electrons inside certain recently discovered materials, usually called topological semimetals. What is peculiar about the flow of electrons inside these materials, is the fact that exotic quantum effects allow to transport electrons inside a wire made of this material without losing energy. To do so, we used techniques familiar in the context of particle physics and gravity. More precisely, our models were built following symmetry principles, and constructed the exotic hydrodynamic theories applicable to these new phases of matter.
The problem of electrons in a large magnetic field is known as the Quantum Hall problem, due to the strong interaction between the electrons, in this problem they behave as a quantum liquid. Even more intringuing is the fact that they have similar properties to certain class of theories called Fracton theories where particles are immobile, however, in tandem they can travel without restriction. In this project we constructed the theoretical framework to describe the hydrodynamic behaviour of liquids made of such exotic particles.
In an ordinary liquid, all sound waves propagate with the same speed, whereas particles diffuse with a decelerating speed until the particle’s distribution becomes homogeneous. In contraposition, our theories predict that certain fracton systems -in liquid phase- can flow, but the speed of sound would take a complex numerical value, indicating an attenuation of the sound waves. In addition, the speed of sound would decrease the larger the wavelength of the wave. Nonetheless, contrary to what we would expect, it has been found that as long as energy in conserved fractons would spread diffusively as in ordinary liquids.
The contribution of this project to science is two-fold, on one hand, we have developed a series of predictions that can be tested in future experiments searching for fracton phases of matter. In particular, we have classified the collective modes of fracton systems in hydrodynamic regime and characterized their dispersion relations. The qualitative difference between the behaviour of collective modes in ordinary liquids and fracton liquids would serve as a smoking gun in the quest of discovering Fracton phases of matter.
On the other hand, we also contributed to more theoretical questions related to apparent relation between fracton systems and theories of gravity. In fact, we managed to relate one class of fracton theories living 3 space dimensions with a gravitational theory in 4 space dimensions. Relation that puzzles theoretical physicist since fracton systems have nothing to do with the theory of General Relativity.
In summary, this project paved the way towards an effective description of many-body systems with constrained dynamics such as ensembles of topological defects, fracton phases of matter, and certain models of glasses.