The fractional quantum Hall effect (FQHE) is a canonical example of a topological phase in a correlated 2D electron gas under strong magnetic field. While electric currents propagate as chiral downstream edge modes, chargeless upstream chiral neutral edge modes were recently observed only in hole-conjugate states (states filling ν, n+1/2<ν<n+1, with n=0,1,2,...), and in the even denominator state ν=5/2. It is believed that spontaneous 'density reconstruction' near the edges of the 2D gas, leads to multiple counter propagating edge channels, being separated from each other by incompressible strips. Unavoidable disorder induces inter-channel tunneling; accompanied by Coulomb interaction it renormalizes the multiple edge channels to a downstream charge mode and upstream neutral edge mode(s), while maintaining the parity requirements (e.g., the heat conductance along the edge) dictated by the bulk. Here, we report of highly sensitive shot noise measurements that revealed unexpected presence of neutral modes in a variety of non-hole-conjugate fractional states. As already reported previously, we did not observe neutral modes in any of the integer states. In addition to the upstream neutral edge modes, we were surprised to find also neutral energy modes that propagate through the incompressible bulk. While along the edge, density reconstruction may account for the edge modes, we are not aware of a model that can account for the bulk modes. The proliferation of neutral modes, in every tested fractional state, changes drastically the accepted picture of FQHE states: an insulating bulk and 1D chiral edge channels. The apparent ubiquitous presence of these energy modes may account for decoherence of fractional quasiparticles - preventing observation of coherent interference in the fractional regime.
A non-local Hall bar geometry is used to detect neutral-current Hall effects in graphene on silicon dioxide. Disorder is tuned by the addition of Au or Ir adatoms in ultra-high vacuum. A reproducible neutral-current Hall effect is found in both as-fabricated and adatom-decorated graphene. The Hall angle exhibits a complex but reproducible dependence on gate voltage and disorder, and notably breaks electron-hole symmetry. An exponential dependence on length between Hall and inverse-Hall probes indicates a neutral current relaxation length of approximately 300 nm. The short relaxation length and…
We study nonequilibrium edge state transport in the fractional quantum Hall regime for states with one or several counter-propagating neutral modes. We consider a setup in which the neutral modes are heated by a hot spot, and where heat transported by the neutral modes causes a temperature difference between the upper and lower edges in a Hall bar. This temperature difference is probed by the excess noise it causes for scattering across a quantum point contact. We find that the excess noise in the quantum point contact provides evidence for counter-propagating neutral modes, and we calculate i…
We study the tunneling current between edge states of quantum Hall liquids across a single long contact region, and predict a resonance at a bias voltage set by the scale of the edge velocity. For typical devices and edge velocities associated with charged modes, this resonance occurs outside the physically accessible bias domain. However, for edge states that are expected to support neutral modes, such as the $ν={2/3}$, and $ν={5/2}$ Pfaffian and anti-Pfaffian states, the neutral velocity can be orders of magnitude smaller than the charged mode and if so the resonance would be accessible. The…
We theoretically study charge noise generated by excited neutral modes, which impinge on the quantum point contact of a quantum Hall bar with filling fraction v=2/3. The noise is computed for thermally excited neutral modes as well as for biased neutral modes with dipole-fermion excitations. Within the dipole-fermion picture, we show that the noise arising from two colliding modes can be suppressed due to Pauli-blocking and be non-universal due to random edge disorder, but becomes universal upon disorder-averaging. The ratio of noise due to two colliding neutral modes and noise due to only one…
The transport properties of the two-dimensional system in HgTe-based quantum wells containing simultaneously electrons and holes of low densities are examined. The Hall resistance, as a function of perpendicular magnetic field, reveals an unconventional behavior, different from the classical N-shaped dependence typical for bipolar systems with electron-hole asymmetry. The quantum features of magnetotransport are explained by means of numerical calculation of the Landau level spectrum based on the Kane Hamiltonian. The origin of the quantum Hall plateau σxy = 0 near the charge neutrality point …
Commencing with the composite fermion description of the $ν=5/2$ fractional quantum Hall effect, we study the dynamics of the edge neutral Majorana fermions. We confirm that these neutral modes are chiral and show that a conventional p-wave pairing interaction between CFs does not contribute to the dynamics of the edge neutral fermions. We find an important bilinear coupling between the charged and neutral modes. We show that owing to this coupling, the dispersion of the neutral modes is linear and their velocities are proportional to the wave vector of the charged mode. This dynamic origin of…
We demonstrate quantum Hall resistance measurements with metrological accuracy in a small cryogen-free system operating at a temperature of around 3.8K and magnetic fields below 5T. Operating this system requires little experimental knowledge or laboratory infrastructure, thereby greatly advancing the proliferation of primary quantum standards for precision electrical metrology. This significant advance in technology has come about as a result of the unique properties of epitaxial graphene on SiC.
