Observation of a quantized hall resistivity in the presence of mesoscopic fluctuations

We present an experimental study of mesoscopic, two-dimensional electronic systems at high magnetic fields. Our samples, prepared from a low-mobility InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance fluctuations. Focusing on the lowest Landau level, we find that, while the diagonal resistivity displays strong fluctuations, the Hall resistivity is free of fluctuations and remains quantized at its nu=1 value, h/e(2). This is true also in the insulating phase that terminates the quantum Hall series. These results extend the validity of the semicircle law of conductivity in the quantum Hall effect to the mesoscopic regime.     

Semi‐Classical Model of Strongly Correlated Coulomb Systems in Weak Magnetic Field

The integer and fractional quantum Hall effects are two remarkable macroscopic quantum phenomena occurring in two‐dimensional strongly correlated electronic systems at high magnetic fields and low temperatures. Quantization of Hall resistivity in the very high magnetic field regime at partial filling of the lowest Landau level indicates the stabilization of an electronic liquid quantum Hall phase of matter. Other interesting phases that differ from the quantum Hall phases take prominence in weaker magnetic fields when many more Landau levels are filled. These states manifest anisotropic magneto‐transport properties and, under certain conditions, appear to mimic charge density waves and/or liquid crystalline phases. One way to understand such a behavior has been in terms of effective interaction potentials confined to the highest Landau level partially filled with electrons. In this work we show that, for weak magnetic fields, such a quantum treatment of these strongly correlated Coulomb systems resembles a semi‐classical model of rotating electrons in which the time‐averaged interaction potential can be expressed solely in terms of guiding center coordinates. We discuss how the features of this semi‐classical effective potential may affect the stability of various strongly correlated electronic phases in the weak magnetic field regime (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anticrossing of spin-split subbands in quasi-one-dimensional wires

In quantum Hall systems, both anticrossings and magnetic phase transitions can occur when opposite-spin Landau levels coincide. Our results indicate that both processes are also possible in quasi-1D quantum wires in an in-plane B field, Bparallel. Crossings of opposite-spin 1D subbands resemble magnetic phase transitions at zero dc source-drain bias, but display anticrossings at high dc bias. Our data also imply that the well-known 0.7 structure may evolve into a spin-hybridized state in finite dc bias.     

Exotic electronic phases in the second Landau level

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.     

Exotic electronic phases in the second Landau level

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.     

Pinning mode resonances of new phases of 2D electron systems in high magnetic fields

A striking rf or microwave resonance is a generic feature of electron solid phases of two-dimensional electron systems. These resonances have served to identify and characterize such solids, in the insulator that terminates the series of fractional quantum Hall effects at high magnetic field, in the range of the integer quantum Hall effect, and in bubble phases in the first excited and higher Landau levels.     

Quantum Hall effect in twisted bilayer graphene

We address the quantum Hall behavior in twisted bilayer graphene transferred from the C face of SiC. The measured Hall conductivity exhibits the same plateau values as for a commensurate Bernal bilayer. This implies that the eightfold degeneracy of the zero energy mode is topologically protected despite rotational disorder as recently predicted. In addition, an anomaly appears. The densities at which these plateaus occur show a magnetic field dependent offset. It suggests the existence of a pool of localized states at low energy, which do not count towards the degeneracy of the lowest band Landau levels. These states originate from an inhomogeneous spatial variation of the interlayer coupling.     

Unveiling the magnetic structure of graphene nanoribbons

We perform magnetotransport measurements in lithographically patterned graphene nanoribbons down to a 70 nm width. The electronic spectrum fragments into an unusual Landau levels pattern, characteristic of Dirac fermion confinement. The two-terminal magnetoresistance reveals the onset of magnetoelectronic subbands, edge currents and quantized Hall conductance. We bring evidence that the magnetic confinement at the edges unveils the valley degeneracy lifting originating from the electronic confinement. Quantum simulations suggest some disorder threshold at the origin of mixing between chiral magnetic edge states and disappearance of quantum Hall effect.     

Quantum anomalous hall effect in Hg1-yMnyTe quantum wells

The quantum Hall effect is usually observed when a two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum anomalous Hall effect, can be realized in Hg{1-y}Mn{y}Te quantum wells, without an external magnetic field and the associated Landau levels. This effect arises purely from the spin polarization of the Mn atoms, and the quantized Hall conductance is predicted for a range of quantum well thickness and the concentration of the Mn atoms. This effect enables dissipationless charge current in spintronics devices.     

The enigma of the quantum Hall effect in graphene

We apply Laughlin’s gauge argument to analyze the ν=0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν=0 quantized Hall effect. We argue that this ν=0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.     

New physics in high Landau levels

Recent magneto-transport experiments on ultra-high mobility 2D electron systems in GaAs/AlGaAs heterostructures have revealed the existence of whole new classes of correlated many-electron states in highly excited Landau levels. These new states, which appear only at extremely low temperatures, are distinctly different from the familiar fractional quantum Hall liquids of the lowest Landau level. Prominent among the recent findings are the discoveries of giant anisotropies in the resistivity near half-filling of the third and higher Landau levels and the observation of re-entrant integer quantum Hall states in the flanks of these same levels. This contribution will survey the present status of this emerging field.     

