| 1. |
- Bergholtz, E. J., et al.
(författare)
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Pfaffian quantum Hall state made simple : Multiple vacua and domain walls on a thin torus
- 2006
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 74:8, s. 081308-
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the Moore-Read Pfaffian state on a thin torus. The known sixfold degeneracy is realized by two inequivalent crystalline states with a four- and twofold degeneracy, respectively. The fundamental quasihole and quasiparticle excitations are domain walls between these vacua, and simple counting arguments give a Hilbert space of dimension 2n−1 for 2n−k holes and k particles at fixed positions and assign each a charge ±e∕4. This generalizes the known properties of the hole excitations in the Pfaffian state as deduced using conformal field theory techniques. Numerical calculations using a model Hamiltonian and a small number of particles support the presence of a stable phase with degenerate vacua and quarter-charged domain walls also away from the thin-torus limit. A spin-chain Hamiltonian encodes the degenerate vacua and the various domain walls.
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| 2. |
- Bergholtz, Emil Johansson, et al.
(författare)
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Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states
- 2008
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Ingår i: Physical Review B Condensed Matter. - 0163-1829 .- 1095-3795. ; 77:16, s. 165325-1-165325-9
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Tidskriftsartikel (refereegranskat)abstract
- Laughlin’s wave functions, which describe the fractional quantum Hall effect at filling factorsν=1/(2k+1), can be obtained as correlation functions in a conformal field theory, and recently, this construction was extended to Jain’s composite fermion wave functions at filling factors ν=n/(2kn+1). Here, we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, which are the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multihole states, make the connection to Wen’s general classification of Abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally, we discuss to what extent our wave functions can be described in the language of composite fermions.
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| 3. |
- Fremling, Mikael, 1985-, et al.
(författare)
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Hall viscosity of hierarchical quantum Hall states
- 2014
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 89:12, s. 125303-
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Tidskriftsartikel (refereegranskat)abstract
- Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. Assuming the absence of Berry phases upon adiabatic variations of the modular parameter tau, we calculate the quantum Hall viscosity and find it to be in agreement with the formula, given by Read, which relates the viscosity to the average orbital spin of the electrons. For the filling factor nu = 2/5 Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex t plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function and the numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution.
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| 4. |
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| 5. |
- Hansson, Thors Hans, et al.
(författare)
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Conformal Field Theory Approach to Abelian and Non-Abelian Quantum Hall Quasielectrons
- 2009
-
Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 102:16, s. 166805-1-166805-4
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Tidskriftsartikel (refereegranskat)abstract
- The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.
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| 6. |
- Hansson, Thors Hans, et al.
(författare)
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Effective field theories for topological states of matter
- 2020
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Ingår i: Springer Proceedings in Physics. - Cham : Springer. - 0930-8989 .- 1867-4941. ; 239, s. 1-68
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Tidskriftsartikel (refereegranskat)abstract
- Since the discovery of the quantum Hall effect in the 1980s it has been clear that there exists states of matter characterized by subtle quantum mechanical effects that renders certain properties surprisingly stable against dirt and noise. The theoretical understanding of these topological quantum phases have continued to develop during the last few decades and it has really surged after the discovery of the time-reversal invariant topological insulators. There are many examples of topological phases that have been important for the theoretical understanding of topological states of matter as well as being of great physical relevance. In this chapter we will focus on some examples that we find particularly enlightening and relevant, but we will not make a complete classification. Some of the most important tools for the understanding of topological quantum matter are based on effective field theory methods. We shall employ two different types of effective field theories. The first, which is valid at intermediate length and time-scales, will not capture the physics at microscopic scales. Such theories are the analogs, for topological phases, of the Ginzburg–Landau theories used to describe the usual symmetry breaking non-topological phases. The second type of theories describe the physics on scales where non-topological gapped states would be very boring, namely at distances and times much larger than the correlation length and the time set by the inverse gap. On these scales everything is independent of any distance and the theories will be topological field theories, which do not describe any dynamics in the bulk, but do carry information about topological properties of the excitations, and also about excitations at the boundaries of the system. Finally, we will also study effective response actions. In a strict sense these are not effective theories, since they do not have any dynamical content, but encode the response of the system to external perturbations, typically an electromagnetic field. As we shall see, however, the effective response action for topological states can be used to extract parts of the dynamic theory through a method called functional bosonization.