We investigate the quantum Hall (QH) states near the charge neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors $ν=\pm1$ depend only on the perpendicular component of the field with respect to the graphene plane, indicating them to be not spin-related. A non-linear magnetic field dependence of the activation energy gap at filling factor $ν=1$ suggests a many-body origin. We therefore propose that the $ν=0$ and $\pm1$ states arise from the lifting of the spin and sub-lattice degeneracy of the $n=0$ LL, respectively.
We study the transport properties of $HgTe$-based quantum wells containing simultaneously electrons and holes in magnetic field B. At the charge neutrality point (CNP) with nearly equal electron and hole densities, the resistance is found to increase very strongly with B while the Hall resistivity turns to zero. This behavior results in a wide plateau in the Hall conductivity $σ_{xy}\approx 0$ and in a minimum of diagonal conductivity $σ_{xx}$ at $ν=ν_p-ν_n=0$, where $ν_n$ and $ν_p$ are the electron and hole Landau filling factors. We suggest that the transport at the CNP point is determined b…
The behavior of electrons in condensed matter systems is mostly determined by the repulsive Coulomb interaction. However, under special circumstances the Coulomb interaction can be effectively attractive, giving rise to electron pairing in unconventional superconductors and specifically designed mesoscopic setups. In quantum Hall systems electron interactions can play a particularly important role due to the huge degeneracy of Landau levels, leading for instance to the emergence of quasi-particles with fractional charge and anyonic statistics. Quantum Hall Fabry-Pérot (FPI) interferometers hav…
Non-abelian quantum Hall states are characterized by the simultaneous appearance of charge and neutral gapless edge modes, with the structure of the latter being intricately related to the existence of bulk quasi-particle excitations obeying non-abelian statistics. In general, it is hard to probe the neutral modes in charge transport measurements and a thermal transport measurement seems to be inevitable. Here we propose a setup which can get around this problem by having two point contacts in series separated by a distance set by the thermal equilibration length of the charge mode. We show th…
Neutral collective excitations in the striped Hall state are studied by using the single mode approximation and Hartree-Fock approximation at the half-filled third and fourth Landau level. We find that the spectrum includes anisotropic NG modes and periodic line nodes.
Counter propagating (upstream) chiral neutral edge modes, which were predicted to be present in hole-conjugate states, were observed recently in a variety of fractional quantum Hall states (v=2/3,v=3/5,v=8/3 & v=5/2), by measuring charge noise that resulted after partitioning the neutral mode by a constriction (denoted, as N\rightarrowC). Particularly noticeable was the observation of such modes in the v=5/2 fractional state - as it sheds light on the non-abelian nature of the state's wavefunction. Yet, the nature of these unique, upstream, chargeless modes and the microscopic process in which…
We have investigated the disorder of epitaxial graphene close to the charge neutrality point (CNP) by various methods: i) at room temperature, by analyzing the dependence of the resistivity on the Hall coefficient ; ii) by fitting the temperature dependence of the Hall coefficient down to liquid helium temperature; iii) by fitting the magnetoresistances at low temperature. All methods converge to give a disorder amplitude of $(20 \pm 10)$ meV. Because of this relatively low disorder, close to the CNP, at low temperature, the sample resistivity does not exhibit the standard value $\simeq h/4e^2…
Electrons living in a two-dimensional world under a strong magnetic field - the so-called fractional quantum Hall effect (FQHE) - often manifest themselves as fractionally charged quasiparticles (anyons). Moreover, being under special conditions they are expected to be immune to the environment, thus may serve as building blocks for future quantum computers. Interference of such anyons is the very first step towards understanding their anyonic statistics. However, the complex edge-modes structure of the fractional quantum Hall states, combined with upstream neutral modes, have been suspected t…