Tilt-induced localization and delocalization in the second Landau level

We have investigated the behavior of electronic phases of the second Landau level under tilted magnetic fields. The fractional quantum Hall liquids at nu=2+1/5 and 2+4/5 and the solid phases at nu=2.30, 2.44, 2.57, and 2.70 are quickly destroyed with tilt. This behavior can be interpreted as a tilt driven localization of the 2+1/5 and 2+4/5 fractional quantum Hall liquids and a delocalization through the melting of solid phases in the top Landau level, respectively. The evolution towards the classical Hall gas of the solid phases is suggestive of antiferromagnetic ordering.     

Electric- and magnetic-field-tuned Landau levels and Hall conductivity in AA-stacked bilayer graphene

We theoretically study the combined effect of magnetic and electric fields on the Landau levels and Hall conductivity in AA-stacked bilayer graphene. From the analytic expressions derived, we obtain explicit criterions for determining the zero-energy Landau level and different level crossings in the graphene bilayer. For providing a scheme of experimental verification, we further explore the quantum Hall effect in such a biased bilayer. It is found that the zero-conductance Hall plateau in this system can vanish at certain specific combinations of magnetic and electric fields, accompanying with the occurrence of resonance Hall conductivity steps.     

Vanishing hall coefficient in the extreme quantum limit in photocarrier-doped SrTiO3

We explore the extreme quantum limit of photogenerated electrons in quantum paraelectric SrTiO3. This regime is distinct from conventional semiconductors, due to the large electron effective mass and large dielectric constant. At low temperature, the magnetoresistance and Hall resistivity saturate at a high magnetic field, deviating from conventional behavior. As a result, the Hall coefficient vanishes on the scale of the ratio of the Landau level splitting to the thermal energy, indicating the essential role of lowest Landau level occupancy, as limited by thermal broadening.     

Stable Pfaffian state in bilayer graphene

Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.     

Evolution of individual quantum Hall edge states in the presence of disorder

By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated.     

Finite-temperature density instability at high landau level occupancy

We study here the onset of charge density wave instabilities in quantum Hall systems at finite temperature for Landau level filling nu>4. Specific emphasis is placed on the role of disorder as well as on an in-plane magnetic field. Beyond some critical value, disorder is observed to suppress the charge density wave melting temperature to zero. In addition, we find that a transition from perpendicular to parallel stripes (relative to the in-plane magnetic field) exists when the electron gas thickness exceeds approximately 60 A. The perpendicular alignment of the stripes is in agreement with the experimental finding that the easy conduction direction is perpendicular to the in-plane field.     

Magnetic field induced metal-insulator transitions in p-SiGe

Low density modulation doped p-SiGe, where the holes lie in a strained SiGe quantum well, frequently exhibits anomalous insulating behaviour between filling factors ν=2 and 1. There is also anomalous metallic behavior with a metal-insulator transition between the two. It is shown that in these samples exchange effects are sufficiently large to induce the paramagnetic-ferromagnetic phase transition predicted by Giuliani and Quinn in 1985, also that the metallic and insulating behavior is associated with the coincidence of two Landau levels of opposite spin. A model calculation shows that while a ferromagnetic polarization may occur at integer filling factors screening suppresses it for non-integer filling factors. It is argued the Landau levels then stick-together and allow a spin-density instability to form. Because of the strong spin-orbit coupling in p-SiGe the transport properties of this state differ from those of other systems where a similar quantum Hall ferromagnet probably forms.     

Influence of excited Landau levels on a two-dimensional electron-hole system in a strong perpendicular magnetic field

The study of the quantum states of a two-dimensional electron-hole system in a strong perpendicular magnetic field is carried out with special attention to the influence of virtual quantum transitions of interacting particles between the Landau levels. These virtual quantum transitions from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their reversion to the lowest Landau levels in second order perturbation theory result in an indirect attraction between the particles. The influence of the indirect interaction on the magnetoexciton ground state, on the chemical potential of the Bose-Einstein condensed magnetoexcitons, and on the ground state energy of the metallic-type electron-hole liquid is investigated in the Hartree-Fock approximation. The coexistence of different phases is suggested.     

Current carrying states in the disordered quantum anomalous Hall effect

In a quantum Hall effect, flat Landau levels may be broadened by disorder. However, it has been found that in the thermodynamic limit, all extended (or current carrying) states shrink to one single energy value within each Landau level. On the other hand, a quantum anomalous Hall effect consists of dispersive bands with finite widths. We numerically investigate the picture of current carrying states in this case. With size scaling, the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit, in a power law way. The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects. The number of current carrying states obeys similar scaling rules, so that the density of states of current carrying states is finite. Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.