We calculate the Landau levels of a Kramers-Weyl semimetal thin slab in a perpendicular magnetic field B. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band...Show moreWe calculate the Landau levels of a Kramers-Weyl semimetal thin slab in a perpendicular magnetic field B. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band width that oscillates periodically in 1/B. We interpret the spectrum in terms of a one-dimensional superlattice induced by magnetic breakdown at Weyl points. The band width oscillations may be observed as 1/B-periodic magnetoconductance oscillations, at much weaker fields than the oscillations due to Landau level quantization. No such spectrum appears in a generic Weyl semimetal, the Kramers degeneracy at time-reversally invariant momenta is essential.Show less
Building on the discovery that a Weyl superconductor in a magnetic field supports chiral Landau level motion along the vortex lines, we investigate its transport properties out of equilibrium. We...Show moreBuilding on the discovery that a Weyl superconductor in a magnetic field supports chiral Landau level motion along the vortex lines, we investigate its transport properties out of equilibrium. We show that the vortex lattice carries an electric current between two normal metal contacts at a voltage difference. This current is proportional to the square of the renormalized charge of Weyl fermions in the superconducting Landau level. Because the charge renormalization is energy dependent, a nonzero thermoelectric coefficient appears even in the absence of energy-dependent scattering processes.Show less
Parafermionic zero-modes are zero-energy excitations with peculiar mutual statistics, which can be realized at the edge of the Fractional Quantum Hall Effect sample. We came up with several...Show moreParafermionic zero-modes are zero-energy excitations with peculiar mutual statistics, which can be realized at the edge of the Fractional Quantum Hall Effect sample. We came up with several protocols for adiabatic quantum pumping with parafermions, which allow to test the statistics of Fractional Quantum Hall quasiparticles and observe universal noise in the pumping current. That is, the noise takes a specific value which is essentially given by universal constants, and is robust with respect to changes in many system parameters.Show less
In this thesis, the necessary elements to build up a quantum switch, the central element in a quantum random access memory, are proposed and analyzed. A network with quantum switches at its nodes...Show moreIn this thesis, the necessary elements to build up a quantum switch, the central element in a quantum random access memory, are proposed and analyzed. A network with quantum switches at its nodes forms the bifurcation path that leads an address register from a root node to an array of memory cells, activating, quantum coherently, only the quantum switches that the register encounters in its path to the memory cells. Transmon qubits and SQUIDs are used to design a superconducting device capable of routing a register of microwave photons through a bifurcation network, allowing for superposition of paths. In order to give rise to all the required interactions between the device and the address register, a non-linear capacitor, composed of two plates with carbon nanotubes in between, is introduced into the transmon. The dynamic operation of the quantum switch is analyzed using Langevin equations and a scattering approach, and probabilities of reflection and transmission of photons by (or through) the switch are computed, both for single- and two-photon processes. Computations show that, with parameters taken from up-to-date similar devices, probabilities of success are above 94%. Applications of quantum random access memories are discussed, as well as other applications of quantum switches. Also, solutions are proposed to the challenges that emerge during the study of the dynamics of the quantum switch.Show less