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| 7. |
- Hansson, Thors Hans, et al.
(författare)
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Effective field theory for a p-wave superconductor in the subgap regime
- 2015
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 91:7
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Tidskriftsartikel (refereegranskat)abstract
- We construct an effective field theory for the 2d spinless p-wave paired superconductor that faithfully describes the topological properties of the bulk state, and also provides a model for the subgap states at vortex cores and edges. In particular, it captures the topologically protected zero modes and has the correct ground-state degeneracy on the torus. We also show that our effective field theory becomes a topological field theory in a well defined scaling limit and that the vortices have the expected non-Abelian braiding statistics.
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| 8. |
- Hansson, Thors Hans, et al.
(författare)
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Quantum Hall physics : Hierarchies and conformal field theory techniques
- 2017
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Ingår i: Reviews of Modern Physics. - : American Physical Society. - 0034-6861 .- 1539-0756. ; 89:2
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Tidskriftsartikel (refereegranskat)abstract
- The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past 30 years, has generated many ground-breaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the 30 years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of non-Abelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.
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| 9. |
- Hansson, Thors Hans, et al.
(författare)
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Quantum Hall quasielectron operators in conformal field theory
- 2009
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Ingår i: Physical Review B Condensed Matter. - : American Physical Society. - 0163-1829 .- 1095-3795. ; 80:16, s. 165330-1-165330-22
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Tidskriftsartikel (refereegranskat)abstract
- In the conformal field theory (CFT) approach to the quantum Hall effect, the multielectron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires nonlocal operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding, and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts additional ones. In particular, we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a long-time controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering that allows us to “fuse” an electron operator with the inverse of an hole operator and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions.
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| 10. |
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| 11. |
- Hermanns, Maria, et al.
(författare)
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Quantum Hall wave functions on the torus
- 2008
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Ingår i: Physical Review B Condensed Matter. - : American Physical Society. - 0163-1829 .- 1095-3795. ; 77:12, s. 125321-1-125321-16
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Tidskriftsartikel (refereegranskat)abstract
- We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at, e.g., ν=4∕11. The techniques we use constitute a nontrivial extension of the conformal field theory methods developed earlier to construct the corresponding wave functions in disk geometry.
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| 12. |
- Hermanns, Maria, 1980-
(författare)
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Quasielectrons in Abelian and non-Abelian Quantum Hall States
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Strongly correlated electron systems continue to attract a lot of interest. Especially two-dimensional electron systems have shown many surprising behaviours. A fascinating example is the quantum Hall effect, which arises when electrons are confined to two dimensions, subjected to a very large magnetic field, and cooled to very low temperatures. Under these conditions, the electrons form new states of matter - the strongly correlated quantum Hall liquids. A hallmark of these quantum liquids is the precise quantization of the Hall conductance, but in recent years more attention has been focused on their exotic excitations. These have fractional electric charge, and fractional exchange statistics. The latter implies that the wave function is multiplied by a phase factor containing a fractional phase when two quasiparticles are moved around each other. Thus, they are neither bosons nor fermions, but so-called anyons. In recent years, there has accumulated theoretical and experimental evidence for some of the quantum Hall liquids having even more exotic excitations with not only fractional but non-Abelian exchange statistics. The quasiparticles of such systems could be used to build topologically protected quantum bits, which are much more robust than presently available quantum bits; they would be the ideal building blocks of a quantum computer. We use conformal field theory to describe the quantum Hall liquids, as well as their excitations. In particular, we represent the electrons and quasiparticles by conformal field theory operators. Even though the operator description for quasiholes is very well understood, it was for a long time unclear how to describe their antiparticles, the quasielectrons. We found an operator that describes quasielectron excitations correctly and shares many of the useful properties of the corresponding quasihole operator. For instance, many of the topological properties of the particles are manifest in the operator. This not only adds a missing piece to the quantum Hall puzzle, but it also opens up new and exciting possibilities. For instance, we were able to extend this construction to the non-Abelian states. A highly non-trivial application of our approach is the condensation of non-Abelian quasielectrons, which yields new non-Abelian quantum Hall states with non-Abelian properties that differ from those of their parent states.