We investigate neutral collective excitations in the striped Hall state. In the striped Hall state, the magnetic translation and rotation symmetries are spontaneously broken. Using the commutation relation between charges and currents corresponding to the broken and unbroken symmetry, the existence of the gapless neutral excitation is proved. The spectrum of the neutral collective excitation at the half-filled third Landau level is obtained in the single mode approximation. We find the periodic line nodes in the spectrum. The spectrum is compared with the particle-hole excitation spectrum in t…
At large parallel magnetic field $B_\parallel$, the ground state of bilayer quantum Hall system forms uniform soliton lattice phase. The soliton lattice will melt due to the proliferation of unbound dislocations at certain finite temperature leading to the Kosterlitz-Thouless (KT) melting. We calculate the KT phase boundary by numerically solving the newly developed set of Bethe ansatz equations, which fully take into account the thermal fluctuations of soliton walls. We predict that within certain ranges of $B_\parallel$, the soliton lattice will melt at $T_{\rm KT}$. Interestingly enough, as…
We consider the edge of a two-dimensional electron system that is in the quantum-Hall-effect regime at filling factor 1-1/m with m being an odd integer, where microscopic theory explaining the occurrence of the quantum Hall effect in the bulk predicts the existence of two counterpropagating edge-excitation modes. These two modes are the classical edge-magnetoplasmon mode and a slow-moving neutral mode. Assuming the electrons to be confined by a coplanar neutralizing background of positive charges, and taking careful account of long-range Coulomb interactions, we determine microscopically the v…
Edges of quantum Hall phases give rise to a multitude of exotic modes supporting quasiparticles of different values of charge and quantum statistics. Among these are neutralons (chargeless anyons with semion statistics), which were found to be ubiquitous in fractional quantum Hall matter. Studying and manipulating the neutral sector is an intriguing and interesting challenge, all the more so since these particles are accessible experimentally. Here we address the limit of strongly-interacting neutralons giving rise to neutralon superconductivity, where pairing is replaced by a quarteting mecha…
In the striped Hall state, a magnetic translation in one direction is spontaneously broken to the discrete translation. The spectrum of the neutral collective excitation is obtained in the single mode approximation at half-filled third and fourth Landau levels. The spectrum is anisotropic and has a multiple line node structure. In one direction, the spectrum resembles the liquid Helium spectrum with the phonon and roton minimum.
Quantum Hall phases are gapped in the bulk but support chiral edge modes, both charged and neutral. Here we consider a circuit where the path from the source of electric current to the drain necessarily passes through a segment consisting solely of neutral modes. We find that upon biasing the source, a dc electric current is detected at the drain, provided there is backscattering between counter-propagating modes under the contacts placed in certain locations. Thus, neutral modes carry information that can be used to nonlocally reconstruct a dc charge current. Our protocol can be used to detec…
In the quantum Hall effect regime, taking place in a two-dimensional-electron gas under strong magnetic field, currents flow along the edges of the sample. For some particle-hole conjugate states of the fractional regime, e.g., with filling between 1/2 and 1 of the lowest Landau level; early predictions suggested the presence of counter-propagating edge currents in addition to the expected ones. When this did not agree with the measured conductance, it was suggested that disorder and interactions will lead to counterpropagating modes that carry only energy - the so called neutral modes. In add…
We use the edge of the quantum Hall sample to study the possibility for counter-propagating neutral collective excitations. A novel sample design allows us to independently investigate charge and energy transport along the edge. We experimentally observe an upstream energy transfer with respect to the electron drift for the filling factors 1 and 1/3. Our analysis indicates that a neutral collective mode at the interaction-reconstructed edge is a proper candidate for the experimentally observed effect.
