| 1. |
- Laraña Aragón, Jorge, 1993-
(författare)
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Linear response theory: from black holes to Weyl systems and back
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Linear response theory is a powerful calculation tool in quantum field theory. We apply this framework to a variety of models originating from distinct areas in theoretical physics and for different reasons. In the context of black hole holography, we consider a quench model where we investigate effective thermalization, as well as the boundary signal of so-called evanescent modes which indicate the presence of a black hole-like object in the bulk. The problem of quantum thermalization plays a central role within the holographic duality between thermal states in the boundary field theory and black hole-like objects in the bulk. However, quantum thermalization is also an interesting question in itself from a fundamental point of view. Inspired by recent progress in understanding how operators in quantum field theories thermalize, which occurs even when considering integrable models, we investigate the so-called operator thermalization hypothesis. We focus on gauge theories at finite temperature with a large number of fields which present a phase transition between the low-temperature and high-temperature regimes. In a separate application of linear response theory, we investigate transport properties in a family of Weyl semimetal systems. Concretely, we develop a general analytic method to compute the magneto-optical conductivity of these systems in the presence of an external magnetic field aligned with the tilt of the spectrum. Last, we examine non-Hermitian Weyl-like systems as potential analogue black hole models and suggest a specific parity-time-symmetric dissipative Hamiltonian displaying analogue Hawking radiation.
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| 2. |
- Abouelkomsan, Ahmed, 1995-
(författare)
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Geometry, Topology and Emergence in Moiré Systems
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The experimental discovery of correlated insulators and superconductivity in highly tunable Van der Waals heterostructures, such as twisted bilayer graphene, has highlighted the role of moiré patterns, resulting from tiny relative twists or lattice constant mismatches, in realizing strongly correlated physics. A key ingredient is the existence of very narrow flat bands where interaction effects are dominant.In this thesis and the accompanying papers, we theoretically study a number of experimentally relevant moiré systems. We generally show that strong interactions combined with the geometry and the topology of the underlying flat bands can result in a plethora of distinct quantum many-body phases ranging from topological order to multiferroicity. Of particular importance are lattice analogues of the fractional quantum Hall effect known as fractional Chern insulators. They harbour peculiar phenomena such as fractional charge and statistics and provide a route towards realizing topologically ordered states at high temperature. A ubiquitous feature of the many-body physics is the emergence of unique particle-hole dualities driven by the geometry of band-projected interactions.
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| 3. |
- Abouelkomsan, Ahmed, 1995-
(författare)
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Strongly Correlated Moiré Materials
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recent advances in materials science have established Moiré materials as a new highly tunable and versatile form of quantum matter. When two dimensional atomic layers are brought into proximity, a tiny relative twist or a slight lattice mismatch produces Moiré patterns manifested in a superlattice structure with a lattice constant that is much larger than the lattice constants of the constituent layers. The new length scale has dramatic consequences for the underlying properties. A particular distinctive feature of Moiré materials is the emergence of nearly flat bands upon tuning external parameters such as the twist angle or the applied gate voltage. In a flat band, the kinetic energy is quenched, and interactions are enhanced bringing us to the realm of strongly correlated systems. A prime example of Moiré materials is twisted bilayer graphene, formed by taking two graphene layers and twisting them relative to each other.On the other hand, a famous class of interaction-induced phases of matter are fractional quantum Hall states and their lattice analogues known as fractional Chern insulators. These topologically ordered phases represent a departure from the conventional Landau symmetry breaking classification of matter, seen in the absence of local order parameters and the presence of global topological properties insensitive to local perturbations. Identifying and manufacturing materials that could host fractional Chern insulator states has a great potential for technological use.In this thesis, we provide the necessary background required for understanding the results of the accompanying papers [Phys. Rev. Lett. 124, 106803 & Phys. Rev. Lett. 126, 026801]. The theory of fractional Chern insulators is discussed followed by an introduction to the Moiré models used. In the two accompanying papers, we theoretically study a number of flat band Moiré materials aiming at identifying the possible phases that occur at fractional band fillings using a combination of analytical and numerical techniques. By reformulating the problem in terms of holes instead of electrons, it's possible to identify a variety of emergent weakly interacting Fermi liquids from an initial strongly interacting problem. In addition, our findings also include several high temperature fractional Chern insulator states at different fillings without external magnetic field.
