Observation of an even-denominator quantum number in the fractional quantum Hall effect

Willett, R. L.; Eisenstein, J. P.; Störmer, H. L.; Tsui, D. C.; Gossard, A. C.; English, J. H.

doi:10.1103/physrevlett.59.1776

Cited by 1,074 publications

(994 citation statements)

References 15 publications

Supporting

Mentioning

958

Contrasting

Unclassified

Order By: Relevance

“…3(b), and extract a quasigap from the temperature dependence of S, as shown in Fig. 3 (c [24,26,27]. The evolution of R xx with temperature at ν = 6/5 clearly shows such behavior.…”

Section: Fig 1 (A)mentioning

confidence: 89%

Fractional quantum Hall effect of two-dimensional electrons in high-mobility Si/SiGe field-effect transistors

Pan

Tsui

et al. 2012

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

The fractional quantum Hall (FQH) regime of the Si two-dimensional electron system (2DES) in enhancement-mode field-effect transistors of Si/SiGe heterostructures was probed via electrical transport measurements. At n ∼ 2.6 × 10 11 /cm 2 with µ = 1.6 × 10 6 cm 2 /V s, signatures of FQH states at filling factors ν = 4/5, 6/5, and 10/7 were observed, in addition to the FQH states reported in previous studies. The temperature dependence of the FQH states is investigated and comparison is made with previous work done on modulation-doped samples. Results indicate that robustness of the FQH states is dependent on the nature of disorder in the 2DES. 1The discoveries of the integer quantum Hall (IQH) effect[1] and the fractional quantum Hall (FQH) effect [2] have spurred much research on the ground states of two-dimensional (2D) electrons in the presence of strong magnetic fields over the past 30 years. Thanks to to the constantly refined III-V epitaxial technology, the quality of GaAs/AlGaAs heterostructures has been continually improving, leading to the observation of a few tens of FQH states in GaAs [3]. While large in number, most of the FQH states can be understood within the theoretical framework of composite fermions (CFs) [4]. In the CF model, the FQH effect, originally arising from electron-electron interaction, is mapped to the IQH effect arising from Landau quantization of the orbital motion of CFs.Soon after the discoveries of the IQH and FQH effects, it was realized that additional degrees of freedom of 2DESs such as spins, layers, subbands, and valleys, may produce new correlated states which do not exist in a one-component 2DES [5]. Celebrated examples include Skyrmions in systems with small Zeeman splitting [6,7], even-denominator FQH states [8,9], and the excitonic superfluid in bilayer systems [10]. While much effort towards the understanding of the roles of spins, layers, and subbands in the FQH regime has been made using high-quality GaAs quantum wells, experimental studies on the effects of valleys have been relatively sparse, only a few reports on 2D electrons in Si [11,12] and AlAs [13][14][15][16] available, partly due to the less impressive material quality of multi-valley semiconductors.Indeed, the electron mobilities of the devices used in these studies were smaller than that of GaAs by almost two orders of magnitude [3,17]. Nevertheless, looking back at the history of discoveries of new states in GaAs, we may expect that more interesting physical phenomena in multi-valley systems will emerge, once materials with higher mobility are available.Recently, we reported a fabrication process for making undoped (100)-oriented Si/SiGe FETs and observed an electron mobility of 1.6 × 10 6 cm 2 /V s [18], approximately eight times higher than that of typical modulation-doped Si/SiGe quantum wells [19]. Such improvement in material quality naturally prompted us to perform magneto-transport experiments and search for new states in Si 2DESs. In this paper, we focus on the FQH regime ν < 2, where the...

show abstract

“…3(b), and extract a quasigap from the temperature dependence of S, as shown in Fig. 3 (c [24,26,27]. The evolution of R xx with temperature at ν = 6/5 clearly shows such behavior.…”

Section: Fig 1 (A)mentioning

confidence: 89%

Fractional quantum Hall effect of two-dimensional electrons in high-mobility Si/SiGe field-effect transistors

Pan

Tsui

et al. 2012

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…A vast array of states has now been observed where, in general, ν takes an odd denominator as a result of the Pauli exclusion principle. The most remarkable exception to this has been the FQHE at ν = 5/2 in GaAs heterostructures 137 . Its most widely accepted explanation is that an attractive interaction occurs between composite fermions within the second Landau level, owing to the nodal nature of the electronic wavefunction.…”