Anomalous Hall effect (AHE) is a fundamental spin-dependent transport property that is widely used in spintronics. It is generally expected that currents carrying net spin polarization are required to drive the AHE. Here we demonstrate that, in contrast to this common expectation, a spin-neutral tunneling AHE (TAHE), i.e. a TAHE driven by spin-neutral currents, can be realized in an antiferromagnetic (AFM) tunnel junction where an AFM electrode with a non-spin-degenerate Fermi surface and a normal metal electrode are separated by a non-magnetic barrier with strong spin-orbit coupling (SOC). Th…
Upstream neutral modes, counter propagating to charge modes and carrying energy without net charge, had been predicted to exist in some of the fractional quantum Hall states and were recently observed via noise measurements. Understanding such modes will assist in identifying the wavefunction of these states, as well as shedding light on the role of Coulomb interactions within edge modes. In this work, performed mainly in the nu=2/3 state, we placed a quantum dot a few micrometers upstream of an ohmic contact, which served as a neutral modes source. We showed the neutral modes heat the input o…
Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a stringent ultra short-range assumption on the symmetry-allowed interactions, predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunnelin…
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, m…
Mach-Zehnder interferometry has been proposed as a probe for detecting the statistics of anyonic quasiparticles in fractional quantum Hall (FQH) states. Here we focus on interferometers made of multimode edge states with upstream modes. We find that the interference visibility is suppressed due to downstream-upstream mode entanglement; the latter serves as a "which path" detector to the downstream interfering trajectories. Our analysis tackles a concrete realization of filling factor 2/3, but its applicability goes beyond that specific case, and encompasses the recent observation of ubiquitous…
Questions on the nature of edge reconstruction and "where does the current flow" in the quantum Hall effect (QHE) have been debated for years. Moreover, the recent observation of proliferation of "upstream" neutral modes in the fractional QHE raised doubts about the present models of edge channels. In this article we focus on hole-conjugate states, nu=2/3 and nu=3/5, and present a new picture of their edge reconstruction. For example, while the present model for nu=2/3 consists of a single downstream charge channel with conductance 2/3 e^2/h and an upstream neutral mode, we show that the curre…
We study dephasing in electron transport through a large quantum dot (a Fabry-Perot interferometer) in the fractional quantum Hall regime with filling factor $2/3$. In the regime of sequential tunneling, dephasing occurs due to electron fractionalization into counterpropagating charge and neutral edge modes on the dot. In particular, when the charge mode moves much faster than the neutral mode, and at temperatures higher than the level spacing of the dot, electron fractionalization combined with tje fractional statistics of the charge mode leads to the dephasing selectively suppressing $h/e$ A…
Constrictions in fractional quantum Hall (FQH) systems not only facilitate backscattering between counter-propagating edge modes, but also may reduce the constriction filling fraction $ν_c$ with respect to the bulk filling fraction $ν_b$. If both $ν_b$ and $ν_c$ correspond to incompressible FQH states, at least part of the constriction region is surrounded by composite edges, whose low energy dynamics is characterized by a charge mode and one or several neutral modes. In the incoherent regime, decay of neutral modes describes the equilibration of composite FQH edges, while in the limit of cohe…
The true nature of the lowest-energy, long-wavelength neutral excitation of the fractional quantum Hall effect has been a long outstanding problem. In this Letter, we establish that it is a two-roton bound state.
Galvanomagnetic effects in graphene Magnetoresistivity and Hole-effect were theoretically investigated for neutral and gated graphene. It is shown that in neutral graphene Hall-effect is totally absent. In gated, exactly monopolar graphene effect of magnetoresistivity vanishes; here Hall-constant does not involve any relaxation characteristic in contrast to result obtained for popular method of relaxation time approximation.
Ohmic contacts are crucial elements of electron optics that have not received a clear theoretical description yet. We propose a model of an Ohmic contact as a piece of metal of the finite capacitance $C$ attached to a quantum Hall edge. It is shown that charged quantum Hall edge states may have weak coupling to neutral excitations in an Ohmic contact. Consequently, despite being a reservoir of neutral excitations, an Ohmic contact is not able to efficiently equilibrate edge states if its temperature is smaller than $\hbarΩ_c$, where $Ω_c$ is the inverse RC time of the contact. This energy scal…
We consider a neutral spinor condensate moving in a periodic magnetic field. The spatially dependent magnetic field induces an effective spin dependent Lorentz force which in turn gives rise to a spin dependent Hall effect. Simulations of the Gross-Pitaevskii equation quantify the Hall effect. We discuss possible experimental realizations.
We have measured the magneto-resistance of freely suspended high-mobility bilayer graphene. For magnetic fields $B>1$ T we observe the opening of a field induced gap at the charge neutrality point characterized by a diverging resistance. For higher fields the eight-fold degenerated lowest Landau level lifts completely. Both the sequence of this symmetry breaking and the strong transition of the gap-size point to a ferromagnetic nature of the insulating phase developing at the charge neutrality point.
