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Concept# Topological order

Résumé

In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition.
Various topologically ordered states have interesting properties, such as (1) topological degeneracy and fractional statistics or non-Abelian statistics that can be used to realize a topological quantum computer; (2) perfect conducting edge states that may have important device applications; (3) emergent gauge field and Fermi statistics that suggest a quantum information origin of elementary particles; (4) topological entanglement entropy that

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PHYS-726: Introduction to Frustrated Magnetism

To provide an introduction to all aspects of the rapidly evolving field of frustrated magnetism:

- New paradigms: spin liquids, spin ice, topological order, ...
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PHYS-309: Solid state physics I

This lecture gives an introduction to Solid State Physics, namely to their crystal and electronic structure, their magnetic properties, as well as to their thermal and electric conductance. The level is that of the book by Ashcroft & Mermin. The lecture is for Physics Students in their 3rd year

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The topological order of a quantum Hall state is mirrored by the gapless edge modes owing to bulk-edge correspondence. The state at the filling of ν = 5/2, predicted to host non-abelian anyons, supports a variety of edge modes (integer, fractional, neutral). To ensure thermal equilibration between the edge modes and thus accurately determine the state’s nature, it is advantageous to isolate the fractional channel (1/2 and neutral modes). In this study, we gapped out the integer modes by interfacing the ν = 5/2 state with integer states ν = 2 and ν = 3 and measured the thermal conductance of the isolated-interface channel. Our measured half-quantized thermal conductance confirms the non-abelian nature of the ν = 5/2 state and its particle-hole Pfaffian topological order. Such an isolated channel may be more amenable to braiding experiments.

2022Soudabeh Sheikholharam Mashhadi

From recent advances in solid state physics, a novel material classification scheme has evolved
which is based on the concept of topology and provides an understanding of different phenomena
ranging from quantum transport to unusual flavors of superconductivity. Spin-orbit
coupling is a major term in defining the topology of materials, and its interplay with electron electron
correlations yields novel, intriguing phenomena. In the weak to intermediate correlation
regime, spin-orbital entanglement leads to the emergence of topological insulators,
which constitute Dirac materials with 2D spin-polarized helical edge or surface
states and an insulating bulk. In the specific case of topological insulators,
theory predicts that their unique band structure leads to a high thermoelectric performance,
which is of practical relevance for energy conversion applications.In the strong correlation regime, the spin-orbit coupling removes the orbital degeneracy,
thereby enhancing quantum fluctuations of the spin-orbit entangled states. This in turn can
lead to the emergence of novel phases such as quantum spin liquids and unconventional
superconductivity. The Kitaev quantum spin liquid (QSL) is a topological state of matter that
exhibits fractionalized excitations in the form of Majorana fermions.
The main aim of this thesis was to study these novel states of matter in the form of two different
materials that fall in the weak and strong correlation regime, respectively. On this basis, it
should furthermore be explored whether benefit can be taken of their properties by combining
them with other quantum materials into heterostructures.In the first part of this thesis, nanoplatelets of bismuth chalcogenide-based 3D topological
insulators were grown by chemical vapor deposition, and characterized by magnetotransport
experiments. Having established charge transport characteristics of the single components, in
the aim to exploit their high thermoelectric efficiency, the lateral heteroctructures of them
are fabricated. Their investigation by scanning photocurrent microscopy revealed strong
photocurrent generation at the p-n junction. The obtained results demonstrate that such type of hybrid
heterostructure is a promising route to enhance the thermoelectric performance in nanostructured
devices.
In the second part of this thesis, the Kitaev spin liquid candidate, RuCl3 was studied. Raman spectroscopy on exfoliated
RuCl3 revealed a broad magnetic continuumat low energies which according to its particular
deviation from bosonic character is assigned to the fractionalized excitations. Furthermore,
in complementary charge transport experiments, it was found that themagnetic fluctuations
and structural changes in thismaterial are highly entangled, and influence the emergence of
the fractionalized excitations.
Finally, it was investigated whether the magnetic insulator character of ®-RuCl3 can be exploited
to alter the graphene band structure through a proximity effect in vertical graphene/
RuCl3 heterostructures. Measurements of their low-temperature, nonlocal resistance confirmed
the possibility to induce pure spin currents in this manner. At the same time, the
charge transport through the graphene served as a probe of the magnetic ordering in RuCl3,
although the complex magnetic behavior in this material necessitates more studies.

We theoretically study the topological properties of the tight-binding model on the breathing kagome lattice with antisymmetric spin-orbit coupling (SOC) between nearest neighbors. We show that the system hosts nontrivial topological phases even without second-nearest-neighbor hopping and that the weakly dispersing band of the kagome lattice can become topological. The main results are presented in the form of phase diagrams, where the Z(2)( )topological index is shown as a function of SOC (intrinsically allowed and Rashba) and lattice trimerization. In addition, exact diagonalization is compared with effective low-energy theories around the high-symmetry points. We find that the weakly dispersing band has a very robust topological property associated with it. Moreover, the Rashba SOC can produce a topological phase rather than hinder it, in contrast to the honeycomb lattice. Finally, we consider the case of a fully spin polarized (ferromagnetic) system, breaking time-reversal symmetry. We find a phase diagram that includes systems with finite Chern numbers. In this case too, the weakly dispersing band is topologically robust to trimerization.

2019