Charge and heat transport in topological systems

In this thesis, I address the intriguing and appealing topic of charge and heat transport in quantum Hall systems, which are among the most famous example of topological phases of matter, in presence of external time-dependent voltages. The interest of condensed matter community towards topological systems has been considerably raised in recent years. For instance, it is worth to recall the Nobel prize for physics 2016 awarded to Professors Thouless, Kosterlitz and Haldane for their contribution to the study of topological states of matter. These states are exotic phases of matter, whose properties are described in terms of quantities that do not depend on the details of a system, are very robust against defects and perturbations. The research field of topological systems takes place due to the interplay between condensed matter physics and mathematics. As a matter of fact, many concepts have been borrowed from the mathematical branch of topology in order to classify these novel states of matter. Quantum Hall effect was discovered almost forty years ago and still attracts a lot of attention from the theoretical and experimental point of view. This remarkable physical phenomenon occurs in two-dimensional electron systems in the limit of strong perpendicular magnetic fields. In quantum Hall systems, the transverse resistance, which is commonly defined Hall resistance, is very precisely quantized in terms of the resistance quantum. When this quantization occurs for integer values, this phenomenology is termed integer quantum Hall effect. It can be understood in a satysfying way by resorting to a non-interacting quantum mechanical description. The hallmark of quantum Hall systems is the emergence of one-dimensional metallic edge states on the boundaries of the system. Along these edge states particles propagate with a definite direction. As a result, they are topologically protected against backscattering. The coherence length ensured by topological protection guarantees to access the wave-like nature of electrons. Intriguingly, this investigation can be pushed to its fundamental limit by exploring quantum transport at the single-electron level. This idea embodies the core of a new field of research, known as electron quantum optics Single-electron source can be realized by applying to a quantum Hall system a periodic train of Lorentzian-shaped pulses, carrying an integer number of particles per period, thus emitting into the edge states minimal single-electron excitations, then termed levitons. Plateaus of the Hall resistance appear also at fractional values of the resistance quantum. Contrarily to the integer case, the physical explanation of fractional quantum Hall effect cannot neglect the correlation between electrons and this phase of matter is inherently strongly-correlated. Intriguingly, elementary excitations of fractional quantum Hall systems are quasi-particle with fractional charge and statistics. Remarkably, one-dimensional conducting edge states arise also in the fractional quantum Hall effect and their excitations inherit the charge and statistical properties of the one in the bulk. By considering the application of a periodic train of Lorentzian pulses to a quantum Hall system, I focus on the transport properties of levitons propagating along integer and fractional edge states. I investigate the charge density of a state composed by many levitons in the fractional quantum Hall regime, thus finding that it is re-arranged into a regular pattern of peaks and valleys, reminiscent of Wigner crystallization in strongly-interacting electronic systems. Then, I analyze heat transport properties of levitons in quantum Hall systems, which represent a new point of view on electron quantum optics, extending and generalizing the results obtained in the charge domain.