Session X40: QHE: Antidots and Bilayers Systems

Realization of a primary-filling e/3 quasiparticle interferometer

We report experiments on a quasiparticle interferometer where the entire system is on the f=1/3 primary fractional quantum Hall plateau. Electron-beam lithography is used to define an electron island separated from the 2D bulk by two wide constrictions, much less depleted than in our prior work [1]. This results in the entire electron island being at filling f=1/3 under quantum-coherent tunneling conditions. For the first time in such devices we report interferometric Aharonov-Bohm-like conductance oscillations. The flux and charge periods of the interferometer device are calibrated with electrons in the integer regime. In the fractional regime, we observe magnetic flux and charge periods $h/e$ and $e/3$, respectively, corresponding to creation of one quasielectron in the island. These periods are the same as in quantum antidots, but the quasiparticle path encloses no electron vacuum in the interferometer. Quantum theory predicts a $3h/e$ flux period for charge $e/3$, integer statistics particles. Accordingly, the observed periods demonstrate anyonic statistics of Laughlin quasiparticles. \newline [1] F. E. Camino et al., PRL 95, 246802 (2005); PRB 72, 075342 (2005).   

$\nu =1$ quantum Hall state in a lateral periodic quantum anti-dot array

The quantum Hall ferromagnetism (QHF) at the Landau level filling $\nu $=1 in 2DES has been extensively studied over the years. Due to strong Columbic interaction, at $\nu $=1, all the electron spins align with the external magnetic, giving rise to a ferromagnetic order. Consequently, the energy gap (Eg) of the $\nu $=1 state is much larger than that of bare Zeeman splitting (Ez). Previous experimental studies focused mostly on the clean limit of sample quality where the electron-electron interaction is strong. On the other hand, theories have shown that a phase transition from the QHF state to a quantum Hall spin glass state can occur as sample disorder increases. To study this phase transition, we used a lateral quantum anti-dot array, where the electronic potential modulation can be viewed as a special form of sample disorder. More importantly, this disorder can be continuously tuned by varying electron density. We observed that for small potential modulation Eg at $\nu $=1 is much larger than Ez, indicating a ferromagnetic order. As the modulation strength increases, Eg first decreases slowly and after a critical value of modulation, the decrease rate accelerates and Eg approaches the Ez limit, signaling a possible transition from a ferromagnetic state to a spin glass state. Tilting magnetic field results will also be discussed.   

Coulomb blockade of anyons: coherent quasiparticle transport in multi-antidot systems

We have developed a model for transport of anyonic quasiparticles of primary quantum Hall liquids through systems of multiple antidots weakly coupled to external edges. At energies smaller than the energy gap of the antidots, the quasiparticles behave as {\em hard-core} anyons, i.e., exhibit fractional exchange statistics, while the on-site Coulomb interaction suppresses the double occupancy of the antidots (thus simulating Fermi exclusion). The hard-core condition implies that the quasiparticle exchanges affect transport only in systems with closed loops. Coherent tunnel coupling of the antidots leads to the formation of stationary states and associated resonant conductance peaks for tunneling between the edges through these states. We have calculated the tunnel conductance for double- and triple-antidot systems and shown that in the case of three antidots connected in a loop, the anyonic exchange statistics manifests itself in both the relative positions and amplitudes of the peaks.   

Tunable-Coupling Quantum Antidot Molecule

We report experiments on two double-antidot devices. The molecule is formed by two equal-size lithographic antidots fabricated from a very low-disorder GaAs/AlGaAs heterostructure. The two antidots are close enough so that the states bound on each antidot become hybridized and form bonding and antibonding states, like in a diatomic molecule or a qubit [1]. We observe resonant tunneling peaks on the f=1 and 1/3 quantum Hall plateaus. The quantum-coherent coupling between the antidots can be tuned by a gate bias and by magnetic field $B$. The f=1 conductance peaks display three regimes as a function of $B$: (i) one peak per period $\Delta =h/2eS$, like in single antidot, but the total area $2S$ contributing. (ii) At higher $B$, the peak splits into two overlapping peaks; (iii) at yet higher $B$, nearly sinusoidal double-frequency (one oscillation per $\Delta /2$) conductance oscillations are observed. The fractional regime shows bonding-antibonding split peaks that display a charge $e/3$ back-gate coupling.\newline [1] Averin and Goldman, Solid State Commun. 121, 25 (2002).   

Shot Noise in Anyonic Mach-Zehnder Interferometer

Recently a new type of interferometer for quantum Hall systems, an electronic Mach-Zehnder interferometer, was designed. We demonstrate that shot noise in such an interferometer can be used to probe the charge and statistics of quantum Hall quasiparticles. The dependence of the noise on the magnetic flux through the interferometer allows for a simple way to distinguish Abelian and non-Abelian quasiparticle statistics. In the Abelian case, the Fano factor is always lower than an electron charge. In the non-Abelian case, the maximal Fano factor as a function of the magnetic flux exceeds the charge of an electron.   

Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime

The concept of fractional charge is central to the theory of the fractional quantum Hall effect (FQHE). Quasiparticles of fractional charge have been first observed by Goldman and Su [1] in resonant tunneling through a quantum antidot. In [1] a periodic sequence of resonant tunneling events was observed as either the magnetic field H or the backgate voltage Vg were varied. The tunneling events are thought of in terms of a quasiparticle tunneling through the bulk of the fractional state between the outer edge of the sample and the inner edge formed around the antidot. The periodicities in H and in Vg were related to the quasiparticle charge e*. Here I use exact diagonalization as well as configuration space renormalization (CSR) to study finite clusters large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The ``computer experiment'' reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5 [2]. \newline [1] V.J. Goldman and B. Su, Science, 267, 1010, 1995. \newline [2] E.V. Tsiper, Phys. Rev. Lett., 97, 76802, 2006.   

Spin Polarization of Bilayer $\nu $=2 Quantum Hall States Probed by NMR

In a bilayer system at total Landau level filling factor $\nu $=2, the interplay between intralayer and interlayer interactions leads to quantum Hall (QH) states with various spin configurations: the ferromagnetic (F), canted antiferromagnetic (CAF) and spin-singlet (SS) states. Recently, by measuring the nuclear spin relaxation rate 1/$T_{1}$, which probes the in-plane spin fluctuations, we have demonstrated the existence of the Goldstone mode predicted for the CAF state [1]. In this study, we report the direct measurement of the spin polarizations of these states by using a current pump and resistively detected NMR technique. The double-quantum-well sample used has a tunneling energy gap of 8 K. Since electron spins add effective Zeeman field to nuclear spins, the electron spin polarization appears as a shift in the nuclear resonant frequency, i.e., the Knight shift. As the bias potential between the two layers is increased, the spin polarization changes from full to zero continuously, indicating the phase transitions from the F to SS states via the CAF state. The combination of the data for the Knight shift and 1/$T_{1}$ allows for more complete understanding of the spin ordering including both in-plane and out-of-plane components and fluctuations in these states. [1] N. Kumada, K. Muraki and Y. Hirayama, Science 313, 329 (2006).   

Collective excitations of a crystal of CP(3) skyrmions in a bilayer quantum Hall system

Recent experiments [1,2] in a bilayer quantum Hall system suggest that the quasiparticles at filling factor $\nu=1$ could have both spin and pseudospin textures i.e. they could be CP3 skyrmions. At very low temperature, these skyrmions condense to form a Skyrme crystal. In a previous work [3], we have identified the regions of stability of this crystal in the parameter space of the bilayer system i.e. as a function of filling factor, interwell separation, potential bias, Zeeman and tunnel couplings. In this talk, we derive the spin and pseudospin response functions as well as the collective excitations of the CP(3) Skyrme crystal in the Generalized Random-Phase Approximation(GRPA). We study the behavior of the NMR relaxation time computed from the GRPA spin response function and discuss its relevance for the experiments of Refs. [1,2]. \\(1) I. B. Spielman et al., Phys. Rev. Lett. {\bf 94}, 76803 (2005).\\(2) N. Kumada et al., Phys. Rev. Lett. {\bf 94}, 96802 (2005). \\(3) J. Bourassa et al., Phys. Rev. B {\bf 74}, 195320 (2006).   

Interlayer tunneling studies of highly imbalanced bilayer 2D electron systems at \boldmath{$\nu_T = 1$}

When the separation between two parallel 2-dimensional electron systems (2DES) becomes comparable to the average distance between electrons within a single layer, the system can support a quantum Hall state with total filling factor $\nu_T=1$. This state can be described as a Bose condensate of excitons. Previous studies [1] have shown that close to the $\nu_T=1$ phase boundary, a small imbalance in the number of electrons in each layer can strengthen the condensate. We report on interlayer tunneling measurements of the effect of large imbalances as a function of the interlayer spacing. We explore the possibility of competing order between the excitonic state and the (1/3, 2/3) fractional states in the individual layers. This work was supported by the NSF and the DOE. \newline [1] I. B. Spielman, et al., Phys. Rev. B {\bf 70}, 081303 (2004).   

