| 1. |
- 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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| 2. |
- Agarwala, Adhip, et al.
(författare)
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Higher-order topological insulators in amorphous solids
- 2020
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Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 2:1
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Tidskriftsartikel (refereegranskat)abstract
- We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Starting from two- and three-dimensional crystalline HOT insulators, accommodating topological corner states, we gradually enhance structural randomness in the system. Within a parameter regime, as long as amorphousness is confined by an outer crystalline boundary, the system continues to host corner states, yielding amorphous HOT insulators. However, as structural disorder percolates to the edges, corner states start to dissolve into amorphous bulk, and ultimately the system becomes a trivial insulator when amorphousness plagues the entire system. These outcomes are further substantiated by computing the quadrupolar (octupolar) moment in two (three) dimensions. Therefore, HOT phases can be realized in amorphous solids, when wrapped by a thin (lithographically grown, for example) crystalline layer. Our findings suggest that crystalline topological phases can be realized even in the absence of local crystalline symmetry.
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| 3. |
- Amundsen, Morten, et al.
(författare)
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Controlling Majorana modes by p-wave pairing in two-dimensional p
- 2022
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Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 4:1
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Tidskriftsartikel (refereegranskat)abstract
- We show that corner Majorana zero modes in a two-dimensional p + id topological superconductor can be controlled by the manipulation of the parent p-wave superconducting order. Assuming that the p-wave superconducting order is in either a chiral or helical phase, we find that when a d(x2-y2) wave superconducting order is induced, the system exhibits quite different behavior depending on the nature of the parent p-wave phase. In particular, we find that while in the helical phase, a localized Majorana mode appears at each of the four corners, in the chiral phase, it is localized along only two of the four edges. We furthermore demonstrate that the Majoranas can be directly controlled by the form of the edges, as we explicitly show in the case of circular edges. We argue that the application of strain may provide additional means of fine-tuning the Majorana zero modes in the system; in particular, it can partially gap them out. Our findings may be relevant for probing the topology in two-dimensional mixed-pairing superconductors.
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| 4. |
- Amundsen, Morten, et al.
(författare)
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Grain-boundary topological superconductor
- 2023
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Ingår i: Communications Physics. - : Springer Nature. - 2399-3650. ; 6:1
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Tidskriftsartikel (refereegranskat)abstract
- Majorana zero modes (MZMs) are of central importance for modern condensed matter physics and quantum information due to their non-Abelian nature, which thereby offers the possibility of realizing topological quantum bits. We here show that a grain boundary (GB) defect can host a topological superconductor (SC), with a pair of cohabitating MZMs at its end when immersed in a parent two-dimensional gapped topological SC with the Fermi surface enclosing a nonzero momentum. The essence of our proposal lies in the magnetic-field driven hybridization of the localized MZMs at the elementary blocks of the GB defect, the single lattice dislocations, due to the MZM spin being locked to the Burgers vector. Indeed, as we show through numerical and analytical calculations, the GB topological SC with two localized MZMs emerges in a finite range of both the angle and magnitude of the external magnetic field. Our work demonstrates the possibility of defect-based platforms for quantum information technology and opens up a route for their systematic search in future.
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| 5. |
- Călugăru, Dumitru, et al.
(författare)
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Higher-order topological phases : A general principle of construction
- 2019
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 99:4
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Tidskriftsartikel (refereegranskat)abstract
- We propose a general principle for constructing higher-order topological (HOT) phases. We argue that if a D-dimensional first-order or regular topological phase involves m Hermitian matrices that anticommute with additional p - 1 mutually anticommuting matrices, it is conceivable to realize an nth-order HOT phase, where n = 1, ..., p, with appropriate combinations of discrete symmetry-breaking Wilsonian masses. An nth-order HOT phase accommodates zero modes on a surface with codimension n. We exemplify these scenarios for prototypical three-dimensional gapless systems, such as a nodal-loop semimetal possessing SU(2) spin-rotational symmetry, and Dirac semimetals, transforming under (pseudo)spin-1/2 or 1 representations. The former system permits an unprecedented realization of a fourth-order phase, without any surface zero modes. Our construction can be generalized to HOT insulators and superconductors in any dimension and symmetry class.
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| 6. |
- D'Ambrosio, Federico, et al.
