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V. J. Goldman

Publications and source records attributed to V. J. Goldman.

At least 19 recordsLinked to original sources
arXiv2009

Superperiods in interference of e/3 Laughlin quasiparticles encircling filling 2/5 fractional quantum Hall island

We report experiments in a large, 2.5 micron diameter Fabry-Perot quantum Hall interferometer with two tunneling constrictions. Interference fringes are observed as conductance oscillations as a function of applied magnetic field (the Aharonov-Bohm flux through the electron island) or a global backgate voltage (electronic charge in the island). Depletion is such that in the fractional quantum Hall regime, filling 1/3 current-carrying chiral edge channels pass through constrictions when the island filling is 2/5. The interferometer device is calibrated with fermionic electrons in the integer quantum Hall regime. In the fractional regime, we observe magnetic flux and charge periods 5h/e and 2e, respectively, corresponding to creation of ten e/5 Laughlin quasiparticles in the island. These results agree with our prior report of the superperiods in a much smaller interferometer device. The observed experimental periods are interpreted as imposed by anyonic statistical interaction of fractionally-charged quasiparticles.

cond-mat.str-el↗
arXiv2009

Electron interferometry in quantum Hall regime: Aharonov-Bohm effect of interacting electrons

An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such sub-period is not expected for non-interacting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ("backscattering"). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward- and back-scattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.

cond-mat.mes-hall↗
arXiv2008

Low-field quantum Hall transport in an electron Fabry-Perot interferometer: Determination of constriction filling vs front-gate voltage

We report systematic quantum Hall transport experiments on Fabry-Perot electron interferometers at ultra-low-temperatures. The GaAs/AlGaAs heterostructure devices consist of two constrictions defined by etch trenches in 2D electron layer, enclosing an approximately circular island. Front gates deposited in etch trenches allow to fine-tune the device for symmetry and to change the constriction filling, relative to the bulk. The low-field longitudinal and Hall magnetotransport shows Shubnikov-de Haas oscillations and integer quantum Hall plateaus. A systematic variation of front-gate voltage affects the constriction and the island electron density, while the bulk density remains unaffected. This results in quantized plateaus in longitudinal resistance, while the Hall resistance is dominated by the low-density, low-filling constriction. At lower fields, when the quantum Hall plateaus fail to develop, we observe bulk Shubnikov-de Haas oscillations in series corresponding to an integer filling of the magnetoelectric subbands in the constrictions. This indicates that the whole interferometer region is still quantum-coherent at these lower fields at 10 mK. Analyzing the data within a Fock-Darwin model, we obtain the constriction electron density as a function of the front gate bias and, extrapolating to the zero field, the number of electric subbands (conductance channels) resulting from the electron confinement in the constrictions.

cond-mat.mes-hall↗
arXiv2008

Electron tunneling spectroscopy of a quantum antidot in the quantum Hall regime

Quantum antidot, a small potential hill introduced into a two-dimensional electron system, presents an attractive tool to study quantum mechanics of interacting electrons.Here, we report experiments on electron resonant tunneling via a quantum antidot on the integer i = 1, 2, 3, 4, 5, and 6 quantum Hall plateaus. Several new features are reported. First, as a function of magnetic field, we observe up to six quasiperiodic resonant tunneling peaks within the fundamental flux period: when flux h/e is added to the area of the antidot there are i peaks on the i-th integer plateau, when i spin-polarized Landau levels are occupied. Corresponding back gate voltage data show one peak per added charge e on all integer plateaus. Second, we observe tunneling dips in four-terminal resistance ("forward scattering") on the even i = 2, 4, and 6 plateaus, when population of both spins is nearly equal. Also, for the first time, we report an internal structure within the h/e period: on the i = 3 spin-split plateau, two of the three resonant tunneling peaks are higher and/or closer than the third. Puzzlingly, in this regime, when back gate voltage is swept, the tunneling peaks are grouped in pairs. These results are attributed to the dominance of the electron-electron Coulomb interaction, effectively mixing Landau level occupation, and to the self-consistent electrostatics of the antidot.

