Tilt-induced localization and delocalization in the second Landau level

Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene

We develop a proposal to realize a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings ν=±3+1/2 and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band structure of bilayer graphene and includes the fluctuations between the n=0 and n=1 cyclotron orbitals of its zeroth Landau level to delineate the most favorable region of parameters to experimentally access this unconventional critical point. We also find evidence for a new anisotropic gapless phase stabilized near the level crossing of n=0/1 orbits.

Piezo-driven sample rotation system with ultra-low electron temperature

Piezo-driven rotator is convenient for tilted magnetic field experiments due to its precise angle control. However, the rotator itself and the sample mounted on it are difficult to be cooled down because of extra heat leaks and presumably bad thermal contacts from the piezo. Here, we report a piezo-driven sample rotation system designed for ultra-low temperature environment. The sample, as well as the rotating sample holder, can be cooled to as low as 25 mK by customized thermal links and thermal contacts. More importantly, the electron temperature in the electrical transport measurements can also be cooled down to 25 mK with the help of home-made filters. To demonstrate the application of our rotation system at ultra-low electron temperature, a measurement revealing tilt-induced localization and delocalization in the second Landau level of two-dimensional electron gas is provided.

A review of the quantum Hall effects in MgZnO/ZnO heterostructures

This review visits recent experimental efforts on high mobility two-dimensional electron systems (2DES) hosted at the Mg _x Zn[Formula: see text]O/ZnO heterointerface. We begin with the growth of these samples, and highlight the key characteristics of ozone-assisted molecular beam epitaxy required for their production. The transport characteristics of these structures are found to rival that of traditional semiconductor material systems, as signified by the high electron mobility ([Formula: see text] cm² Vs^-1) and rich quantum Hall features. Owing to a large effective mass and small dielectric constant, interaction effects are an order of magnitude stronger in comparison with the well studied GaAs-based 2DES. The strong correlation physics results in robust Fermi-liquid renormalization of the effective mass and spin susceptibility of carriers, which in turn dictates the parameter space for the quantum Hall effect. Finally, we explore the quantum Hall effect with a particular emphasis on the spin degree of freedom of carriers, and how their large spin splitting allows control of the ground states encountered at ultra-low temperatures within the fractional quantum Hall regime. We discuss in detail the physics of even-denominator fractional quantum Hall states, whose observation and underlying character remain elusive and exotic.

Competing ν = 5/2 fractional quantum Hall states in confined geometry

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

Electron-Hole Asymmetric Chiral Breakdown of Reentrant Quantum Hall States

Reentrant integer quantum Hall (RIQH) states are believed to be correlated electron solid phases, although their microscopic description remains unclear. As bias current increases, longitudinal and Hall resistivities measured for these states exhibit multiple sharp breakdown transitions, a signature unique to RIQH states. A comparison of RIQH breakdown characteristics at multiple voltage probes indicates that these signatures can be ascribed to a phase boundary between broken-down and unbroken regions, spreading chirally from source and drain contacts as a function of bias current and passing voltage probes one by one. The chiral sense of the spreading is not set by the chirality of the edge state itself, instead depending on electron- or holelike character of the RIQH state.

Optical Emission Spectroscopy Study of Competing Phases of Electrons in the Second Landau Level

Quantum phases of electrons in the filling factor range 2≤ν≤3 are probed by the weak optical emission from the partially populated second Landau level and spin wave measurements. Observations of optical emission include a multiplet of sharp peaks that exhibit a strong filling factor dependence. Spin wave measurements by resonant inelastic light scattering probe breaking of spin rotational invariance and are used to link this optical emission with collective phases of electrons. A remarkably rapid interplay between emission peak intensities manifests phase competition in the second Landau level.

Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene

The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.

Spin transition in the ν=8/3 fractional quantum Hall effect

We present here the results from a density dependent study of the activation energy gaps of the fractional quantum Hall effect states at Landau level fillings ν=8/3 and 7/3 in a series of high quality quantum wells. In the density range from 0.5×10(11) to 3×10(11) cm(-2), the 7/3 energy gap increases monotonically with increasing density, supporting its ground state being spin polarized. For the 8/3 state, however, its energy gap first decreases with increasing density, almost vanishes at n~0.8×10(11) cm(-2), and then turns around and increases with increasing density, clearly demonstrating a spin transition.

