In 1988, in cooperation with a team of experimental physicists, a Condensed Matter theorist, X, published in Physical Review Letters a crucial experimental result dealing with a revolutionary new theory. The conclusions of the paper were proved incorrect a few months later. I discuss the various factors – scientific, instrumental, but also psychological, sociological ones – which led to this blunder. I believe this story sheds some light on the process of scientific discovery, explanation, falsification, confirmation, and errors.

This paper deals with Nancy Cartwright's views on the measurement problem in Quantum Mechanics, as exposed in her book {\it{How the Laws of Physics Lie}}. She does not accept the logic of Quantum Mechanics. It is argued that her proposals, which are at variance with many facts results and epistemics of Quantum Mechanics are the result of her choice of classical logic, which leads her to propose the transition rate as the fundamental object of Quantum Mechanics. I argue that this is incorrect. The positions which Nancy Cartwright defends on the reduction of the wave packet do not address the fundamental issue, i.e. the duality of a world where quantum and classical objects coexist and interact. I suggest that the main problem with Nancy Cartwright's positions is her difficulty in accepting that the contradiction at the basis of Quantum Mechanics, i.e. the simultaneous corpuscular and wave-like nature of quantum objects, is a fact of nature. Recent experiments, described in this paper, shed a new light on the foundations of Quantum Mechanics and on the topic of this paper. The limits of the no-contradiction principle are discussed; modern dialectical materialism is argued to offer a useful framework for the interplay between knowledge and reality.

The early development of conflicting theories about the microscopic mechanism of High Temperature Superconductivity is described. The biographical roots of this diversity are stressed, as well as its subjective/objective roots. This study of a specific case of knowledge about a specific fact of nature allows to discuss the subjective and objective roots of scientific pluralism. Relativism, the Duhem-Quine thesis on the underdetermination of theory by facts, are discussed from the stand point of the materialist view on the dialectics of knowledge and nature. Developments of dialectic materialism seem to be suggested by this study.

The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as complementarity, gauge invariance, strong interactions, emergence of new theoretical concepts. This paper focuses on some related philosophical questions. Hacking's views on Scientific Realism, Chalmers' on Non Figurative Realism are discussed. It is argued that the difficulties with those versions of realism may be resolved within a dialectical materialist approach. The latter is shown to provide a rational approach to the phenomena, the theory and the ontology of the Quantum Hall Effects.

This paper deals with the Berry phase, and the ontology of the electromagnetic vector potential. When the state of the system is gauge symmetric, the vector potential may be interpreted as a convenient tool of a mathematical formulation, with no ontological meaning. I argue that this interpretation is in difficulty because the vector potential depends linearly on the supercurrent in the superfluid state, which is a spontaneously broken gauge symmetry state, where particle number is not conserved. I suggest that when gauge symmetry is spontaneously broken, the vector potential becomes an emergent material object of nature. The revised version includes sections on scientific realism, and emergence, and new references on Noether's theorem, among others.

We discuss charged topological spin textures in quantum Hall ferromagnets in which the electrons carry a pseudospin, as well as the usual spin degree of freedom, as is the case in bilayer GaAs or monolayer graphene samples. We develop a theory which treats spin and pseudospin on a manifestly equal footing, which may also be of help in visualizing the relevant spin textures. We in particular consider the entanglement of spin and pseudospin in the presence of realistic anisotropies. An entanglement operator is introduced, which generates families of degenerate skyrmions with differing entanglement properties. We propose a local characterization of the latter and touch on the role entangled skyrmions play in the nuclear relaxation time of quantum Hall ferromagnets.

This work explores a simple approximation to describe isolated impurity scattering in a strongly correlated host. The approximation combines conventional one-electron scattering theory and the Dynamic Mean-Field Theory to describe strong correlations in the host. It becomes exact in several limits, including those of very strong interactions. We study the problem for a large range of parameter strengths and focus on the case of a strongly correlated metal host near the Mott metal-insulator transition. We find interesting effects on the electronic structure at the impurity site with the appearence of bound states at frequencies that are strongly renormalized from the bare impurity potential value. However, the strength of the threshold potential for the onset of the bound states remains of the order of the bare host bandwidth, i.e. essentially unrenormalized with respect to the non-interacting case. Our results may provide useful guidance for interpretation of scanning tunneling microscopy experiments in strongly correlated systems.

. We suggest that a magnetic-field-induced Peierls instability accounts for the recent experiment of Zhang et al. in which unexpected quantum Hall plateaus were observed at high magnetic fields in graphene on a substrate. This Peierls instability leads to an out-of-plane lattice distortion resulting in a charge density wave (CDW) on sublattices A and B of the graphene honeycomb lattice. We also discuss alternative microscopic scenarios proposed in the literature and leading to a similar CDW ground state in graphene.

We propose that the inversion symmetry of the graphene honeycomb lattice is spontaneously broken via a magnetic-field-dependent Peierls distortion. This leads to valley splitting of the n=0 Landau level but not of the other Landau levels. Compared to Quantum Hall valley ferromagnetism recently discussed in the literature, lattice distortion provides an alternative explanation to all of the currently observed Quantum Hall plateaus in graphene.

Most states of the fractional quantum Hall effect may be interpreted in terms of an integral quantum Hall effect of weakly-interacting quasiparticles (composite fermions). The recently discovered 411 state does not belong to these states because its formation is due to the residual interactions between composite fermions, which become relevant when the composite-fermion levels are only partially filled. We have derived a model of interacting composite fermions, which reveals the self-similarity of the fractional quantum Hall effect and which allows for a systematic study of higher generations of composite fermions. Here, we derive the form of the interaction potential between these hierarchical composite fermions and provide some stability criteria for such states.