cond-mat.mes-hall↗
arXiv2007

Flux period scaling in the Laughlin quasiparticle interferometer

We report experiments on electron interferometer devices in the quantum Hall regime, where edge channels circle a 2D electron island. The main confinement is produced by etch trenches, into which front gate metal is deposited. We find a linear dependence of the Aharonov-Bohm period on gate voltage for electrons (integer filling f=1) and for Laughlin quasiparticles (fractional 2/5 embedded in 1/3). The capacitance of a large 2D electron island with respect to the front gates is approximately proportional to the island radius. Comparing the experimental data for the integer and the fractional fillings and for two samples, we find the magnetic field period and its slope scale with the radius of the Aharonov-Bohm orbit. Analysis of the directly measured integer and fractional slope data allows to determine the interferometer area in the fractional regime, and thus the Laughlin quasiparticle flux period of 5h/e, within the experimental accuracy.

cond-mat.mes-hall↗
arXiv2007

Experimental realization of Laughlin quasiparticle interferometers

Laughlin quasiparticles are the elementary excitations of a highly-correlated fractional quantum Hall electron fluid. They have fractional charge and obey fractional statistics. The quasiparticles can propagate quantum-coherently in chiral edge channels, and constructively or destructively interfere. Unlike electrons, the interference condition for Laughlin quasiparticles has a non-vanishing statistical contribution that can be observed experimentally. Two kinds of interferometer devices have been realized. In the primary-filling interferometer, the entire device has filling 1/3, and the e/3 edge channel quasiparticles encircle identical e/3 island quasiparticles. Here the flux period is h/e, same as for electrons, but the back-gate charge period is e/3. In the second kind of interferometer, a lower density edge channel at filling 1/3 forms around a higher density island at filling 2/5, so that e/3 edge quasiparticles encircle e/5 island quasiparticles. Here we observe superperiodic oscillations with 5h/e flux and 2e charge periods, both corresponding to excitation of ten island quasiparticles. These periods can be understood as imposed by the anyonic braiding statistics of Laughlin quasiparticles.

cond-mat.mes-hall↗
arXiv2007

Quantum transport in electron Fabry-Perot interferometers

We report experiments on Fabry-Perot electron interferometers in the integer quantum Hall regime. The GaAs/AlGaAs heterostructure devices consist of two constrictions defined by etch trenches in 2D electron layer, enclosing an approximately circular island. The interferometer is formed by counterpropagating chiral edge channels coupled by tunneling in the two constrictions. Interference fringes are observed as conductance oscillations, similar to the Aharonov-Bohm effect. Front gates deposited in etch trenches allow to fine-tune the device and to change the constriction filling f relative to the bulk filling. Quantum-coherent conductance oscillations are observed on the f = 1 - 4 plateaus. On plateau f we observe f conductance oscillations per fundamental flux period h/e. This is attributed to the dominance of the electron-electron Coulomb interaction, effectively mixing Landau level occupation. On the other hand, the back-gate charge period is the same (one electron) on all plateaus, independent of filling. This is attributed to the self-consistent electrostatics in the large electron island. We also report dependence of the oscillation period on front-gate voltage for f = 1, 2 and 4 for three devices. We find a linear dependence, with the slope inversely proportional to f for f = 1 and 2.

cond-mat.mes-hall↗
arXiv2006

Experimental realization of a primary-filling e/3 quasiparticle interferometer

We report experiments on a Laughlin quasiparticle interferometer where the entire system is on the 1/3 primary fractional quantum Hall plateau. Electron-beam lithography is used to define an approximately circular 2D electron island separated from the 2D bulk by two wide constrictions. The interferometer consists of counterpropagating chiral edge channels coupled by quantum-coherent tunneling in the two constrictions, thus enclosing an island area. Interference fringes are observed as conductance oscillations, similar to the Aharonov-Bohm effect. The flux and charge periods of the interferometer device are calibrated with electrons in the integer quantum Hall 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. Quantum theory predicts a 3h/e flux period for charge e/3, integer statistics particles. Accordingly, the observed periods demonstrate the anyonic statistics of Laughlin quasiparticles.

