Dirac cones are ubiquitous to non-trivial quantum matter and are expected to boost and reshape the field of modern electronics. Particularly relevant examples where these cones arise are topological insulators and graphene. From a fundamental perspective, this thesis proposes schemes towards modifying basic properties of these cones in the aforementioned materials. The thesis begins with a brief historical introduction which is followed by an extensive chapter that endows the reader with the basic tools of symmetry and topology needed to understand the remaining text. The subsequent four chapters are devoted to the reshaping of Dirac cones by external fields and delta doping. At all times, the ideas discussed in the second chapter are always a guiding principle to understand the phenomena discussed in those four chapters. As a result, the thesis is cohesive and represents a major advance in our understanding of the physics of Dirac materials.
Dirac cones are ubiquitous to non-trivial quantum matter and are expected to boost and reshape the field of modern electronics. Particularly relevant examples where these cones arise are topological insulators and graphene. From a fundamental perspective, this thesis proposes schemes towards modifying basic properties of these cones in the aforementioned materials. The thesis begins with a brief historical introduction which is followed by an extensive chapter that endows the reader with the basic tools of symmetry and topology needed to understand the remaining text. The subsequent four chapters are devoted to the reshaping of Dirac cones by external fields and delta doping. At all times, the ideas discussed in the second chapter are always a guiding principle to understand the phenomena discussed in those four chapters. As a result, the thesis is cohesive and represents a major advance in our understanding of the physics of Dirac materials.
Christian Pauly demonstrates the strong topological properties of the technologically relevant phase change materials Sb2Te3 and Ge2Sb2Te5 by using two powerful techniques for mapping the surface electronic structure: scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES). In the case of a phase change material, this opens up the possibility of switching between an insulating amorphous and a conducting topological phase on nanosecond-time scales. Moreover, the author presents first experimental results of a weak topological insulator, namely on the bismuth-based graphene-like sheet system Bi14Rh3I9, revealing a topologically protected one-dimensional edge channel as its fingerprint. The edge state is as narrow as 0.8 nm, making it extremely attractive to device physics. Those strong and weak topological insulators are a new phase of quantum matter giving rise to robust boundary states which are protected from backscattering and localization.
This thesis elucidates electron correlation effects in topological matter whose electronic states hold nontrivial topological properties robust against small perturbations. In addition to a comprehensive introduction to topological matter, this thesis provides a new perspective on correlated topological matter. The book comprises three subjects, in which electron correlations in different forms are considered. The first focuses on Coulomb interactions for massless Dirac fermions. Using a perturbative approach, the author reveals emergent Lorentz invariance in a low-energy limit and discusses how to probe the Lorentz invariance experimentally. The second subject aims to show a principle for synthesizing topological insulators with common, light elements. The interplay between the spin–orbit interaction and electron correlation is considered, and Hund's rule and electron filling are consequently found to play a key role for a strong spin–orbit interaction important for topological insulators. The last subject is classification of topological crystalline insulators in the presence of electron correlation. Unlike non-interacting topological insulators, such two- and three-dimensional correlated insulators with mirror symmetry are demonstrated to be characterized, respectively, by the Z4 and Z8 group by using the bosonization technique and a geometrical consideration.
Silicon has been reaching physical limits as the semiconductor industry moves to smaller device feature sizes, increased integration densities and faster operation speeds. There is a strong need to engineer alternative materials, which can become foundation of new computational paradigms or lead to other applications such as efficient solid-state energy conversion. Recently discovered Dirac materials, which are characterized by the liner electron dispersion, are examples of such alternative materials. In this dissertation, I investigate two representatives of Dirac materials - graphene and topological insulators. Specifically, I focus on the (i) effects of electron beam irradiation on graphene properties and (ii) electronic and thermal characteristics of exfoliated films of Bi [subscript 2] Te [subscript 3] -family of topological insulators. I carried out Raman investigation of changes in graphene crystal lattice induced by the low and medium energy electron-beam irradiation (5.20 keV). It was found that radiation exposures result in appearance of the disorder D band around 1345 cm [superscript -1]. The dependence of the ratio of the intensities of D and G peaks, I(D)/I(G), on the irradiation dose is non-monotonic suggesting graphene.s transformation to polycrystalline and then to disordered state. By controlling the irradiation dose one can change the carrier mobility and increase the resistance at the minimum conduction point. The obtained results may lead to new methods of defect engineering of graphene properties. They also have important implications for fabrication of graphene nanodevices, which involve electron beams. Bismuth telluride and related compounds are the best thermoelectric materials known today. Recently, it was determined that they reveal the topological insulator properties. We succeeded in the first "graphene-like" exfoliation of large-area crystalline films and ribbons of Bi [subscript 2] Te [subscript 3] with the thickness going down to a single quintuple. The presence of van der Waals gaps allowed us to disassemble Bi [subscript 2] Te [subscript 3] crystal into the five mono-atomic sheets consisting of Te [superscript (1)] -Bi-Te [superscript (2)] -Bi-Te [superscript (1)]. The exfoliated films had extremely low thermal conductivity and electrical resistance in the range required for thermoelectric applications. The obtained results may pave the way for producing Bi [subscript 2] Te [subscript 3] films and stacked superlattices with strong quantum confinement of charge carriers and predominantly surface transport, and allow one to obtain theoretically predicted order-of-magnitude higher thermoelectric figure-of-merit.
Abstract from dissertation: My research program is focused on the study of elastic deformation and topological defects in two materials: graphene and topological insulators. In both systems at low energies the electrons have a nearly linear spectrum, i.e. they behave like relativistic fermions. This allows the study of the effects of defects and deformations on the dynamics of electrons trough the formalism of Dirac equation on curved space-time. In this setting it's possible to derive correction to observables properties of the systems like the conductivity for example. In the case of graphene I have derived the contribution to conductivity in the Born approximation of the metric arising from the so-called bumps and made a comparison with the scattering on the gauge potential arising from the elastic deformation. A particular defect, the edge dislocation, is found to be a possible responsible for the behaviour of the conductivity at low energies. The topological insulators are a class of band insulators showing gapless edge states, capable of conduction. This situation is similar to Quantum Hall Effect, both physically and formally. Indeed, as in QHE topological invariants (Chern numbers) classify the behaviour of the material. I am thus focused on the study of these material both formally, on the ground of differential geometry, and physically, studying topological defect in topological insulators. Further investigation has been devoted to the analysis of electron-phonon interaction at the surface of a 3D TI, analysing superconductive instability.
Angle resolved photoemission spectroscopy (ARPES) study on TlBiTe2 and TlBiSe2 from a Thallium-based III-V-VI2 ternary chalcogenides family revealed a single surface Dirac cone at the center of the Brillouin zone for both compounds. For TlBiSe2, the large bulk gap (≈ 200meV) makes it a topological insulator with better mechanical properties than the previous binary 3D topological insualtor family. For TlBiTe2, the observed negative bulk gap indicates it as a semi-metal, rather than a narrow gap semi-conductor as conventionally believed; this semi-metality naturally explains its mysteriously small thermoelectric figure of merit comparing to other compounds in the family. Finally, the unique band structures of TlBiTe2 also suggests it as a candidate for topological superconductors.