The zeroth Landau level (0LL) in graphene has emerged as a flat-band platform in which distinct many-body phases can be explored with unprecedented control by simply tuning the strength and/or direction of magnetic fields1-22. A rich set of quantum Hall ferromagnetic (QHFM) phases with different lattice-scale symmetry-breaking orders are predicted to be realized in high magnetic fields when the 0LL in graphene is half filled1-8,13-16. Here we report a field-tuned continuous quantum phase transition of different valley orderings in QHFM of charge-neutral graphene on insulating tungsten diseleni…
A study of the effect of unscreened Coulomb interactions on the quantum spin Hall (QSH) phase of finite-width neutral zigzag graphene ribbons is presented. By solving a tight-binding Hamiltonian that includes the intrinsic spin-orbit interaction (I-SO), exact expressions for band-structures and edge-states wavefunctions are obtained. These analytic results, supported by tight-binding calculations, show that chiral spin-filtered edge states are composed of localized and damped oscillatory wavefunctions, reminiscent of the ones obtained in armchair ribbons. The addition of long-range Coulomb int…
Neutral graphene in strong magnetic fields is believed to be an (exchange stabilized) integer Hall state of completely filled up spin (say) and empty down spin bands of n = 0, two fold valley degenerate Landau levels. We suggest that correlation energy gain from a nearly SU(4) singlet (2 spin $\times$ 2 valley) composite fermi sea formation, at $ν\approx$ \hlf filling for each component, destabilizes ferromagnetic integer quantum Hall state. This radically different scenario is consistent with a dissipative gapless state seen in experiments in neutral graphene. Interesting paired Hall states a…
The ν=5/2 anti-Pfaffian state and the ν=2/3 state are believed to have an edge composed of counter-propagating charge and neutral modes. This situation allows the generation of a pure thermal bias between two composite edge states across a quantum point contact (QPC) as was experimentally established in Nature 466, 585 (2010). We show that replacing the QPC by a quantum dot provides a natural way for detecting the neutral modes via the finite current generated by the thermoelectric response of the dot. We also show that the degeneracies of the dot spectrum, dictated by the conformal field theo…
Elevated Hall Responses as Indicators of Edge Reconstruction
Indian Institute of Science Education and Research Kolkata（印度科学教育研究所加尔各答分校）；Aix Marseille Univ, Université de Toulon, CNRS, CPT（艾克斯马赛大学、土伦大学、法国国家科学研究中心、理论物理中心）
A system of electrons in two dimensions and strong magnetic fields can be tuned to create a gapped 2D system with one dimensional channels along the edge. Interactions among these edge modes can lead to independent transport of charge and heat, even in opposite directions. Measuring the chirality and transport properties of these charge and heat modes can reveal otherwise hidden structure in the edge. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream along the edge of the heater, we can measure both the che…
The formation and possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the relevant negatively and positively charged quasiparticles (e.g., conduction electrons and valence holes, reversed-spin electrons and spin holes, Laughlin quasielectrons and quasiholes, composite Fermions) that can occur in a 2D electron in the presence of a strong magnetic field. Examples of such bound states are interband neutral and charged excitons, fractionally charge…
Charge fractionalization is a possible emergent excitation in a low-dimensional system of interacting electrons. A known example is that of fractional charges in the fractional quantum Hall effect (FQHE) regime, which is a consequence of strong Coulomb interaction among the electrons whose kinetic energy is quenched by the strong magnetic field. Alternatively, the integer QHE (IQHE), with electrons behaving largely as independent particles in Landau levels (LLs), lacks such fractionalization. However, for integer LLs filling v=2, 3,... electrons propagate in copropagating adjacent chiral edge …
Melting of quantum Hall Wigner and bubble crystals
International Center for Quantum Materials, Peking University（北京大学量子材料科学中心）；Division of Physics and Applied Physics, Nanyang Technological University（南洋理工大学物理与应用物理系）；Leiden Institute of Physics, Leiden University（莱顿大学莱顿物理研究所）；Department of Electrical Engineering, Princeton University（普林斯顿大学电气工程系）；Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）；Materials Research Laboratory, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校材料研究实验室）；Hefei National Laboratory（合肥国家实验室）；Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University（北京大学轻元素量子材料交叉研究院暨轻元素先进材料研究中心）
We show model wavefunctions for neutral collective modes in fractional quantum Hall (FQH) states have simple analytic forms obtained from judicially reducing the powers of selected pairs in the ground state Jastrow factor. This scheme of "pair excitations" works for the magneto-roton modes of single-component Abelian and non-Abeliean FQH states, as well as neutral fermion mode for the Moore-Read (MR) state. The analytic wavefunctions enable computations in the thermodynamic limit previous inaccessible to numerics, and the long wavelength limit of the neutral energy gap of the magneto-roton mod…
The possibility of using quantum Hall systems for thermoelectric energy conversion is investigated. It is shown that the massive degeneracy and the metallicity of a partially-filled Landau level enable thermoelectric cooling and power generation with unprecedented efficiency at low temperature. The figure of merit is explicitly derived for a transverse thermoelectric device using the $ν=0$ quantum Hall state of Dirac materials at charge neutrality, where due to electron-hole symmetry electrical Hall effect vanishes but thermoelectric Hall effect peaks.