Section: Quantum Computingmentioning

confidence: 99%

Emergent functions of quantum materials

2017

View full text Add to dashboard Cite

Materials can harbour quantum many-body systems, most typically in the form of strongly correlated electrons in solids, that lead to novel and remarkable functions thanks to emergence-collective behaviours that arise from strong interactions among the elements. These include the Mott transition, high-temperature superconductivity, topological superconductivity, colossal magnetoresistance, giant magnetoelectric e ect, and topological insulators. These phenomena will probably be crucial for developing the next-generation quantum technologies that will meet the urgent technological demands for achieving a sustainable and safe society. Dissipationless electronics using topological currents and quantum spins, energy harvesting such as photovoltaics and thermoelectrics, and secure quantum computing and communication are the three major fields of applications working towards this goal. Here, we review the basic principles and the current status of the emergent phenomena and functions in materials from the viewpoint of strong correlation and topology.E mergence is a concept developed for many-body systems, indicating the properties, phenomena, and functions that never appear in the individual elements but are realized only when a huge number of elements get together 1 . Inside materials, emergent phenomena are often seen due to the interaction of electronic states; with recent developments on electronic states in solids schematically summarized in Fig. 1a. Electrons in solids have several degrees of freedom: charge, spin and orbital, and are characterized by the topological nature determined by the atomic potential on the crystal lattice structure, as schematically shown in Fig. 1b. These five attributes are coupled together and determine the overall responses to stimuli, which appear as materials' electrical, magnetic, optical, thermal, and mechanical properties.These collective electrons demonstrate various macroscopic quantum phenomena, the representative example of which is superconductivity. One of the big challenges in condensed matter physics is to increase the temperature (T c ) at which superconductivity can be observed to above room temperature. However, there are many other macroscopic quantum phenomena that are already observable above room temperature. One is magnetism (by the Bohr-van Leeuwen theorem), and the other is ferroelectricity 2,3 . Remarkably, there are common features of these three macroscopic quantum phenomena: the order parameter, which is of quantum origin, behaves as a classical quantity, and the quantum topology plays a crucial role.The topological nature of the electronic states is the key concept in the most recent developments in understanding quantum materials. The quantum Hall effect, topological insulators, and topological superconductors are all characterized by nontrivial topologies in Hilbert space. The Berry phase, which describes the connection and curvature of the subspace of Hilbert space, plays the central role in the unified principle to describe this topological nature 4 . ...

show abstract

“…When the direction of the magnetic field B is tilted, the orbital LL splitting is given by the field component B ⊥ normal to the two-dimensional electron system (2DES) while the total field strength B determines the Zeeman splitting E Z . Early experiments on GaAs revealed that the ν = 4/3, 5/3, and 8/5 states behaved differently upon tilting the sample [4,5]: While the ν = 4/3 and 8/5 states were undergoing a transition from a spinunpolarized state to a polarized one, the ν = 5/3 state was always fully spin polarized.Although the FQHE has been reported in quite a number of different materials [6][7][8][9][10][11][12], the FQHE has never been observed in a diluted magnetic semiconductor in which atoms with magnetic moment (e.g., Mn 2+ ) are placed in a 2DES. Then, the localized spins in the magnetic impurities' d orbitals interact with the correlated electron system via the quantum mechanical s-d exchange interaction, causing giant Zeeman splitting [13] which is tunable in magnitude, sign, and field dependence [14].…”

mentioning

confidence: 99%

Fractional quantum Hall effect in a dilute magnetic semiconductor

Betthausen

Giudici²,

Iankilevitch³

et al. 2014

Phys. Rev. B

View full text Add to dashboard Cite

We report the observation of the fractional quantum Hall effect in the lowest Landau level of a two-dimensional electron system (2DES), residing in the diluted magnetic semiconductor Cd 1−x Mn x Te. The presence of magnetic impurities results in a giant Zeeman splitting leading to an unusual ordering of composite fermion Landau levels. In experiment, this results in an unconventional opening and closing of fractional gaps around the filling factor ν = 3/2 as a function of an in-plane magnetic field, i.e., of the Zeeman energy. By including the s-d exchange energy into the composite Landau level spectrum the opening and closing of the gap at filling factor 5/3 can be modeled quantitatively. The widely tunable spin-splitting in a diluted magnetic 2DES provides a means to manipulate fractional states. The fractional quantum Hall effect (FQHE) is a collective high-magnetic field phenomenon, originating from Coulomb repulsion of electrons confined in two dimensions. At certain fractional fillings, ν = p/q, of the Landau levels (LLs) (ν = filling factor, p,q = integers), quantized plateaus in the Hall resistance ρ xy and the vanishing longitudinal resistance ρ xx herald the presence of peculiar electron correlations [1,2]. Here, the electrons condense into a liquidlike ground state that is separated by a gap from the excited states. Most experiments to date have been carried out on GaAsbased systems, being still the cleanest material system with the highest electron mobilities [3]. When the direction of the magnetic field B is tilted, the orbital LL splitting is given by the field component B ⊥ normal to the two-dimensional electron system (2DES) while the total field strength B determines the Zeeman splitting E Z . Early experiments on GaAs revealed that the ν = 4/3, 5/3, and 8/5 states behaved differently upon tilting the sample [4,5]: While the ν = 4/3 and 8/5 states were undergoing a transition from a spinunpolarized state to a polarized one, the ν = 5/3 state was always fully spin polarized.Although the FQHE has been reported in quite a number of different materials [6][7][8][9][10][11][12], the FQHE has never been observed in a diluted magnetic semiconductor in which atoms with magnetic moment (e.g., Mn 2+ ) are placed in a 2DES. Then, the localized spins in the magnetic impurities' d orbitals interact with the correlated electron system via the quantum mechanical s-d exchange interaction, causing giant Zeeman splitting [13] which is tunable in magnitude, sign, and field dependence [14]. The constant αN 0 specifies the s-d exchange strength and is the largest energy scale in the system. It hence has remained unclear whether FQHE states survive in the presence of magnetic impurities. Below we demonstrate that (i) the FQHE indeed exists in magnetic 2DESs and (ii) the opening and closing of gaps in an in-plane field can be described within a modified composite fermion (CF) picture, in which the s-d exchange is taken into account.Let us first recall the CF model which maps the FQHE onto the integer quantum Hall effe...

show abstract

Observation of an even-denominator quantum number in the fractional quantum Hall effect

Cited by 1,074 publications

References 15 publications

Fractional quantum Hall effect of two-dimensional electrons in high-mobility Si/SiGe field-effect transistors

Fractional quantum Hall effect of two-dimensional electrons in high-mobility Si/SiGe field-effect transistors

Emergent functions of quantum materials

Fractional quantum Hall effect in a dilute magnetic semiconductor

Contact Info

Product

Resources

About