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| 4. |
- Edvardsson, Elisabet, 1994-
(författare)
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Bulk-boundary correspondence and biorthogonality in non-Hermitian systems
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In topological insulators, the bulk-boundary correspondence describes the relationship between the bulk invariant -- computed for a system with periodic boundary conditions -- and the number of topological boundary states in the corresponding system with open boundary conditions. This is a well-known property of these systems and is important for predicting how they will behave. In recent years, however, the modeling of dissipative and non-equilibrium systems using non-Hermitian Hamiltonians has become increasingly popular. These systems feature many novel phenomena; in particular the bulk-boundary correspondence breaks down since the spectrum of the system with periodic boundary conditions typically differs fundamentally from the spectrum of the system with open boundary conditions. In this thesis, the behavior of the boundary states in non-Hermitian lattice models is studied. The framework of biorthogonal quantum mechanics is used to develop the biorthogonal bulk-boundary correspondence, which predicts the (dis)appearance of the boundary states in these systems. Closely related to the drastic change in spectra between boundary conditions is the non-Hermitian skin effect. This refers to the exponential localization of almost all eigenstates to the boundaries and is typically seen in non-Hermitian lattice models. How to predict this, and how to quantify the sensitivity of the spectrum to the boundary conditions are therefore questions that are also studied in this thesis.
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| 5. |
- Edvardsson, Elisabet
(författare)
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Bulk-boundary correspondence in non-Hermitian systems
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The bulk-boundary correspondence, which in topological insulators describes the relationship between the bulk invariant computed for a system with periodic boundary conditions and the number of boundary states in the corresponding system with open boundary conditions, is well-known and important for predicting the behavior of these systems. In recent years, however, the modeling of dissipative and non-equilibrium systems using non-Hermitian Hamiltonians has become increasingly popular. These systems feature many novel phenomena, but in particular the bulk-boundary correspondence breaks down since the spectrum of the system with periodic boundary conditions now differs fundamentally from the spectrum of the system with open boundary conditions. It is thus no longer possible to use the Bloch Hamiltonian to predict the appearance of boundary states.Integral to understanding the behavior of these systems, is to understand how the boundary states behave. This is what is studied in the accompanying papers, Biorthogonal bulk-boundary correspondence in non-Hermitian systems, Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence, and Phase transitions and generalized biorthogonal trace polarization in non-Hermitian systems, of this thesis, where also a new kind of biorthogonal bulk-boundary correspondence is developed.The aim of this licentiate thesis is to give the background necessary to understand the accompanying papers. It is divided into two parts. The first part describes the well-established theory of boundary states in a certain class of Hermitian systems for which there exist exact solutions that are straightforward to analyze, which then are generalized to the non-Hermitian case in the accompanying papers. The second part gives some background to non-Hermitian systems, the unusual phenomena that occur in them, and an introduction to biorthogonal quantum mechanics and why it is necessary to redefine the inner product one uses when calculating quantum mechanical probabilities.
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| 6. |
- Johansson Bergholtz, Emil, 1978-
(författare)
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One-dimensional theory of the quantum Hall system
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The quantum Hall (QH) system---cold electrons in two dimensions in a perpendicular magnetic field---is a striking example of a system where unexpected phenomena emerge at low energies. The low-energy physics of this system is effectively one-dimensional due to the magnetic field. We identify an exactly solvable limit of this interacting many-body problem, and provide strong evidence that its solutions are adiabatically connected to the observed QH states in a similar manner as the free electron gas is related to real interacting fermions in a metal according to Landau's Fermi liquid theory. The solvable limit corresponds to the electron gas on a thin torus. Here the ground states are gapped periodic crystals and the fractionally charged excitations appear as domain walls between degenerate ground states. The fractal structure of the abelian Haldane-Halperin hierarchy is manifest for generic two-body interactions. By minimizing a local k+1-body interaction we obtain a representation of the non-abelian Read-Rezayi states, where the domain wall patterns encode the fusion rules of the underlying conformal field theory. We provide extensive analytical and numerical evidence that the Laughlin/Jain states are continuously connected to the exact solutions. For more general hierarchical states we exploit the intriguing connection to conformal field theory and construct wave functions that coincide with the exact ones in the solvable limit. If correct, this construction implies the adiabatic continuation of the pertinent states. We provide some numerical support for this scenario at the recently observed fraction 4/11. Non-QH phases are separated from the thin torus by a phase transition. At half-filling, this leads to a Luttinger liquid of neutral dipoles which provides an explicit microscopic example of how weakly interacting quasiparticles in a reduced (zero) magnetic field emerge at low energies. We argue that this is also smoothly connected to the bulk state.