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| 13. |
- Imamura, Yukihisa, et al.
(författare)
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From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
- 2019
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 100:12
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we use a close connection between the coupled-wire construction (CWC) of Abelian quantum Hall states and the theory of composite bosons to extract the Laughlin wave function and the hydrodynamic effective theory in the bulk, including the Wen-Zee topological action, directly from the CWC. We show how rotational invariance can be recovered by fine tuning the interactions. A simple recipe is also given to construct general Abelian quantum Hall states described by the multicomponent Wen-Zee action.
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| 14. |
- Jiang, Qing-Dong, et al.
(författare)
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Geometric Induction in Chiral Superconductors
- 2020
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 124:19
-
Tidskriftsartikel (refereegranskat)abstract
- We consider a number of effects due to the interplay of superconductivity, electromagnetism, and elasticity, which are unique for thin membranes of layered chiral superconductors. Some of them should be within the reach of present technology, and could be useful for characterizing materials. More speculatively, the enriched control of Josephson junctions they afford might find useful applications.
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| 15. |
- Kailasvuori, Janik, 1975-
(författare)
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Quasiparticles in the Quantum Hall Effect
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The fractional quantum Hall effect (FQHE), discovered in 1982 in a two-dimensional electron system, has generated a wealth of successful theory and new concepts in condensed matter physics, but is still not fully understood. The possibility of having nonabelian quasiparticle statistics has recently attracted attention on purely theoretical grounds but also because of its potential applications in topologically protected quantum computing.This thesis focuses on the quasiparticles using three different approaches. The first is an effective Chern-Simons theory description, where the noncommutativity imposed on the classical space variables captures the incompressibility. We propose a construction of the quasielectron and illustrate how many-body quantum effects are emulated by a classical noncommutative theory.The second approach involves a study of quantum Hall states on a torus where one of the periods is taken to be almost zero. Characteristic quantum Hall properties survive in this limit in which they become very simple to understand. We illustrate this by giving a simple counting argument for degeneracy 2n-1, pertinent to nonabelian statistics, in the presence of 2n quasiholes in the Moore-Read state and generalise this result to 2n-k quasiholes and k quasielectrons.In the third approach, we study the topological nature of the degeneracy 2n-1 by using a recently proposed analogy between the Moore-Read state and the two-dimensional spin-polarized p-wave BCS state. We study a version of this problem where one can use techniques developed in the context of high-Tc superconductors to turn the vortex background into an effective gauge field in a Dirac equation. Topological arguments in the form of index theory gives the degeneracy 2n-1 for 2n vortices.
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| 16. |
- Kjäll, Jonas, et al.
(författare)
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Matrix product state representation of quasielectron wave functions
- 2018
-
Ingår i: Journal of Statistical Mechanics-Theory and Experiment. - : IOP Publishing. - 1742-5468.
-
Tidskriftsartikel (refereegranskat)abstract
- Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.