Zero Bias Tunneling Resonance at Filling Factor $\nu_T=1$ in GaAs Hole Bilayers

Previous tunneling and transport measurements on bilayer two dimensional carrier systems at total filling factor $\nu_T = 1$ provide strong evidence for an excitonic ground state with small but finite dissipation. We present, for the first time, tunneling conductance measurements of bilayer two dimensional {\it hole} systems in a strongly interacting regime ($1.1 < d/l_B < 1.3$, where $d$ is the interlayer distance and $l_B$ is the magnetic length). We find that the zero bias tunneling resonance at $d/l_B=1.2$ has a larger amplitude and a weaker temperature dependence than existing data from electron samples ($d/l_B=1.5-1.8$) for the range of temperatures where we have taken data ($300mK-600mK$). This work was supported by the DOE and NSF.   

Activation Energies and Dissipation in Biased Quantum Hall Bilayer Systems at Total Filling Factor $\nu=1$.

Electrons in a closely spaced bilayer semiconductor structure, such as a double quantum well, are thought to form an interlayer coherent state when a perpendicular magnetic field is applied such that the total Landau level filling factor $\nu$ is 1. When the Zeeman energy is sufficiently large to polarize electron spins, the low energy excitations are thought to be topological pseudospin meron-antimeron pairs[1]. These objects carry charge $\pm e/2$,vorticity, and electric dipole moments perpendicular to the layers. Disorder is likely to unbind merons from antimerons and allow them to diffuse through the system independently[2]. Due to their different dipole moments, the various types of merons and antimerons may then in principle be distinguished in transport activation energies by an interlayer bias potential. We report on estimates of these energy differences in various circumstances, and discuss the connection of our results with recent experiments[3].\newline [1]K.Moon,et. al., PRB {\bf 51},5138(1995). \newline [2]H.A.Fertig,G.Murthy, PRL {\bf 95},156802(2005). \newline [3]R.D.Wiersma,et.al., PRL {\bf 93},266805(2004).   

Increases in Electron Drag in Intermediate Magnetic Fields

\\It has been reported that measurements of electron drag in intermediate magnetic fields show anomalous dependences on temperature and magnetic field. Although extensive theoretical investigations of drag in magnetic fields have been done, the behavior currently lacks a theoretical explanation. The experimental findings show that for intermediate magnetic fields, where the Landau level spacing is comparable to temperature, electron drag is substantially increased, even while very little change is observed in the longitudinal resistivity, suggesting that the effect's origin does not lie in changes in the density of states. There is, furthermore, very little dependence on temperature, and the increase varies roughly as the cube of magnetic field. We report drag measurements designed to examine the potential role of spin in the effect and detailed measurements examining the specific temperature dependence, as approaches towards the identification of the source of this unusual behavior.   

Electron Drag in High Filling Factors

Electron drag measurements, which permit direct detection of electron-electron scattering rates, have revealed a number of surprising behaviors in bilayer electron systems in the presence of magnetic fields. Among these is an oscillation in the polarity of the drag voltage with the difference in filling factors of the two layers, measured at high filling factors. Recent theoretical examinations of this sign reversal have pointed to particle-hole asymmetry induced by Landau quantization[1], and disorder induced mixing of Landau levels[2] as the source. In addition to the sign reversal is an unusual temperature dependence. Experiments[3] have suggested an activated behavior in this regime, with the activation energy related to the Zeeman energy. This result, however, differs functionally from the theoretical calculation in [1]. We report on measurements that examine this potential contradiction in order to investigate the nature of Coulomb drag in this regime. \newline [1]I. V. Gornyi, et al, PRB 70, 245302 (2004) \newline [2]R. Bistritzer, A. Stern, PRL 96, 226801 (2006) \newline [3]K. Muraki, et al, PRL 92, 246801 (2004)   

Interedge coherent line junctions in Quantum Hall systems

In this talk I will address the properties of quantum Hall line junctions (QHLJ) that occur near barriers separating electron gases on quantum Hall plateaus. In narrow barriers where electron tunneling can occur at any point, the low energy physics of the QHLJ is described by the massive quantum sine-Gordon model. We propose procedures to study a sort of properties of these systems in relation with recent experimental studies. The spectrum of the quantum sine-Gordon model consists of topological particles, solitons, antisolitons, and when forward interactions are strong enough also their bound states can form. In presence of a chemical potential however that couples with these charges the spectral gap can be suppressed. When this chemical potential exceeds the mass of the soliton ($\Delta/2$), a finite density of solitons appears in the ground state, distributed on a Fermi sea according to their statistics, embedded in their interactions (or their scattering matrix). The low-energy physics of this system then will be of particle-hole type formed around these Fermi points. The properties of this metallic state, namely the value of the Luttinger liquid (LL) parameter $K$ and the Fermi velocity can be accessed with the thermodynamic Bethe ansatz. Experimentally there are two quantities that offer the measurement of two combinations, the product and the ratio of the LL parameter $K$ and the Fermi velocity, namely the Drude weight and charge susceptibility, respectively.