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| 7. |
- Stålhammar, Marcus, 1994-
(författare)
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Knots and Transport in Topological Matter
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Topology has manifestations in physics ranging from the field of condensed matter to photonics. This dissertation provides a two-fold study on the impact of topology in Hermitian and non-Hermitian band structures. Salient examples include the notion of topological invariants and knots, which are both used to describe characteristics of eigenvalue intersections. The first part focuses on Hermitian topological phases of matter, where general methods predicting transport properties in both gapped and gapless phases are presented. The second part turns to non-Hermitian phases and revolves around the topological properties of their exceptional eigenvalue degeneracies. Through a generic construction originating in knot theory, it is shown that such degeneracies take the form of knots, which furthermore bound open Fermi surfaces coinciding with the respective Seifert surfaces. This construction is then extended and applied in a similar fashion to parity-time-symmetric systems, where the exceptional points form surfaces and curves of any topology, as well as points. These theoretical descriptions constitute a fruitful platform to study dissipative systems—in particular in optics where parity-time symmetry implies a balance between gain and loss in photonic crystals—but also give rise to interesting connections to gravity in the context of analogue black holes.
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| 8. |
- Abouelkomsan, Ahmed, 1995-, et al.
(författare)
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Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Van der Waals heterostructures have recently emerged as an exciting platform for investigating the effects of strong electronic correlations, including various forms of magnetic or electrical orders. Here, we perform an unbiased exact diagonalization study of the effects of interactions on topological flat bands of twisted transition metal dichalcogenides (TMDs) at odd integer fillings. We find that Chern insulator phases, expected from interaction-induced spin and valley polarization of the bare band structure, are quite fragile, and give way to spontaneous multiferroic order -- coexisting ferroelectricity and ferromagnetism, in presence of long-range Coulomb repulsion. We provide a simple real-space picture to understand the phase diagram as a function of interaction range and strength. Our findings establish twisted TMDs as a novel and highly tunable platform for multiferroicity, with potential applications to electrical control of magnetism.
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| 9. |
- Abouelkomsan, Ahmed, 1995-, et al.
(författare)
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Quantum metric induced phases in Moiré materials
- 2023
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Ingår i: Physical Review Research. - 2643-1564. ; 5:1
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Tidskriftsartikel (refereegranskat)abstract
- We show that, quite generally, quantum geometry plays a major role in determining the low-energy physics in strongly correlated lattice models at fractional band fillings. We identify limits in which the Fubini-Study metric dictates the ground states and show that this is highly relevant for Moiré materials leading to symmetry breaking and interaction driven Fermi liquids. This phenomenology stems from a remarkable interplay between the quantum geometry and interaction which is absent in continuum Landau levels but generically present in lattice models where these terms tend to destabilize, e.g., fractional Chern insulators. We explain this as a consequence of the fundamental asymmetry between electrons and holes for band projected normal ordered interactions, as well as from the perspective of a self-consistent Hartree-Fock calculation. These basic insights about the role of the quantum metric, when dominant, turn an extremely strongly coupled problem into an effectively weakly coupled one, and may also serve as a guiding principle for designing material setups. We argue that this is a key ingredient for understanding symmetry-breaking phenomena recently observed in Moiré materials.
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| 10. |
- El Hassan, Ashraf, 1976-, et al.
(författare)
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Corner states of light in photonic waveguides
- 2019
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Ingår i: Nature Photonics. - : Springer Science and Business Media LLC. - 1749-4885 .- 1749-4893. ; 13:10, s. 697-700
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Tidskriftsartikel (refereegranskat)abstract
- The recently established paradigm of higher-order topological states of matter has shown that not only edge and surface states but also states localized to corners, can have robust and exotic properties. Here we report on the experimental realization of novel corner states made out of visible light in three-dimensional photonic structures inscribed in glass samples using femtosecond laser technology. By creating and analysing waveguide arrays, which form two-dimensional breathing kagome lattices in various sample geometries, we establish this as a platform for corner states exhibiting a remarkable degree of flexibility and control. In each sample geometry we measure eigenmodes that are localized at the corners in a finite frequency range, in complete analogy with a theoretical model of the breathing kagome. Here, measurements reveal that light can be ‘fractionalized,’ corresponding to simultaneous localization to each corner of a triangular sample, even in the presence of defects.
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