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Register a new userForbidden transitions between quantum Hall and insulating phases in p-SiGe heterostructures
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We show that in dilute metallic p-SiGe heterostructures, magnetic field can cause multiple quantum Hall-insulator-quantum Hall transitions. The insulating states are observed between quantum Hall states with filling factors u=1 and 2 and, for the first time, between u=2 and 3 and between u=4 and 6. The latter are in contradiction with the original global phase diagram for the quantum Hall effect. We suggest that the application of a (perpendicular) magnetic field induces insulating behavior in metallic p-SiGe heterostructures in the same way as in Si MOSFETs. This insulator is then in competition with, and interrupted by, integer quantum Hall states leading to the multiple re-entrant transitions. The phase diagram which accounts for these transition is similar to that previously obtained in Si MOSFETs thus confirming its universal character.
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Quantum many particle systems in which the kinetic energy, strong correlations, and band topology are all important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these elements are present. We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the Lowest Landau Level (LLL). This is the familiar quantum Hall regime with rich physics determined by the particle filling and statistics. A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a Chern band with a finite bandwidth. The states obtained in the quantum Hall regime evolve into conducting states in the limit of large bandwidth. We study this evolution in detail for the specific case of bosons at filling factor $ u = 1$. In the quantum Hall regime the ground state at this filling is a gapped quantum hall state (the bosonic Pfaffian) which may be viewed as descending from a (bosonic) composite fermi liquid. At large bandwidth the ground state is a bosonic superfluid. We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite fermi liquid, we show that the evolution into the superfluid can be usefully described by a non-commutative quantum field theory in a periodic potential.
The nature of the state at low Landau-level filling factors has been a longstanding puzzle in the field of the fractional quantum Hall effect. While theoretical calculations suggest that a crystal is favored at filling factors $ ulesssim 1/6$, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $ u=$ 1/7, 2/11, 2/13, 3/17, 3/19, 1/9, 2/15 and 2/17, which belong to the standard sequences $ u=n/(6npm 1)$ and $ u=n/(8npm 1)$. To address this paradox, we investigate the nature of some of the low-$ u$ states, specifically $ u=1/7$, $2/13$, and $1/9$, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.
We present a coupled-wire construction of a model with chiral fracton topological order. The model combines the known construction of $ u=1/m$ Laughlin fractional quantum Hall states with a planar p-string condensation mechanism. The bulk of the model supports gapped immobile fracton excitations that generate a hierarchy of mobile composite excitations. Open boundaries of the model are chiral and gapless, and can be used to demonstrate a fractional quantized Hall conductance where fracton composites act as charge carriers in the bulk. The planar p-string mechanism used to construct and analyze the model generalizes to a wide class of models including those based on layers supporting non-Abelian topological order. We describe this generalization and additionally provide concrete lattice-model realizations of the mechanism.
We present a pedagogical overview of recent theoretical work on unconventional quantum phases and quantum phase transitions in condensed matter systems. Strong correlations between electrons can lead to a breakdown of two traditional paradigms of solid state physics: Landaus theories of Fermi liquids and phase transitions. We discuss two resulting exotic states of matter: topological and critical spin liquids. These two quantum phases do not display any long-range order even at zero temperature. In each case, we show how a gauge theory description is useful to describe the new concepts of topological order, fractionalization and deconfinement of excitations which can be present in such spin liquids. We make brief connections, when possible, to experiments in which the corresponding physics can be probed. Finally, we review recent work on deconfined quantum critical points. The tone of these lecture notes is expository: focus is on gaining a physical picture and understanding, with technical details kept to a minimum.
Shubnikov-de Haas data is presented for a p-SiGe sample exhibiting strongly insulating behaviour at nu = 3/2. In addition to the fixed points defining a high field metal- insulator transition into this phase separate fixed points can also be identified for the nu = 3 --> 2 and 2 --> 1 Integer quantum Hall transitions. Another feature of the data, that the Hall resistivity approaches zero in the insulating phase, indicates it is not a re-entrant Hall insulator. The behaviour is explained in terms of the strong exchange interactions. At integer filling factors these cause the 0 uparrow and 1 downarrow Landau levels to cross and be well separated but at non-integer values of nu screening reduces exchange effects and causes the levels to stick together. It is suggested the insulating behaviour, and high field metal/insulator transition, is a consequence of the strong exchange interactions.
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