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| 17. |
- Kvorning, Thomas, 1986-
(författare)
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Non-local behaviour from local interactions
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- With the discovery of the quantum Hall effect more than thirty years ago, a whole new field emerged—that of topological quantum matter. This field is now a very mature one, and many different aspects are covered in the literature. The main text of this thesis introduces the field and gives a background to topological quantum matter, as well as topological aspects of superconductivity and the Abelian fractional quantum Hall (FQH) states. Together with the main text there are five articles that address five different questions, all connected to topological quantum matter.In the first article, representative wave functions for the Abelian FQH states are calculated using conformal field theory methods. Before this paper was published, similar constructions had been restricted to flat geometries, but in this paper we generalize the analysis to the simplest curved geometry, namely the sphere. On top of being of interest for numerical studies (which usually are performed on a sphere), the response of the FQH liquids to curvature can be used to detect a topological quantity, the shift, which is the average orbital spin of the constituent electrons.In the second article, we construct an effective field theory for the two-dimensional spinless, chiral p-wave superconductor that faithfully describes the topological properties of the bulk state, and also provides a model for the subgap states at vortex cores and edges. In particular, it captures the topologically protected zero-modes and has the correct ground state degeneracy on the torus.In the third paper, tools for a hydrodynamic theory for insulators in three dimensions are derived. Specifically, we use functional bosonization to write insulators as a condensation phase of the U(1) gauge theory obtained in the functional bosonization language.In the fourth paper, we investigate the edge Majorana modes in the two-dimensional chiral p-wave superconductor. We define the model on surfaces with different geometries—the annulus, the cylinder, the Möbius band, and a cone—and with different configurations of magnetic flux threading holes in these surfaces. In particular, we address the following question: Given that, in the absence of magnetic flux, the ground state on the annulus does not support Majorana modes, while the one on the cylinder does, how is it possible that the conical geometry can interpolate smoothly between the two?In the fifth and last article, we demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. We propose this geo-Meissner effect as an unequivocal signature of chiral superconductivity that could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of Majorana modes.
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| 18. |
- Kvorning, Thomas, et al.
(författare)
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The geo-Meissner effect
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. We propose this geo-Meissner effect as an unequivocal signature of chiral superconductivity that could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of Majorana modes.
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| 19. |
- Li, Xiang, et al.
(författare)
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Gauge-independent description of the Aharonov-Bohm effect
- 2022
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - 2469-9926 .- 2469-9934. ; 106:3
-
Tidskriftsartikel (refereegranskat)abstract
- The Aharonov-Bohm (AB) effect is a pure quantum effect that implies a measurable phase shift in the wave function for a charged particle that encircles a magnetic flux located in a region inaccessible to the particle. Classically, such a nonlocal effect appears to be impossible since the Lorentz force depends on only the magnetic field at the location of the particle. In quantum mechanics, the Hamiltonian, and thus the Schrödinger equation, has a local coupling between the current due to the particle and the electromagnetic vector potential A, which extends to the entire space beyond the region with finite magnetic field. This has sometimes been interpreted as meaning that in quantum mechanics A is in some sense more “fundamental” than B in spite of the former being gauge dependent and thus unobservable. Here we shall, with a general proof followed by a few examples, demonstrate that the AB effect can be fully accounted for by considering only the gauge-invariant B field, as long as it is included as part of the quantum action of the entire isolated system. The price for the gauge-invariant formulation is that we must give up locality—the AB phase for the particle will arise from the change in the action for the B field in the region inaccessible to the particle.
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| 20. |
- Marino, E C, et al.
(författare)
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Screening and topological order in thin superconducting films
- 2018
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Ingår i: New Journal of Physics. - : Institute of Physics (IOP). - 1367-2630. ; 20, s. 1-13
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Tidskriftsartikel (refereegranskat)abstract
- We derive an effective two-dimensional low-energy theory for thin superconducting films coupled to a three-dimensional fluctuating electromagnetic field. Using this theory we discuss plasma oscillations, interactions between charges and vortices and extract the energy of a vortex. Having found that the effective theory properly describes the long-distance physics, we then use it to investigate to what extent the superconducting film is a topologically ordered phase of matter.
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| 21. |
- Niemi, Antti, et al.