cond-mat.mes-hall↗
arXiv2006

Primary-Filling e/3 Quasiparticle Interferometer

We report experimental realization of a quasiparticle interferometer where the entire system is in 1/3 primary fractional quantum Hall state. The interferometer consists of chiral edge channels coupled by quantum-coherent tunneling in two constrictions, thus enclosing an Aharonov-Bohm area. We observe magnetic flux and charge periods h/e and e/3, equivalent to creation of one quasielectron in the island. Quantum theory predicts a 3h/e flux period for charge e/3, integer statistics particles. Accordingly, the observed periods demonstrate the anyonic statistics of Laughlin quasiparticles.

cond-mat.mes-hall↗
arXiv2006

Superperiods and quantum statistics of Laughlin quasiparticles

Superperiodic conductance oscillations were recently observed in the quasiparticle interferometer, where an edge channel of the 1/3 fractional quantum Hall fluid encircles an island of the 2/5 fluid. We present a microscopic model of the origin of the 5h/e flux superperiod based on the Haldane-Halperin fractional-statistics hierarchical construction of the 2/5 condensate. Since variation of the applied magnetic field does not affect the charge state of the island, the fundamental period comprises the minimal 2/5 island neutral reconstruction. The period consists of incrementing by one the state number of the e/3 Laughlin quasielectron circling the island and the concurrent excitation of ten e/5 quasiparticles out of the island 2/5 condensate. The Berry phase quantization condition yields anyonic quasiparticle braiding statistics consistent with the hierarchical construction. We further discuss a composite fermion representation of quasiparticles consistent with the superperiods. It is shown to be in one-to-one correspondence with the Haldane-Halperin theory, provided a literal interpretation of the 2/5 condensate as comprised of an integer multiple of two-composite fermion, one-vortex blocks is postulated.

cond-mat.mes-hall↗
arXiv2006

Transport in the Laughlin quasiparticle interferometer: Evidence for topological protection in an anyonic qubit

We report experiments on temperature and Hall voltage bias dependence of the superperiodic conductance oscillations in the novel Laughlin quasiparticle interferometer, where quasiparticles of the 1/3 fractional quantum Hall fluid execute a closed path around an island of the 2/5 fluid. The amplitude of the oscillations fits well the quantum-coherent thermal dephasing dependence predicted for a two point-contact chiral edge channel interferometer in the full experimental temperature range 10.2<T<141 mK. The temperature dependence observed in the interferometer is clearly distinct from the behavior in single-particle resonant tunneling and Coulomb blockade devices. The 5h/e flux superperiod, originating in the anyonic statistical interaction of Laughlin quasiparticles, persists to a relatively high T~140 mK. This temperature is only an order of magnitude less than the 2/5 quantum Hall gap. Such protection of quantum logic by the topological order of fractional quantum Hall fluids is expected to facilitate fault-tolerant quantum computation with anyons.

cond-mat.mes-hall↗
arXiv2005

Observation of Aharonov-Bohm Superperiod in a Laughlin Quasiparticle Interferometer

We report an Aharonov-Bohm superperiod of five magnetic flux quanta (5h/e) observed in a Laughlin quasiparticle interferometer, where an edge channel of the 1/3 fractional quantum Hall fluid encircles an island of the 2/5 fluid. This result does not violate the auge invariance argument of the Byers-Yang theorem because the magnetic flux, in addition to affecting the Aharonov-Bohm phase of the encircling 1/3 quasiparticles, creates the 2/5 quasiparticles in the island. The superperiod is accordingly understood as imposed by the anyonic statistical interaction of Laughlin quasiparticles.

cond-mat.mes-hall↗
arXiv2005

Thermal Dephasing in the Laughlin Quasiparticle Interferometer: Chiral Luttinger Liquid Behavior