On the basis of energy calculations, we investigate the competition between quantum-liquid and electron-solid phases in intermediate Landau levels as a function of their partial filling factor. An alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains an observed reentrance of the integral quantum Hall effect. The phase transitions are identified as first-order. Recent transport measurements under micro-wave irradiation reveal the crystalline origin of the reentrant points, and a mixed phase of a coexisting Wigner crystal and a 2-electron bubble phase is found in a Landau-level filling-factor range 4,15? ν? 4.26, as expected from our calculations.

Résumé Alors que l’on commémore en 2005 le soixantième anniversaire de la libération des camps de la mort du régime nazi, il est nécessaire de se pencher sur les origines de la Solution finale imaginée par les dirigeants du III e Reich. En effet, rarement ces questions de fond ont été abordées, laissant la place à l’expression unique de l’horreur indépassable sans toutefois en éclaircir les causes apparentes. Est-ce en raison de la peur de la controverse ou de la peur des spectres ? Cet article aborde quelques-unes de ces questions.

The spin-excitations of a fractional quantum Hall system are evaluated within a bosonization approach. In a first step, we generalize Murthy and Shankar's Hamiltonian theory of the fractional quantum Hall effect to the case of composite fermions with an extra discrete degree of freedom. Here, we mainly investigate the spin degrees of freedom, but the proposed formalism may be useful also in the study of bilayer quantum-Hall systems, where the layer index may formally be treated as an isospin. In a second step, we apply a bosonization scheme, recently developed for the study of the two-dimensional electron gas, to the interacting composite-fermion Hamiltonian. The dispersion of the bosons, which represent quasiparticle-quasihole excitations, is analytically evaluated for fractional quantum Hall systems at \nu = 1/3 and \nu = 1/5. The finite width of the two-dimensional electron gas is also taken into account explicitly. In addition, we consider the interacting bosonic model and calculate the lowest-energy state for two bosons. Besides a continuum describing scattering states, we find a bound-state of two bosons. This state is interpreted as a pair excitation, which consists of a skyrmion of composite fermions and an antiskyrmion of composite fermions. The dispersion relation of the two-boson state is evaluated for \nu = 1/3 and \nu = 1/5. Finally, we show that our theory provides the microscopic basis for a phenomenological non-linear sigma-model for studying the skyrmion of composite fermions.

Residual interactions between composite fermions, the quasi-particles responsible for the fractional quantum Hall effect, may be neglected at the Landau-level filling factors nu = p/(2sp + 1), at which most fractional quantum Hall states are observed. However, they become relevant at fillings in between states of this series. We have derived the form of the interaction potential of composite fermions within a recently developed Hamiltonian formalism, and we show flow these residual interaction may give rise to novel phases, such as crystals and stripes of composite fermions, as well as higher-generation states. The latter may be responsible for a recently observed fractional quantum Hall effect at nu = 4/11.

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu = 4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu = 4/11. The alternation between solid and liquid phases when varying the magnetic field may lead to reentrance phenomena in analogy with the observed reentrant integral quantum Hall effect.

In the framework of a recently developed model of interacting composite fermions restricted to a single level, we calculate the activation gaps of a second generation of spin-polarized composite fermions. These composite particles consist each of a composite fermion of the first generation and a vortex-like excitation and may be responsible for the recently observed fractional quantum Hall states at unusual filling factors such as nu=4/11,5/13,5/17, and 6/17. Because the gaps of composite fermions of the second generation are found to be more than one order of magnitude smaller than those of the first generation, these states are less visible than the usual states observed at filling factors nu=p/(2ps+1). Their stability is discussed in the context of a pseudopotential expansion of the composite-fermion interaction potential.

On the basis of energy calculations we investigate the competition between quantum-liquid and electron-solid phases in the Landau levels n=1,2, and 3 as a function of their partial filling factor. Whereas the quantum-liquid phases are stable only in the vicinity of quantized values 1/(2s+1) of the partial filling factor, an electron solid in the form of a triangular lattice of clusters with a few number of electrons (bubble phase) is energetically favorable between these fillings. This alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains a recently observed reentrance of the integral quantum Hall effect in the Landau levels n=1 and 2. Around half-filling of the last Landau level, a uni-directional charge density wave (stripe phase) has a lower energy than the bubble phase.

The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this fractal structure emerges naturally in the Hamiltonian formulation of composite fermions. After a set of transformations on the electronic model, we show that the model, which describes interacting composite fermions in a partially filled energy level, is self-similar. This mathematical property allows for the construction of a basis of higher generations of composite fermions. The collective-excitation dispersion of the recently observed 4/11 fractional-quantum-Hall state is discussed within the present formalism.

We compare the energies of different electron solids, such as bubble crystals with triangular and square symmetry and stripe phases, to those of correlated quantum liquids in partially filled intermediate Landau levels. Multiple transitions between these phases when varying the filling of the top-most partially filled Landau level explain the observed reentrance of the integer quantum Hall effect. The phase transitions are identified as first-order. This leads to a variety of measurable phenomena such as the phase co-existence between a Wigner crystal and a two-electron bubble phase in a Landau-level filling-factor range 4.15≲ν≲4.26, which has recently been observed in transport measurements under micro-wave irradiation.