(författare)
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Nobel Symposium 148 : Graphene and quantum matter
- 2012
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Ingår i: Physica scripta. T. - 0281-1847. ; :T146
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- The 2010 Nobel Symposium on Graphene and Quantum Matter, was held at the Grand Hotel in Saltsjöbaden south of Stockholm on 27-31 May. The main theme of the meeting was graphene, and the symposium turned out to be very timely: two of the participants, Andre Geim and Kanstantin Novoselov returned to Stockholm less then six months later to receive the 2010 Nobel Prize in Physics. In these proceedings leading experts give up-to-date, historical, experimental, theoretical and technological perspectives on the remarkable material graphene, and several papers also make connections to other states of quantum matter. Saltsjöbaden is beautifully situated in the inner archipelago of Stockholm. It provided a pleasant setting for the talks and the ensuing discussions that took place in an enthusiastic and friendly atmosphere. The social programme included a boat trip in the light summer night and a dinner at the renowned Grand Hotel. These proceedings are ordered thematically, starting with historical overviews, followed by first experimental and then theoretical papers on the physics of graphene. Next are several papers addressing more general topics in quantum matter and finally contributions on the technological applications of graphene. We hope that this volume will serve as a source of knowledge and inspiration for any physicist interested in graphene, and at the same time provide a snapshot of a young field of research that is developing at very high speed. We are grateful to Marja Fahlander for excellent administrative support, and to the Nobel Foundation who funded the symposium.
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| 22. |
- Quelle, A., et al.
(författare)
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Edge Majoranas on locally flat surfaces : The cone and the Möbius band
- 2016
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 94:12
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we investigate the edge Majorana modes in the simplest possible p(x) + ip(y) superconductor defined on surfaces with different geometries, the annulus, the cylinder, the Mobius band, and a cone (by cone we mean a cone with the tip cut away so it is topologically equivalent to the annulus and cylinder), and with different configurations of magnetic fluxes threading holes in these surfaces. In particular, we shall address two questions: Given that, in the absence of any flux, the ground state on the annulus does not support Majorana modes while the one on the cylinder does, how is it possible that the conical geometry can interpolate smoothly between the two? Given that in finite geometries edge Majorana modes have to come in pairs, how can a p(x) + ip(y) state be defined on a Mobius band, which has only one edge? We show that the key to answering these questions is that the ground state depends on the geometry, even though all the surfaces are locally flat. In the case of the truncated cone, there is a nontrivial holonomy, while the nonorientable Mobius band must necessarily support a domain wall.
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| 23. |
- Spånslätt, Christian, et al.
(författare)
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Topological aspects of π phase winding junctions in superconducting wires
- 2015
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Ingår i: Journal of Physics. - : IOP Publishing. - 0953-8984 .- 1361-648X. ; 27:40
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Tidskriftsartikel (refereegranskat)abstract
- We theoretically investigate Josephson junctions with a phase shift of pi in various proximity induced one-dimensional superconductor models. One of the salient experimental signatures of topological superconductors, namely the fractionalized 4 pi periodic Josephson effect, is closely related to the occurrence of a characteristic zero energy bound state in such junctions. We make a detailed analysis of a more general type of pi-junctions coined 'phase winding junctions' where the phase of the order parameter rotates by an angle pi while its absolute value is kept finite. Such junctions have different properties, also from a topological viewpoint, and there are no protected zero energy modes. We compare the phenomenology of such junctions in topological (p-wave) and trivial (s-wave) superconducting wires, and briefly discuss possible experimental probes. Furthermore, we propose a topological field theory that gives a minimal description of a wire with defects corresponding to p-junctions. This effective theory is a one-dimensional version of similar theories describing Majorana bound states in half-vortices of two-dimensional topological superconductors.
