Resonant tunneling in the quantum Hall regime: measurement of fractional charge

In experiments on resonant tunneling through a "quantum antidot" (a potential hill) in the quantum Hall (QH) regime, periodic conductance peaks were observed as a function of both magnetic field and back gate voltage. A combination of the two periods constitutes a measurement of the charge of the tunneling particles and implies that charge deficiency on the antidot is quantized in units of the charge of quasi-particles of the surrounding QH condensate. The experimentally determined value of the electron charge e is 1.57 x 10(-19) coulomb = (0.98 +/- 0.03) e for the states v = 1 and v = 2 of the integer QH effect, and the quasi-particle charge is 5.20 x 10(-20) coulomb = (0.325 +/- 0.01)e for the state v = (1/3) of the fractional QH effect.     

Quantized Transport in Graphene p-n Junctions in a Magnetic Field

Recent experimental work on locally gated graphene layers resulting in p-n junctions has revealed the quantum Hall effect in their transport behavior. We explain the observed conductance quantization, which is fractional in the bipolar regime and an integer in the unipolar regime, in terms of quantum Hall edge modes propagating along and across the p-n interface. In the bipolar regime, the electron and hole modes can mix at the p-n boundary, leading to current partition and quantized shot-noise plateaus similar to those of conductance, whereas in the unipolar regime transport is noiseless. These quantum Hall phenomena reflect the massless Dirac character of charge carriers in graphene, with particle/hole interplay manifest in mode mixing and noise in the bipolar regime.     

Quasi-particle properties from tunneling in the v = 5/2 fractional quantum Hall state

Quasi-particles with fractional charge and statistics, as well as modified Coulomb interactions, exist in a two-dimensional electron system in the fractional quantum Hall (FQH) regime. Theoretical models of the FQH state at filling fraction v = 5/2 make the further prediction that the wave function can encode the interchange of two quasi-particles, making this state relevant for topological quantum computing. We show that bias-dependent tunneling across a narrow constriction at v = 5/2 exhibits temperature scaling and, from fits to the theoretical scaling form, extract values for the effective charge and the interaction parameter of the quasi-particles. Ranges of values obtained are consistent with those predicted by certain models of the 5/2 state.     

The fractional quantum Hall effect

Recent research has uncovered a fascinating quantum liquid made up solely of electrons confined to a plane surface. Found only at temperatures near absolute zero and in extremely strong magnetic fields, this liquid can flow without friction. The excited states of this liquid consist of peculiar particle-like objects that carry an exact fraction of an electron charge. Called quasiparticles, these excitations can themselves condense into new liquid states. Each such liquid is characterized by a fractional quantum number that is directly observable in a simple electrical measurement. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect.     

Ultraslow electron spin dynamics in GaAs quantum wells probed by optically pumped NMR

Optically pumped nuclear magnetic resonance (OPNMR) measurements were performed in two different electron-doped multiple quantum well samples near the fractional quantum Hall effect ground state nu = 13. Below 0.5 kelvin, the spectra provide evidence that spin-reversed charged excitations of the nu = 13 ground state are localized over the NMR time scale of about 40 microseconds. Furthermore, by varying NMR pulse parameters, the electron spin temperature (as measured by the Knight shift) could be driven above the lattice temperature, which shows that the value of the electron spin-lattice relaxation time tau1s is between 100 microseconds and 500 milliseconds at nu = 13.     

Unconventional sequence of fractional quantum Hall states in suspended graphene

Graphene provides a rich platform to study many-body effects, owing to its massless chiral charge carriers and the fourfold degeneracy arising from their spin and valley degrees of freedom. We use a scanning single-electron transistor to measure the local electronic compressibility of suspended graphene, and we observed an unusual pattern of incompressible fractional quantum Hall states that follows the standard composite fermion sequence between filling factors ν = 0 and 1 but involves only even-numerator fractions between ν = 1 and 2. We further investigated this surprising hierarchy by extracting the corresponding energy gaps as a function of the magnetic field. The sequence and relative strengths of the fractional quantum Hall states provide insight into the interplay between electronic correlations and the inherent symmetries of graphene.     