(författare)
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Discontinuous evolution of the structure of stretching polycrystalline graphene
- 2019
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 100:16
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Tidskriftsartikel (refereegranskat)abstract
- Polycrystalline graphene has an inherent tendency to buckle, i.e., develop out-of-plane, three-dimensional structure. A force applied to stretch a piece of polycrystalline graphene influences the out-of-plane structure. Even if the graphene is well relaxed, this happens in nonlinear fashion: Occasionally, a tiny increase in stretching force induces a significant displacement, in close analogy to avalanches, which in turn can create vibrations in the surrounding medium. We establish this effect in computer simulations: By continuously changing the strain, we follow the displacements of the carbon atoms that turn out to exhibit a discontinuous evolution. Furthermore, the displacements exhibit a hysteretic behavior upon the change from low to high stress and back. These behaviors open up another direction in studying dynamical elasticity of polycrystalline quasi-two-dimensional systems, and in particular the implications on their mechanical and thermal properties.
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| 7. |
- Dong, Junkai, et al.
(författare)
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Topolectric circuits : Theory and construction
- 2021
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Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 3:2
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Tidskriftsartikel (refereegranskat)abstract
- We highlight a general theory to engineer arbitrary Hermitian tight-binding lattice models in electrical LC circuits, where the lattice sites are replaced by the electrical nodes, connected to its neighbors and to the ground by capacitors and inductors. In particular, by supplementing each node with n subnodes, where the phases of the current and voltage are the n distinct roots of unity, one can in principle realize arbitrary hopping amplitude between the sites or nodes via the shift capacitor coupling between them. This general principle is then implemented to construct a plethora of topological models in electrical circuits, topolectric circuits, where the robust zero-energy topological boundary modes manifest through a large boundary impedance, when the circuit is tuned to the resonance frequency. The simplicity of our circuit constructions is based on the fact that the existence of the boundary modes relies only on the Clifford algebra of the corresponding Hermitian matrices entering the Hamiltonian and not on their particular representation. This in turn enables us to implement a wide class of topological models through rather simple topolectric circuits with nodes consisting of only two subnodes. We anchor these outcomes from the numerical computation of the on-resonance impedance in circuit realizations of first-order (m = 1), such as Chern and quantum spin Hall insulators, and second- (m = 2) and third- (m = 3) order topological insulators in different dimensions, featuring sharp localization on boundaries of codimensionality d(c) = m. Finally, we subscribe to the stacked topolectric circuit construction to engineer three-dimensional Weyl, nodal-loop, quadrupolar Dirac, and Weyl semimetals, respectively, displaying surface- and hinge-localized impedance.
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| 8. |
- Dunnett, Kirsty, et al.
(författare)
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Dynamic Multiferroicity of a Ferroelectric Quantum Critical Point
- 2019
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Ingår i: Physical Review Letters. - : AMER PHYSICAL SOC. - 0031-9007 .- 1079-7114. ; 122:5
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Tidskriftsartikel (refereegranskat)abstract
- Quantum matter hosts a large variety of phases, some coexisting, some competing; when two or more orders occur together, they are often entangled and cannot be separated. Dynamical multiferroicity, where fluctuations of electric dipoles lead to magnetization, is an example where the two orders are impossible to disentangle. Here we demonstrate an elevated magnetic response of a ferroelectric near the ferroelectric quantum critical point (FE QCP), since magnetic fluctuations are entangled with ferroelectric fluctuations. We thus suggest that any ferroelectric quantum critical point is an inherent multiferroic quantum critical point. We calculate the magnetic susceptibility near the FE QCP and find a region with enhanced magnetic signatures near the FE QCP and controlled by the tuning parameter of the ferroelectric phase. The effect is small but observable-we propose quantum paraelectric strontium titanate as a candidate material where the magnitude of the induced magnetic moments can be similar to 5 x 10(-7) mu(B) per unit cell near the FE QCP.
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| 9. |
- 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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| 10. |
- Geilhufe, Matthias, et al.
(författare)
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Dynamically induced magnetism in KTaO3
- 2021
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Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 3:2
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Tidskriftsartikel (refereegranskat)abstract
- Dynamical multiferroicity features entangled dynamic orders: fluctuating electric dipoles induce magnetization. Hence, the material with paraelectric fluctuations can develop magnetic signatures if dynamically driven. We identify the paraelectric KTaO3 (KTO) as a prime candidate for the observation of the dynamical multiferroicity. We show that when a KTO sample is exposed to a circularly polarized laser pulse, the dynamically induced ionic magnetic moments are of the order of 5% of the nuclear magneton per unit cell. We determine the phonon spectrum using ab initio methods, and we identify T-1u as relevant phonon modes that couple to the external field and induce magnetic polarization. We also predict a corresponding electron effect for the dynamically induced magnetic moment, which is enhanced by several orders of magnitude due to the significant mass difference between electron and ionic nucleus.
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