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| 24. |
- Spånslätt, Christian, 1987-
(författare)
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Topological states of matter in low dimensions
- 2018
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A central theme in condensed matter physics is the classification and characterization of states of matter. In the recent decades, it has become evident that there exists a large class of quantum mechanical systems that must be classified according to properties deeply rooted in the mathematical field of topology, rather than in terms of which symmetries they break. Together with rapid technological developments, such topological states of matter pose a promising path for a fundamentally new generation of quantum devices and exotically engineered materials, with applications in quantum metrology, quantum sensing, and quantum computations.This doctoral thesis comprises a study of a general theoretical framework describing topological states of matter, followed by applications in systems of low dimension. Together, these two parts form the foundation for the following accompanying papers:PAPERS I-II concerns Majorana zero modes in various Josephson junction setups of one-dimensional topological superconductors. In addition to determining the mathematical conditions for the existence of such exotic states, the papers also provide experimental proposals for their detection. PAPER III deals with the nature of a widely used model of a synthetically engineered one-dimensional topological superconductor. It is shown that in a certain parameter limit, the superconducting order parameter obtains a geometric contribution, which originates from the directional nature of the Rashba spin-orbit coupling. This geometrical dependence is argued to manifest itself in various Josephson junction setups, and in particular as a direct connection between the charge current density and the local curvature.PAPER IV proposes a method of constructing non-local order parameters for two-dimensional Chern insulators, and describes how such operators can be used to distinguish between different topological sectors.
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| 25. |
- Stålhammar, Marcus, et al.
(författare)
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Electromagnetic response of topological superconductors
- 2021
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 103:23
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Tidskriftsartikel (refereegranskat)abstract
- We resolve several puzzles related to the electromagnetic response of topological superconductors in 3+1 dimensions. In particular we show by an analytical calculation that the interface between a topological and normal superconductor does not exhibit any quantum Hall effect as long as time reversal invariance is preserved. We contrast this with the analogous case of a topological insulator to normal insulator interface. The difference is that in the topological insulator the electromagnetic vector potential couples to a vector current in a theory with a Dirac mass, while in the superconductor a pair of Weyl fermions is gapped by Majorana masses and the electromagnetic vector potential couples to its axial currents.
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| 26. |
- Suorsa, J., et al.
(författare)
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A general approach to quantum Hall hierarchies
- 2011
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 13, s. 075006-
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Tidskriftsartikel (refereegranskat)abstract
- The Abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-Abelian states emanating from the nu = 5/2 Moore-Read state in the second Landau level. Extending a recently developed formalism for hierarchical quasihole condensation, we present a theory that allows for the explicit construction of the ground state wave function, as well as its quasiparticle excitations, for any state based on the Abelian hierarchy. We relate our construction to structures in rational conformal field theory and stress the importance of using coherent state wave functions, which allows us to formulate an extension of the bulk-edge correspondence that was conjectured by Moore and Read. Finally, we study the proposed ground state wave functions in the limiting geometry of a thin torus and argue that they coincide with the known exact results.
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| 27. |
- Suorsa, J., et al.
(författare)
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Quasihole condensates in quantum Hall liquids
- 2011
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 83:23, s. 235130-
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Tidskriftsartikel (refereegranskat)abstract
- We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinations of quasielectron and quasihole condensates.
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| 28. |
- Tournois, Yoran, et al.
(författare)
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Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
- 2020
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Ingår i: SciPost Physics. - : SCIPOST FOUNDATION. - 2542-4653. ; 8:5
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Tidskriftsartikel (refereegranskat)abstract
- We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized "flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field.
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| 29. |
- Åkesson, Torsten, et al.
(författare)
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Relativisera inte synen på människoliv
- 2022
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Ingår i: Altinget.
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Det sägs ofta att mätt i överdödlighet är Sverige ett av de länder som har klarat coronapandemin bäst. Men de hittills gjorda studierna av överdödlighet hjälper oss inte att bedöma den svenska pandemistrategin. Det skriver forskarna Joacim Rocklöv, Peter Jagers, Holger Rootzen, Thors Hans Hansson och Torsten Åkesson.
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