Multilayer Quantum Hall Systems Research Articles

Edge States and Chiral Solitons in Topological Hall and Chern–Simons Fields

The multi-component extension problem of the (2+1) D -gauge topological Jackiw–Pi model describing the nonlinear quantum dynamics of charged particles in multi-layer Hall systems is considered. By applying the dimensional reduction (2 + 1) D → (1 + 1) D to Lagrangians with the Chern–Simons topologic fields , multi-component nonlinear Schrodinger equations for particles are constructed with allowance for their interaction. With Hirota‘s method, an exact two-soliton solution is obtained, which is of interest in quantum information transmission systems due to the stability of their propagation. An asymptotic analysis t →±∞ of soliton-soliton interactions shows that there is no backscattering processes. We identify these solutions with the edge (topological protected) states – chiral solitons – in the multi-layer quantum Hall systems. By applying the Hirota bilinear operator algebra and a current theorem, it is shown that, in contrast to the usual vector solitons, the dynamics of new solutions (chiral vector solitons) has exclusively unidirectional motion. The article is published in the author’s wording.

INTERLAYER SURFACE TRANSPORT IN MULTILAYER QUANTUM HALL SYSTEMS UNDER TILTED MAGNETIC FIELDS

We have studied interlayer surface transport in multilayer quantum Hall systems under tilted magnetic fields. Under the fields normal to layers, edge state of each layer couples with each other due to interlayer tunneling forming the chiral surface state, which causes the surface transport. Once the field is tilted to the normal of the surface, the inter-edge tunneling is suppressed except at the certain magic angles. On the other hands, when the field is tilted in the surface, the inter-edge tunneling reflects the density distribution of the edge state. We carried out the experiments to confirm these features using GaAs/AlGaAs superlattices.

Interlayer phase coherence and superfluidity of electron–hole pairs in multilayer quantum Hall systems

The states with spontaneous interlayer phase coherence in multilayer quantum Hall systems are studied. It is shown that in systems with the average filling factor per layer equal to one half the phase coherence establishes only in bilayer complexes of adjacent layers, and there is no coherence between layers belonging to different complexes. Conditions of stability for such a state against transitions to the uniform charge-ordered state and the charge density wave state are analyzed. It is shown that in systems with finite number of layers N the state with interlayer phase coherence may exist at interlayer distances d < d c , and the critical distance d c decreases under increasing N.

Quantum phase transition in multilayer fractional quantum Hall systems

Energetically stable states are studied for the infinite multilayer quantum Hall system. Two-dimensional incompressible quantum Hall states are stable for appropriate fillings in the limit of infinite interlayer separation, while three-dimensional compressible states are stabilized by interlayer couplings such as tunneling and Coulomb interaction in the case of small separation. Trial states are introduced for typical cases and their Coulomb energies are calculated with use of the variational Monte Carlo method and the Hartree–Fock approximation. On energetical grounds, possible quantum phase transitions are discussed in this system.

Temperature dependence of interlayer surface transport in multilayer quantum Hall system

We have studied interlayer surface transport in GaAs/AlGaAs multilayer quantum Hall systems. By canceling bulk conductance between different shaped samples, we have successfully extracted only the conductivity of surface transport over wide temperature range. At low temperatures, the surface conductivity in an integer quantum Hall state is much smaller than e 2/ h and independent of temperature. These are the theoretically predicted natures of the chiral surface state. As the temperature is increased, the surface transport is enhanced by mixing with bulk states, and finally the surface transport vanishes reflecting the disappearance of the quantum Hall effect.

Weakly Coupled Antiferromagnetic Quantum Spin Chains

Quasi-one-dimensional quantum antiferromagnets formed by a d-dimensional hypercubic lattice of weakly coupled spin-1/2 antiferromagnetic Heisenberg chains are studied by combining exact results in one-dimension and renormalization group analyses of the interchain correlations. It is shown that d-dimensional magnetic long-range order develops at zero-temperature for infinitesimal antiferromagnetic or ferromagnetic interchain couplings. In the presence of weak bond alternations, the order-disorder transition occurs at a finite interchain coupling. Relevances to the lightly doped quantum antiferromagnets and multi-layer quantum Hall systems are discussed.