solitons in quantum Hall systems

We present here an elementary pedagogical introduction to CP_N solitons in quantum Hall systems. We begin with a brief introduction to both CP_N models and to quantum Hall (QH) physics. We then focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact CP_N fields for N = 1 and N = 3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding CP_N field equations. We conclude with a brief summary of our own recent work in this area, done with Sankalpa Ghosh. Received 17 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: doug0700@mail.jnu.ac.in     

Tunneling, dissipation, and superfluid transition in quantum Hall bilayers

We study bilayer quantum Hall systems at total Landau level filling factor nu=1 in the presence of interlayer tunneling and coupling to a dissipative normal fluid. Describing the dynamics of the interlayer phase by an effective quantum dissipative XY model, we show that there exists a critical dissipation sigma(c) set by the conductance of the normal fluid. For sigma>sigma(c), interlayer tunnel splitting drives the system to a nu=1 quantum Hall state. For sigma相似文献   

Tunneling spectroscopy of localized states near the quantum Hall edge

In this paper, we discuss the experimental results of M. Grayson et al. on tunneling I–V characteristics of the quantum Hall edge. We suggest a two-step tunneling mechanism involving localized electron states near the edge, which might account for the discrepancy between the experimental data and the predictions of the chiral Luttinger liquid theory of the quantum Hall edge.     

Electron spin transitions in quantum Hall systems

A system of two-dimensional electron gas in a strong magnetic field exhibits a remarkable phenomenon known as the fractional quantum Hall effect. Rapid advances in experimental techniques and intense theoretical work for well over a decade have significantly contributed to our understanding of the mechanism behind the effect. It is now a well established fact that electron correlations are largely responsible for the occurrence of this phenomenon. In recent years, theoretical and experimental investigations have revealed that those electron correlations, which are responsible for the quantum Hall effect, are also the reason for various spin transitions in the system. In this review, we systematically follow the theoretical studies of the role spin degree of freedom play in the quantum Hall effect regime and also describe several ingenious experiments reported in recent years which are in good agreement with the emerging theoretical picture.     

Interlayer transport in bilayer quantum Hall systems

Bilayer quantum Hall systems have a broken symmetry ground state at a filling factor which can be viewed either as an excitonic superfluid or as a pseudospin ferromagnet. We present a theory of interlayer transport in quantum Hall bilayers that highlights remarkable similarities and critical differences between transport in Josephson junction and ferromagnetic metal spin-transfer devices. Our theory is able to explain the size of the large but finite low-bias interlayer conductance and the voltage width of this collective transport anomaly.     

Metal insulator transition in modulated quantum Hall systems

The quantum Hall effect is studied numerically in modulated two-dimensional electron systems in the presence of disorder. Based on the scaling property of the Hall conductivity as well as the localization length, the critical energies where the states are extended are identified. We find that the critical energies, which are distributed to each of the subbands, combine into one when the disorder becomes strong, in the way depending on the symmetry of the disorder and/or the periodic potential.     

Anisotropic multicomponent terahertz photoconductivity in quantum Hall systems

The decay times of the terahertz photoconductivity signal are studied for samples in the quantum Hall regime. The photoconductivity signal has both the longitudinal components caused by the photoinduced change in the longitudinal resistance and the transverse components due to the photoinduced transverse current. The signal kinetics are qualitatively different for samples with relatively low (500 000 cm²/Vs and lower) and relatively high (900 000 cm²/Vs and higher) charge-carrier mobilities.     

Notes on infinite layer quantum Hall systems

We study the fractional quantum Hall effect in three-dimensional systems consisting of infinitely many stacked two-dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics such as quasiparticles with non-trivial internal structure, irrational braiding phases, and the necessity of a boundary hierarchy construction for interlayer correlated states. The bulk states host a family of surface phases obtained by hybridizing the edge states in each layer. We analyze the surface conduction in these phases by means of sum rule and renormalization group arguments and by explicit computations at weak tunneling in the presence of disorder. We find that in cases where the interlayer electron tunneling is not relevant in the clean limit, the surface phases are chiral semi-metals that conduct only in the presence of disorder or at finite temperature. We show that this class of problems which are naturally formulated as interacting bosonic theories can be fermionized by a general technique that could prove useful in the solution of such “one and a half” dimensional problems.     

Fractional charges and quantum phase transitions in imbalanced bilayer quantum Hall systems

We extend the composite boson theory to study slightly imbalanced bilayer quantum Hall systems. In the global U(1) symmetry breaking excitonic superfluid side, as the imbalance increases, the system supports continuously changing fractional charges. In the translational symmetry breaking pseudospin density wave (PSDW) side, there are two quantum phase transitions from the commensurate PSDW to an incommensurate PSDW and then to the excitonic superfluid state. We compare our theory with experimental data and also the previous microscopic calculations.     

Theory of activated transport in bilayer quantum Hall systems

We analyze the transport properties of bilayer quantum Hall systems at total filling factor nu=1 in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.     

Electron entanglement detected by quantum spin Hall systems

We propose a promising electron entanglement detector consisting of two quantum spin Hall systems weakly coupled to a superconductor. The detection of electron spins along various polarization directions, which is a prerequisite for testing Bell's inequality on solid state spins, can be achieved in an all-electrical-controlled manner utilizing the helical edge states. It is found that the violation of Bell's inequality exists in a large range of the tunneling parameters, which can be realized in mercury telluride quantum wells.     

Effects of disorder on modulated quantum Hall systems

The Hall conductivity and the localization length are calculated for weakly modulated two-dimensional systems within the lowest Landau level approximation. We find that the fractal character of the Hofstadter butterfly is reflected on the coincidence in the localization and the Hall conductivity among a series of fluxes φ+2n with integers n.