This dissertation is devoted to theoretical studies of strongly interacting one-dimensional and quasi one-dimensional electron systems. The properties of one-dimensional electron systems can be studied within the bosonization technique, which presents fermions as collective bosonic density excitations. The power of this approach is the ability to treat electron-electron interaction exactly in the low-energy limit. The approach predicts the failure of Fermi liquid and an absence of long-range order in one-dimensions. The low-energy description of one-dimensional interacting systems is called the Tomonaga-Luttinger liquid theory. For example, the edges of quantum Hall systems are one-dimensional and described by a chiral Tomonaga-Luttinger liquid. Another example is a quantum spin Hall system with helical edge states, which are also described by a Tomonaga-Luttinger liquid. In our first work, a study of magnetized edge states of quantum spin-Hall system is presented. A magnetic field dependent signature of such edges is obtained, which can be verified in a Coulomb drag experiment. The second part of the dissertation is devoted to quasi-one dimensional antiferromagnetic lattices. A spatially anisotropic lattice antiferromagnet can be viewed as an array of one dimensional spin chains coupled in a way to match the lattice symmetry. This allows to use the non-Abelian bosonization technique to describe the low-energy physics of spin chains and study the inter-chain interactions perturbatively. The work presented in the dissertation studies the effect of Dzyaloshinskii-Moriya interaction on the magnetic phase diagram of the spatially anisotropic kagome antiferromagnet. We predict a Dzyaloshinskii-Moriya interaction driven phase transition from Neel to Neel+dimer state. In the third work, a novel model of the fractional quantum Hall effect is given. Wave functions of two-dimensional electrons in strong and quantizing magnetic field are essentially one-dimensional. That invites one to use the one-dimensional phenomenological bosonization to describe the density fluctuations of the two-dimensional interacting electrons in magnetic field. Remarkably, the constructed trial bosonized fermion operator describing the electron states with a fixed Landau gauge momentum is effectively two-dimensional. / text

When energy relaxation between electrons and the lattice is slow, an elevated electronic temperature different from that of the lattice persists. In this regime, hot charge carriers control the energy transport in a material. In this thesis, I show how hot carriers can dominate graphene's response enabling it to exhibit novel properties. First, I examine how light is converted to electrical currents in graphene and show that hot carriers play an integral role in this multi-stage process. I show that photocurrent in graphene p-n junctions is dominated by a Photo-thermoelectric effect in which a light-induced elevated hot carrier temperature drives a thermoelectric current. Furthermore, I show that the generation and cooling of hot carriers in graphene during photoexcitation proceeds in an unusual way. In the former, carrier-carrier scattering dominates the initial photoexcitation cascade enabling efficient hot carrier generation. In the latter, a new cooling mechanism - disorder-assisted scattering (supercollisions) - dominates electron-lattice cooling over a wide range of temperatures (including room temperature). Second, I examine the transport characteristics of double layer graphene heterostructures (specifically, G/h-BN/G heterostructures). I show that Coulomb coupling results in vertical (out-of-plane) energy transfer between electrons in proximal (but electrically insulated) graphene layers. This couples lateral (in-plane) charge and energy transport of electrons in the two layers to give rise to a new energy-driven Coulomb drag (inter-layer transresistance) that dominates when the two layers are at charge neutrality. Third, I examine energy transport in charge neutral graphene. I show that the combination of fast carrier-carrier scattering, high electronic quality, and slow electron-lattice cooling (hot carriers) gives rise to a regime of ballistic heat transport. This manifest as electronic energy waves with velocity on the order of graphene's Fermi velocity. The new phenomena enabled by hot carriers and the ideas/approaches described in this thesis provide a basis with which to exploit hot carrier effects in graphene and opens new vistas for controlling and harnessing energy flows on the nanoscale. / Engineering and Applied Sciences

No description available.

The first part of this thesis deals with the study of mesoscopic fluctuations of the Coulomb drag resistance in double-layer GaAs/AlGaAs heterostructures, both in weak magnetic fields and strong magnetic fields. In the second part, measurements are made in a monolayer graphene structure, specifically of the quantum lifetime, and the mesoscopic resistance fluctuations at quantising magnetic fields.

Two graphene layers placed in close proximity offer a unique system to investigate interacting electron physics as well as to test novel electronic device concepts. In this system, the interlayer spacing can be reduced to value much smaller than that achievable in semiconductor heterostructures, and the zero energy band-gap allows the realization of coupled hole-hole, electron-hole, and electron-electron two-dimensional systems in the same sample. Leveraging the fabrication technique and electron transport study in dual-gated graphene field-effect transistors, we realize independently contacted graphene double layers separated by an ultra-thin dielectric. We probe the resistance and density of each layer, and quantitatively explain their dependence on the backgate and interlayer bias. We experimentally measure the Coulomb drag between the two graphene layers for the first time, by flowing current in one layer and measuring the voltage drop in the opposite layer. The drag resistivity gauges the momentum transfer between the two layers, which, in turn, probes the interlayer electron-electron scattering rate. The temperature dependence of the Coulomb drag above temperatures of 50 K reveals that the ground state in each layer is a Fermi liquid. Below 50 K we observe mesoscopic fluctuations of the drag resistivity, as a result of the interplay between coherent intralayer transport and interlayer interaction. In addition, we develop a technique to directly measure the Fermi energy in an electron system as a function of carrier density using double layer structure. We demonstrate this method in the double layer graphene structure and probe the Fermi energy in graphene both at zero and in high magnetic fields. Last, we realize dual-gated bilayer graphene devices, where we investigate quantum Hall effects at zero energy as a function of transverse electric field and perpendicular magnetic field. Here we observe a development of v = 0 quantum Hall state at large electric fields and in high magnetic fields, which is explained by broken spin and valley spin symmetry in the zero energy Landau levels. / text