Signatures of electron fractionalization in ultraquantum bismuth

Because of the long Fermi wavelength of itinerant electrons, the quantum limit of elemental bismuth (unlike most metals) can be attained with a moderate magnetic field. The quantized orbits of electrons shrink with increasing magnetic field. Beyond the quantum limit, the circumference of these orbits becomes shorter than the Fermi wavelength. We studied transport coefficients of a single crystal of bismuth up to 33 tesla, which is deep in this ultraquantum limit. The Nernst coefficient presents three unexpected maxima that are concomitant with quasi-plateaus in the Hall coefficient. The results suggest that this bulk element may host an exotic quantum fluid reminiscent of the one associated with the fractional quantum Hall effect and raise the issue of electron fractionalization in a three-dimensional metal.     

The relationship between high-temperature superconductivity and the fractional quantum Hall effect

The case is made that the spin-liquid state of a Mott insulator, hypothesized to exist by Anderson and identified by him as the correct context for discussing high-temperature superconductors, occurs in these materials and exhibits the principles of fractional quantization identified in the fractional quantum Hall effect. The most important of these is that particles carrying a fraction of an elementary quantum number, in this case spin, attract one another by a powerful gauge force, which can lead to a new kind of superconductivity. The temperature scale for the superconductivity is set by an energy gap in the spin-wave spectrum, which is also the fundamental measure of how "liquid" the spins are.     

Quantum spin hall insulator state in HgTe quantum wells

Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e(2)/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.     

Quantum hall ferromagnetism in a two-dimensional electron system

Experiments on a nearly spin degenerate two-dimensional electron system reveals unusual hysteretic and relaxational transport in the fractional quantum Hall effect regime. The transition between the spin-polarized (with fill fraction nu = 1/3) and spin-unpolarized (nu = 2/5) states is accompanied by a complicated series of hysteresis loops reminiscent of a classical ferromagnet. In correlation with the hysteresis, magnetoresistance can either grow or decay logarithmically in time with remarkable persistence and does not saturate. In contrast to the established models of relaxation, the relaxation rate exhibits an anomalous divergence as temperature is reduced. These results indicate the presence of novel two-dimensional ferromagnetism with a complicated magnetic domain dynamic.     

Unraveling the spin polarization of the ν = 5/2 fractional quantum Hall state

The fractional quantum Hall (FQH) effect at filling factor ν = 5/2 has recently come under close scrutiny, as its ground state may possess quasi-particle excitations obeying nonabelian statistics, a property sought for topologically protected quantum operations. However, its microscopic origin remains unknown, and candidate model wave functions include those with undesirable abelian statistics. We report direct measurements of the electron spin polarization of the ν = 5/2 FQH state using resistively detected nuclear magnetic resonance. We find the system to be fully polarized, which unambiguously rules out the most likely abelian contender and lends strong support for the ν = 5/2 state being nonabelian. Our measurements reveal an intrinsically different nature of interaction in the first excited Landau level underlying the physics at ν = 5/2.     

Topological phase transition and texture inversion in a tunable topological insulator

The recently discovered three-dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice, driving the system through a topological quantum phase transition. By directly measuring the topological quantum numbers and invariants, we report the observation of a phase transition in a tunable spin-orbit system, BiTl(S(1-δ)Se(δ))(2), in which the topological state formation is visualized. In the topological state, vortex-like polarization states are observed to exhibit three-dimensional vectorial textures, which collectively feature a chirality transition as the spin momentum-locked electrons on the surface go through the zero carrier density point. Such phase transition and texture inversion can be the physical basis for observing fractional charge (±e/2) and other fractional topological phenomena.     

Quantum Hall effect in polar oxide heterostructures

We observed Shubnikov-de Haas oscillation and the quantum Hall effect in a high-mobility two-dimensional electron gas in polar ZnO/Mg(x)Zn(1-x)O heterostructures grown by laser molecular beam epitaxy. The electron density could be controlled in a range of 0.7 x 10(12) to 3.7 x 10(12) per square centimeter by tuning the magnesium content in the barriers and the growth polarity. From the temperature dependence of the oscillation amplitude, the effective mass of the two-dimensional electrons was derived as 0.32 +/- 0.03 times the free electron mass. Demonstration of the quantum Hall effect in an oxide heterostructure presents the possibility of combining quantum Hall physics with the versatile functionality of metal oxides in complex heterostructures.     

