Textured Edges in Quantum Hall Systems

Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases

Chiral gapless boundary modes are characteristic of quantum Hall (QH) states. For hole-conjugate fractional QH phases counterpropagating edge modes (upstream and downstream) are expected. In the presence of electrostatic interactions and disorder these modes may renormalize into charge and upstream neutral modes. Orthodox models of Laughlin phases anticipate only a downstream charge mode. Here we show that in the latter case, in the presence of a smooth confining potential, edge reconstruction leads to the emergence of pairs of counterpropagating modes, which, by way of mode renormalization, may give rise to nontopological upstream neutral modes, possessing nontrivial statistics. This may explain the experimental observation of ubiquitous neutral modes, and the overwhelming suppression of anyonic interference in Mach-Zehnder interferometry platforms. We also point out other signatures of such edge reconstruction.

Edge Reconstruction of a Time-Reversal Invariant Insulator: Compressible-Incompressible Stripes

Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of quantum Hall phases, and time-reversal invariant topological insulators. Here we study the edge of a 2D, topologically trivial insulating phase, as a function of the strength of the electronic interactions and the steepness of the confining potential. For sufficiently smooth confining potentials, alternating compressible and incompressible stripes appear at the edge. Our findings signal the emergence of gapless edge modes which may give rise to finite conductance at the edge. This would suggest a novel scenario of a nontopological metal-insulator transition in clean 2D systems. The incompressible stripes appear at commensurate fillings and may exhibit broken translational invariance along the edge in the form of charge density wave ordering. These are separated by structureless compressible stripes.

Spin Mode Switching at the Edge of a Quantum Hall System

Quantum Hall states can be characterized by their chiral edge modes. Upon softening the edge potential, the edge has long been known to undergo spontaneous reconstruction driven by charging effects. In this Letter we demonstrate a qualitatively distinct phenomenon driven by exchange effects, in which the ordering of the edge modes at ν=3 switches abruptly as the edge potential is made softer, while the ordering in the bulk remains intact. We demonstrate that this phenomenon is robust, and has many verifiable experimental signatures in transport.

Negative and positive cross-correlations of current noises in quantum Hall edge channels at bulk filling factor [Formula: see text]

Cross-correlation noise in electrical currents generated from a series connection of two quantum point contacts (QPCs), the injector and the detector, is described for investigating energy relaxation in quantum Hall edge channels at bulk filling factor [Formula: see text]. We address the importance of tuning the energy bias across the detector for this purpose. For a long channel with a macroscopic floating ohmic contact that thermalizes the electrons, the cross-correlation turns from negative values to the maximally positive value (identical noise in the two currents) by tuning the effective energy bias to zero. This can be understood by considering competition between the low-frequency charge fluctuation generated at the injector, which contributes positive correlation, and the partition noise at the detector, which gives negative correlation. Strikingly, even for a short channel without intentional thermalization, significantly large positive correlation is observed in contrast to negative values expected for coherent transport between the two QPCs.

Density-Functional Theory of the Fractional Quantum Hall Effect

A conceptual difficulty in formulating the density-functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.

How universal is the entanglement spectrum?

It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this Letter, we show that this belief is false in general. Most significantly, we show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low-energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the low-energy ES and the Rényi entropies can mislead entirely, while for quantum Hall systems, the ES has much less universal content than assumed to date.

Realizing universal edge properties in graphene fractional quantum Hall liquids

Universal chiral Luttinger liquid behavior has been predicted for fractional quantum Hall edge states, but so far has not been observed experimentally in semiconductor-based two-dimensional electron gases. One likely cause of this absence of universality is the generic occurrence of edge reconstruction in such systems, which is the result of a competition between confinement potential and Coulomb repulsion. We show that due to a completely different mechanism of confinement, edge reconstruction can be avoided in graphene, which allows for the observation of the predicted universality.

Luttinger liquid at the edge of undoped graphene in a strong magnetic field

We demonstrate that an undoped two-dimensional carbon plane (graphene) whose bulk is in the integer quantum Hall regime supports a nonchiral Luttinger liquid at an armchair edge. This behavior arises due to the unusual dispersion of the noninteracting edge states, causing a crossing of bands with different valley and spin indices at the edge. We demonstrate that this stabilizes a domain wall structure with a spontaneously ordered phase degree of freedom. This coherent domain wall supports gapless charged excitations, and has a power law tunneling I-V with a nonintegral exponent. In proximity to a bulk lead, the edge may undergo a quantum phase transition between the Luttinger liquid phase and a metallic state.