The formation and various possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the relevant negatively and positively charged quasiparticles (e.g., conduction electrons and valence holes, reversed-spin electrons and spin holes, Laughlin quasielectrons and quasiholes, composite fermions) that occur in an electron system under specific conditions (e.g., electron density, well width, electric and magnetic fields, or hydrostatic pressure). The examp…
Impacts of domain textures on low-lying neutral excitations in the bulk of fractional quantum Hall effect (FQHE) systems are probed by resonant inelastic light scattering. We demonstrate that large domains of quantum fluids support long-wavelength neutral collective excitations with well-defined wave vector (momentum) dispersion that could be interpreted by theories for uniform phases. Access to dispersive low-lying neutral collective modes in large domains of FQHE fluids such as long wavelength magnetorotons at filling factor v=1/3 offer significant experimental access to strong electron corr…
In a recent experimental paper [1] a qualitative confirmation of the existence of upstream neutral modes at $ν= 2/3$ quantum Hall edge was reported. Using the chiral Luttinger liquid theory of quantum Hall edge we develop a quantitative model of the experiment [1]. A good quantitative agreement of our theory with the experimental data reinforces the conclusion of existence of the upstream neutral mode. Our model also enables us to extract important quantitative information about non-equilibrium processes in Ohmic and tunneling contacts from the experimental data. In particular, for $ν= 2/3$, w…
Despite the fact that composite fermions may be regarded as electrically neutral objects at Landua-level filling factor $ν=1/2$, carrying only an electric dipole moment, we argue that the long-wavelength compressibility of the system is finite.
We present a pure Chern-Simons formulation of families of interesting Conformal Field Theories describing edge states of non-Abelian Quantum Hall states. These theories contain two Abelian Chern-Simons fields describing the electromagnetically charged and neutral sectors of these models, respectively. The charged sector is the usual Abelian Chern-Simons theory that successfully describes Laughlin-type incompressible fluids. The neutral sector is a 2+1-dimensional theory analogous to the 1+1-dimensional orbifold conformal field theories. It is based on the gauge group O(2) which contains a ${\b…
Measurement and theory of the two-terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped samples to be distinguished, including N-shaped distortions of quantum Hall plateaus and conductance peaks and dips at the charge neutrality point. Generally good agreement is found between measurement and theory. Possible origins of discrepancies are discussed.
Starting from a collective description of the incompressible fractional quantum Hall liquid as an elastic medium that supports gapped neutral excitations I show that the one-electron spectral function of this system exhibits a sharp peak at the lowest available excitation energy, well separated from the continuum spectrum at higher energy. I interpret this peak as the signature of the integral charge quasiparticle recently predicted by Peterson and Jain\cite{Jain05}, and calculate its spectral weight for different filling factors.
We present a particle-hole symmetric theory for a two-dimensional electron gas at filling factor one half. In this theory, elementary excitations are dipole-like fermions floating on top of the $ν=1/2$ boson quantum Hall liquid. In the absence of disorder these dipoles can form a Fermi-liquid. Disorder can break them apart and drive the ground state into a quantum critical state.