Imaging coherent electron flow from a quantum point contact

Scanning a charged tip above the two-dimensional electron gas inside a gallium arsenide/aluminum gallium arsenide nanostructure allows the coherent electron flow from the lowest quantized modes of a quantum point contact at liquid helium temperatures to be imaged. As the width of the quantum point contact is increased, its electrical conductance increases in quantized steps of 2 e(2)/h, where e is the electron charge and h is Planck's constant. The angular dependence of the electron flow on each step agrees with theory, and fringes separated by half the electron wavelength are observed. Placing the tip so that it interrupts the flow from particular modes of the quantum point contact causes a reduction in the conductance of those particular conduction channels below 2 e(2)/h without affecting other channels.     

Fine structure constant defines visual transparency of graphene

There are few phenomena in condensed matter physics that are defined only by the fundamental constants and do not depend on material parameters. Examples are the resistivity quantum, h/e2 (h is Planck's constant and e the electron charge), that appears in a variety of transport experiments and the magnetic flux quantum, h/e, playing an important role in the physics of superconductivity. By and large, sophisticated facilities and special measurement conditions are required to observe any of these phenomena. We show that the opacity of suspended graphene is defined solely by the fine structure constant, a = e2/hc feminine 1/137 (where c is the speed of light), the parameter that describes coupling between light and relativistic electrons and that is traditionally associated with quantum electrodynamics rather than materials science. Despite being only one atom thick, graphene is found to absorb a significant (pa = 2.3%) fraction of incident white light, a consequence of graphene's unique electronic structure.     

The quantized Hall effect

Quantization of the Hall effect is one of the most surprising discoveries in recent experimental solid-state research. At low temperatures and high magnetic fields the ratio of the Hall voltage to the electric current in a two-dimensional system is quantized in units of h/e(2), where h is Planck's constant and e is the electronic charge. Concomitantly, the electrical resistance of the specimen drops to values far below the resistances of the best normal metals.     

Universal signatures of fractionalized quantum critical points

Ground states of certain materials can support exotic excitations with a charge equal to a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive unusual quantum phase transitions. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly nonclassical critical exponent η = 1.493 and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z(2) gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.     

Chaotic Dirac billiard in graphene quantum dots

The exceptional electronic properties of graphene, with its charge carriers mimicking relativistic quantum particles and its formidable potential in various applications, have ensured a rapid growth of interest in this new material. We report on electron transport in quantum dot devices carved entirely from graphene. At large sizes (>100 nanometers), they behave as conventional single-electron transistors, exhibiting periodic Coulomb blockade peaks. For quantum dots smaller than 100 nanometers, the peaks become strongly nonperiodic, indicating a major contribution of quantum confinement. Random peak spacing and its statistics are well described by the theory of chaotic neutrino billiards. Short constrictions of only a few nanometers in width remain conductive and reveal a confinement gap of up to 0.5 electron volt, demonstrating the possibility of molecular-scale electronics based on graphene.     

Broken-symmetry states in doubly gated suspended bilayer graphene

The single-particle energy spectra of graphene and its bilayer counterpart exhibit multiple degeneracies that arise through inherent symmetries. Interactions among charge carriers should spontaneously break these symmetries and lead to ordered states that exhibit energy gaps. In the quantum Hall regime, these states are predicted to be ferromagnetic in nature, whereby the system becomes spin polarized, layer polarized, or both. The parabolic dispersion of bilayer graphene makes it susceptible to interaction-induced symmetry breaking even at zero magnetic field. We investigated the underlying order of the various broken-symmetry states in bilayer graphene suspended between top and bottom gate electrodes. We deduced the order parameter of the various quantum Hall ferromagnetic states by controllably breaking the spin and sublattice symmetries. At small carrier density, we identified three distinct broken-symmetry states, one of which is consistent with either spontaneously broken time-reversal symmetry or spontaneously broken rotational symmetry.     

Topographic mapping of the quantum hall liquid using a few-electron bubble

A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded two-dimensional (2D) electron gas. Under quantum Hall effect conditions, applying a positive voltage to the tip locally enhanced the 2D electron density and created a "bubble" of electrons in an otherwise unoccupied Landau level. As the tip scanned along the sample surface, the bubble followed underneath. The tip sensed the motions of single electrons entering or leaving the bubble in response to changes in the local 2D electrostatic potential.