| 1. |
- Abouelkomsan, Ahmed, 1995-
(author)
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Geometry, Topology and Emergence in Moiré Systems
- 2022
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Doctoral thesis (other academic/artistic)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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| 2. |
- Johansson Bergholtz, Emil, 1978-
(author)
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One-dimensional theory of the quantum Hall system
- 2008
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Doctoral thesis (other academic/artistic)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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| 3. |
- Stålhammar, Marcus, 1994-
(author)
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Knots and Transport in Topological Matter
- 2022
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Doctoral thesis (other academic/artistic)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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| 4. |
- Abouelkomsan, Ahmed, 1995-, et al.
(author)
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Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides
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Other publication (other academic/artistic)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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| 5. |
- Abouelkomsan, Ahmed, 1995-, et al.
(author)
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Quantum metric induced phases in Moiré materials
- 2023
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In: Physical Review Research. - 2643-1564. ; 5:1
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Journal article (peer-reviewed)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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| 6. |
- Fleckenstein, Christoph, et al.
(author)
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Non-Hermitian topology in monitored quantum circuits
- 2022
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In: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 4:3
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Journal article (peer-reviewed)abstract
- We demonstrate that genuinely non-Hermitian topological phases and corresponding topological phase transitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic non-Hermitian Su-Schrieffer-Heeger model. We emulate this model by a 1D chain of spinless electrons evolving under unitary dynamics and subject to periodic measurements that are stochastically invoked. The non-Hermitian topology is visible in topological invariants adapted to the context of monitored circuits. For instance, the topological phase diagram of the monitored realization of the non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal polarization computed from an effective Hamiltonian of the monitored system. Importantly, our monitored circuit realization allows direct access to steady-state biorthogonal expectation values of generic observables, and hence, to measure physical properties of a genuine non-Hermitian model. We expect our results to be applicable more generally to a wide range of models that host non-Hermitian topological phases.
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| 7. |
- He, Yuchi, et al.
(author)
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Superconductivity of repulsive spinless fermions with sublattice potentials
- 2023
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In: Physical Review Research. - 2643-1564. ; 5:1
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Journal article (peer-reviewed)abstract
- We explore unconventional superconductivity of repulsive spinless fermions on square and honeycomb lattices with staggered sublattice potentials. The two lattices can exhibit staggered d-wave and f-wave pairing, respectively, at low doping stemming from an effective two-valley band structure. At higher doping, in particular, the square lattice displays a much richer phase diagram including topological p+ip superconductivity which is induced by a qualitatively different mechanism compared to the d-wave pairing. We illuminate this from several complementary perspectives: We analytically perform sublattice projection to analyze the effective continuum low-energy description and we numerically calculate the binding energies for pair and larger bound states for few-body doping near half filling. Furthermore, for finite doping, we present phase diagrams based on extensive functional renormalization group and and density matrix renormalization group calculations.
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| 8. |
- König, J. Lukas K., et al.
(author)
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Braid-protected topological band structures with unpaired exceptional points
- 2023
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In: Physical Review Research. - 2643-1564. ; 5:4
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Journal article (peer-reviewed)abstract
- We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e., the necessity of compensating the topological charge of a stable nodal point by an antidote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how nonommuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy represents a sweet spot within a larger topological phase that cannot be fully gapped by any local perturbation. Instead, it may only split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels, and provide insights into the topological robustness of non-Hermitian systems and their non-Abelian phase transitions.
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| 9. |
- König, J. Lukas K., 1996-, et al.
(author)
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Nodal phases in non-Hermitian wallpaper crystals
- 2024
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In: Applied Physics Letters. - 0003-6951 .- 1077-3118. ; 124:5
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Journal article (peer-reviewed)abstract
- Symmetry and non-Hermiticity play pivotal roles in photonic lattices. While symmetries, such as parity-time (PT) symmetry, have attracted ample attention, more intricate crystalline symmetries have been neglected in comparison. Here, we investigate the impact of the 17 wallpaper space groups of two-dimensional crystals on non-Hermitian band structures. We show that the non-trivial space group representations enforce degeneracies at high symmetry points and dictate their dispersion away from these points. In combination with either T or PT, the symmorphic p4 mm symmetry and the non-symmorphic p2mg, p2gg, and p4gm symmetries protect exceptional chains intersecting at the pertinent high symmetry points.
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| 10. |
- Molignini, Paolo, 1988-, et al.
(author)
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Anomalous skin effects in disordered systems with a single non-Hermitian impurity
- 2023
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In: Physical Review Research. - 2643-1564. ; 5:3
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Journal article (peer-reviewed)abstract
- We explore anomalous skin effects at non-Hermitian impurities by studying their interplay with potential disorder and by exactly solving a minimal lattice model. A striking feature of the solvable single-impurity model is that the presence of anisotropic hopping terms can induce a scale-free accumulation of all eigenstates opposite to the bulk hopping direction, although the nonmonotonic behavior is fine tuned and further increasing such hopping weakens and eventually reverses the effect. The interplay with bulk potential disorder, however, qualitatively enriches this phenomenology leading to a robust nonmonotonic localization behavior as directional hopping strengths are tuned. Nonmonotonicity persists even in the limit of an entirely Hermitian bulk with a single non-Hermitian impurity.
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