Enhancement of the ν = 5/2 fractional quantum Hall state in a small in-plane magnetic field

Using a 50-nm-width ultraclean GaAs/AlGaAs quantum well, we have studied the Landau level filling factor ν=5/2 fractional quantum Hall effect in a perpendicular magnetic field B∼1.7  T and determined its dependence on tilted magnetic fields. Contrary to all previous results, the 5/2 resistance minimum and the Hall plateau are found to strengthen continuously under an increasing tilt angle 0<θ<25° (corresponding to an in-plane magnetic field 0<B(∥)<0.8  T). In the same range of θ, the activation gaps of both the 7/3 and the 8/3 states are found to increase with tilt. The 5/2 state transforms into a compressible Fermi liquid upon tilt angle θ>60°, and the composite fermion series [2+p/(2p±1), p=1,2] can be identified. Based on our results, we discuss the relevance of a Skyrmion spin texture at ν=5/2 associated with small Zeeman energy in wide quantum wells, as proposed by Wójs et al. [Phys. Rev. Lett. 104, 086801 (2010)].

Collective nature of the reentrant integer quantum Hall states in the second Landau level

We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature.

Rapid collapse of spin waves in nonuniform phases of the second Landau level

The spin degree of freedom in quantum phases of the second Landau level is probed by resonant light scattering. The long wavelength spin wave, which monitors the degree of spin polarization, is at the Zeeman energy in the fully spin-polarized state at ν = 3. At lower filling factors, the intensity of the Zeeman mode collapses, indicating loss of polarization. A novel continuum of low-lying excitations emerges that dominates near ν = 8/3 and ν = 5/2. Resonant Rayleigh scattering reveals that quantum fluids for ν < 3 break up into robust domain structures. While the state at ν = 5/2 is considered to be fully polarized, these results reveal unprecedented roles for spin degrees of freedom.

Tilt-induced anisotropic to isotropic phase transition at ν = 5/2

A modest in-plane magnetic field B(∥) is sufficient to destroy the fractional quantized Hall states at ν = 5/2 and 7/2 and replace them with anisotropic compressible phases. Remarkably, we find that at larger B(∥) these anisotropic phases can themselves be replaced by isotropic compressible phases reminiscent of the composite fermion fluid at ν = 1/2. We present strong evidence that this transition is a consequence of the mixing of Landau levels from different electric subbands. We also report surprising dependences of the energy gaps at ν = 5/2 and 7/3 on the width of the confinement potential.

Contrasting behavior of the 5/2 and 7/3 fractional quantum Hall effect in a tilted field

Using a tilted-field geometry, the effect of an in-plane magnetic field on the even denominator nu=5/2 fractional quantum Hall state is studied. The energy gap of the nu=5/2 state is found to collapse linearly with the in-plane magnetic field above approximately 0.5 T. In contrast, a strong enhancement of the gap is observed for the nu=7/3 state. The radically distinct tilted-field behavior between the two states is discussed in terms of Zeeman and magneto-orbital coupling within the context of the proposed Moore-Read Pfaffian wave function for the 5/2 fractional quantum Hall effect.

Intrinsic gap of the nu=5/2 fractional quantum Hall state

The fractional quantum Hall effect is observed at low magnetic field where the cyclotron energy is smaller than the Coulomb interaction energy. The nu=5/2 excitation gap at 2.63 T is measured to be 262+/-15 mK, similar to values obtained in samples with twice the electronic density. Examining the role of disorder on the 5/2 state, we find that a large discrepancy remains between theory and experiment for the intrinsic gap extrapolated from the infinite mobility limit. The observation of a 5/2 state in the low-field regime suggests that inclusion of nonperturbative Landau level mixing may be necessary to fully understand the energetics of half-filled fractional quantum Hall liquids.