We report experimental temperature dependence of the amplitude of Aharonov-Bohm oscillations in the Laughlin quasiparticle interferometer. The results fit very well the thermal dephasing dependence predicted for a g = 1/3 chiral Luttinger liquid interferometer, and are clearly distinct from the activated behavior observed in single-particle resonant tunneling and Coulomb blockade devices. The small deviation from the zero-bias theory seen below 20 mK indicates yet unrecognized source of experimental decoherence, not included in theory.

cond-mat.mes-hall↗
arXiv2005

Aharonov-Bohm electron interferometer in the integer quantum Hall regime

We report experiments on a quantum electron interferometer fabricated from high mobility, low density GaAs/AlGaAs heterostructure material. In this device, a nearly circular electron island is defined by four front gates deposited in etched trenches. The island is separated from the 2D electron bulk by two nearly open constrictions. In the quantum Hall regime, two counterpropagating edge channels are coupled by tunneling in the constrictions, thus forming a closed electron interference path.For several fixed front gate voltages, we observe periodic Aharonov-Bohm interference oscillations in four-terminal resistance as a function of the enclosed flux. The oscillation period DeltaB gives the area of the interference path S via quantization condition S=h/eDeltaB. We experimentally determine the dependence of S on the front gate voltage, and find that the Aharonov-Bohm quantization condition does not require significant corrections due to the confining potential. These results can be interpreted as a constant integrated compressibility of the island with respect to the front gates. We also analyze experimental results using two classical electrostatics models: one modeling the 2D electron density due to depletion from an etch trench, and another modeling the gate voltage dependence of the electron density profile in the island.

cond-mat.mes-hall↗
arXiv2005

Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics

In two dimensions, the laws of physics permit existence of anyons, particles with fractional statistics which is neither Fermi nor Bose. That is, upon exchange of two such particles, the quantum state of a system acquires a phase which is neither 0 nor π, but can be any value. The elementary excitations (Laughlin quasiparticles) of a fractional quantum Hall fluid have fractional electric charge and are expected to obey fractional statistics. Here we report experimental realization of a novel Laughlin quasiparticle interferometer, where quasiparticles of the 1/3 fluid execute a closed path around an island of the 2/5 fluid and thus acquire statistical phase. Interference fringes are observed as conductance oscillations as a function of magnetic flux, similar to the Aharonov-Bohm effect. We observe the interference shift by one fringe upon introduction of five magnetic flux quanta (5h/e) into the island. The corresponding 2e charge period is confirmed directly in calibrated gate experiments. These results constitute direct observation of fractional statistics of Laughlin quasiparticles.

cond-mat.mes-hall↗
arXiv2001

Quantum computation with quasiparticles of the Fractional Quantum Hall Effect

We propose an approach that enables implementation of anyonic quantum computation in systems of antidots in the two-dimensional electron liquid in the FQHE regime. The approach is based on the adiabatic transfer of FQHE quasiparticles in the antidot systems, and uses their fractional statistics to perform quantum logic. Advantages of our scheme over other semiconductor-based proposals of quantum computation include the energy gap in the FQHE liquid that suppresses decoherence, and the topological nature of quasiparticle statistics that makes it possible to entangle two quasiparticles without their direct dynamic interaction.

cond-mat.mes-hall↗
arXiv2001

Formation of an Edge Striped Phase in Fractional Quantum Hall Systems

We have performed an exact diagonalization study of up to N=12 interacting electrons on a disk at filling $ν={1/3}$ for both Coulomb and $V_1$ short-range interaction for which Laughlin wave function is the exact solution. For Coulomb interaction and $N\geq 10$ we find persistent radial oscillations in electron density, which are not captured by the Laughlin wave function. Our results srongly suggest formation of a chiral edge striped phase in quantum Hall systems. The amplitude of the charge density oscillations decays slowly, perhaps as a square root of the distance from the edge; thus the spectrum of edge excitations is likely to be affected.

cond-mat.mes-hall↗