We report quantitative measurements of the impact of alloy disorder on the ν = 5/2 fractional quantum Hall state. Alloy disorder is controlled by the aluminum content x in the Al(x)Ga(1-x)As channel of a quantum well. We find that the ν = 5/2 state is suppressed with alloy scattering. To our surprise, in samples with alloy disorder the ν = 5/2 state appears at significantly reduced mobilities when compared to samples in which alloy disorder is not the dominant scattering mechanism. Our results highlight the distinct roles of the different types of disorder present in these samples, such as the short-range alloy and the long-range Coulomb disorder.

In this work we report the opening of an energy gap at the filling factor ν = 3 + 1/3, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the ν = 3 + 1/3 and 3 + 1/5 states from the upper spin branch are reversed when compared to the ν = 2 + 1/3 and 2 + 1/5 counterpart states in the lower spin branch. Our findings raise the possibility that the former states have a non-conventional origin.Over the last three decades we have wittnessed an ongoing exploration of topological phenomena in electronic systems. Topological ground states may arise from either single-particle band structure effects [1,2] or from emergent many-body effects in strongly interacting systems. One example of the latter is the fractional quantum Hall state (FQHS) at the Landau level filling factor ν = 1/3 [3], a ground state belonging to the larger class of conventional Laughlin-Jain FQHSs [4,5].More recently it was realized that the family of topological ground states may be much richer than previously thought. Of the novel FQHSs the ones supporting nonAbelian quasiparticles have generated the most excitement [6][7][8]. The FQHS at ν = 5/2 is believed to be such a non-Abelian state [9]. However, several other FQHSs in the region 2 < ν < 4, commonly called the second Landau level (SLL), are also thought to be non-Abelian [10][11][12][13][14][15].Despite sustained efforts in theory [10][11][12][13][14][15], the nature of the prominent odd-denominator FQHSs forming in the SLL,such as the ones at ν = 2 + 1/3 and 2 + 1/5, remains unknown. The FQHSs at ν = 2 + 1/3 [16-22] admits both non-Abelian candidate states [10,11] as well as a conventional Laughlin-Jain description [4,5]. The relatively poor overlap between the exact and numerically obtained wavefunctions [23][24][25][26][27][28] and the unusual excitations [15] does not provide firm evidence for Laughlin correlations in the ν = 2 + 1/3 FQHS. A number of recent experiments of the ν = 2 + 1/3 FQHS, however, found its bulk [21] and edge [29][30][31] properties consistent with a Laughlin description. The other prominent FQHS at ν = 2 + 1/5 [19,20] is generally believed to be of the conventional Laughlin type [25][26][27][28], although there is a non-Abelian construction for it as well [11]. It is therefore currently not clear whether or not the prominent odd-denominator FQHSs in the SLL, such as the ones at ν = 2 + 1/3 and 2 + 1/5, require a description beyond the conventional Laughlin-Jain theory.Experiments on the odd-denominator FQHS in the SLL have been restricted almost exclusively to the 2 < ν < 3 range, called the lower spin branch of the SLL (LSB SLL). Motivated by their poor understanding, we have performed transport studies of these FQHSs in the little known upper spin branch of the SLL (USB SLL), i.e. in the 3 < ν < 4 region. We establish a new FQHS at ν = 3+1/3 by detecting the opening of an energy gap. A quanti...

Reports of weak local minima in the magnetoresistance at ν = 2 + 3/5, 2 + 3/7, 2 + 4/9, 2 + 5/9, 2 + 5/7, and 2 + 5/8 in second Landau level of the electron gas in GaAs/AlGaAs left open the possibility of fractional quantum Hall states at these filling factors. In a high quality sample we found that the magnetoresistance exhibits peculiar features near these filling factors of interest. These features, however, cannot be associated with fractional quantum Hall states; instead they originate from magnetoresistive fingerprints of the electronic bubble phases. We found only two exceptions: at ν = 2 + 2/7 and 2 + 5/7 there is evidence for incipient fractional quantum Hall states at intermediate temperatures. As the temperature is lowered, these fractional quantum Hall states collapse due to a phase competition with bubble phases.

We present a dc Superconducting QUantum Interference Device (SQUID)-based current amplifier with an estimated input referred noise of only 2.3 fA/Hz. Because of such a low amplifier noise, the circuit is useful for Johnson noise thermometry of quantum resistors in the kΩ range down to mK temperatures. In particular, we demonstrate that our circuit does not contribute appreciable noise to the Johnson noise of a 3.25 kΩ resistor down to 16 mK. Our circuit is a useful alternative to the commonly used High Electron Mobility Transistor-based amplifiers, but in contrast to the latter, it offers a much reduced 1/f noise. In comparison to SQUIDs interfaced with cryogenic current comparators, our circuit has similar low noise levels, but it is easier to build and to shield from magnetic pickup.

We describe sensitive magnetometry using lumped-element resonators fabricated from a superconducting thin film of NbTiN. Taking advantage of the large kinetic inductance of the superconductor, we demonstrate a continuous resonance frequency shift of 27 MHz for a change in magnetic field of 1.8 µT within a perpendicular background field of 60 mT. By using phase-sensitive readout of microwaves transmitted through the sensors, we measure phase shifts in real time with a sensitivity of 1 degree/nT. We present measurements of the noise spectral density of the sensors, and find their field sensitivity is at least within one to two orders of magnitude of superconducting quantum interference devices operating with zero background field. Our superconducting kinetic inductance field-frequency sensors enable real-time magnetometry in the presence of moderate perpendicular background fields up to at least 0.2 T. Applications for our sensors include the stabilization of magnetic fields in long coherence electron spin resonance measurements and quantum computation.Disordered superconductors such as NbTiN, TiN and NbN have become ubiquitous in several fields of study due to their large kinetic inductance and resilience to large background magnetic fields 1,2 . Microwave kinetic inductance detectors 3-5 and superconducting nanowire single-photon detectors 6,7 fabricated from kinetic inductors are now routinely used in astronomy and imaging. Kinetic inductors can also be used in applications such as current-sensing 8 , magnetometry 9 , parametric amplification 10,11 , generation of frequency combs 12 , and superconducting qubits 13,14 .In this work, we take advantage of the kinetic inductance of a thin film of NbTiN to fabricate lumped-element resonators whose resonance frequencies are strongly dependent on the perpendicular magnetic field, changing by as much as 27 MHz for a field change of 1.8 µT.We demonstrate a method for real-time measurement of AC magnetic fields based on phase-sensitive readout of microwave transmission through the resonators, finding a detection sensitivity of 1 degree/nT. Our Superconducting Kinetic Inductance Field-Frequency Sensors (SKIFFS) are able to operate in perpendicular background magnetic fields at least as large as 0.2 T, and may find applications in quantum computation, where superconducting quantum interference devices (SQUIDs) based on Josephson junctions may not be applicable due to the large magnetic fields.Our SKIFFS are fabricated from a 7 nm NbTiN thin film (T C ∼ 9 K, R sheet = 252 Ω/ ) DC-sputtered reactively on a c-axis sapphire substrate using a NbTi alloy target and an Ar/N environment 15 . The device features are patterned using electron-beam lithography followed by reactive-ion etching with an SF 6 /Ar plasma. A scanning electron micrograph of a SKIFFS is shown in figure Fig. 1a. The sensor is a lumped-element microwave resonator fabricated from a 100 µm × 100 µm rectangular a) Electronic mail: asfaw@princeton. edu FIG. 1. (a) Scanning electron micrograph of a SKIFFS resonato...