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H. A. Fertig

Publications and source records attributed to H. A. Fertig.

At least 109 records · Page 6Linked to original sources

Stripes in Quantum Hall Double Layer Systems

We present results of a study of double layer quantum Hall systems in which each layer has a high-index Landau level that is half-filled. Hartree-Fock calculations indicate that, above a critical layer separation, the system becomes unstable to the formation of a unidirectional coherent charge density wave (UCCDW), which is related to stripe states in single layer systems. The UCCDW state supports a quantized Hall effect when there is tunneling between layers, and is {\it always} stable against formation of an isotropic Wigner crystal for Landau indices $N \ge 1$. The state does become unstable to the formation of modulations within the stripes at large enough layer separation. The UCCDW state supports low-energy modes associated with interlayer coherence. The coherence allows the formation of charged soliton excitations, which become gapless in the limit of vanishing tunneling. We argue that this may result in a novel {\it ``critical Hall state''}, characterized by a power law $I-V$ in tunneling experiments.

cond-mat.mes-hall↗

Collective Modes of Quantum Hall Stripes

The collective modes of striped phases in a quantum Hall system are computed using the time-dependent Hartree-Fock approximation. Uniform stripe phases are shown to be unstable to the formation of modulations along the stripes, so that within the Hartree-Fock approximation the groundstate is a stripe crystal. Such crystalline states are generically gapped at any finite wavevector; however, in the quantum Hall system the interactions of modulations among different stripes is found to be remarkably weak, leading to an infinite collection of collective modes with immeasurably small gaps. The resulting long wavelength behavior is derivable from an elastic theory for smectic liquid crystals. Collective modes for the phonon branch are computed throughout the Brillouin zone, as are spin wave and magnetoplasmon modes. A soft mode in the phonon spectrum is identified for partial filling factors sufficiently far from 1/2, indicating a second order phase transition. The modes contain several other signatures that should be experimentally observable.

cond-mat.mes-hall↗

Electromagnetic absorption of a pinned Wigner crystal at finite temperatures

We investigate the microwave absorption of a pinned, two-dimensional Wigner crystal in a strong magnetic field at finite temperatures. Using a model of a uniform commensurate pinning potential, we analyze thermal broadening of the electromagnetic absorption resonance. Surprisingly, we find that the pinning resonance peak should remain sharp even when the temperature is comparable or greater than the peak frequency. This result agrees qualitatively with recent experimental observations of the ac conductivity in two-dimensional hole systems in a magnetically induced insulating state. It is shown, in analogy with Kohn's theorem, that the electron-electron interaction does not affect the response of a harmonically pinned Wigner crystal to a spatially uniform external field at any temperature. We thus focus on anharmonicity in the pinning potential as a source of broadening. Using a 1/N expansion technique, we show that the broadening is introduced through the self-energy corrections to the magnetophonon Green's functions.

cond-mat.mes-hall↗

H_c_3 for a thin-film superconductor with a ferromagnetic dot

We investigate the effect of a ferromagnetic dot on a thin-film superconductor. We use a real-space method to solve the linearized Ginzburg-Landau equation in order to find the upper critical field, H_c_3. We show that H_c_3 is crucially dependent on dot composition and geometry, and may be significantly greater than H_c_2. H_c_3 is maximally enhanced when (1) the dot saturation magnetization is large, (2) the ratio of dot thickness to dot diameter is of order one, and (3) the dot thickness is large.

cond-mat.supr-con↗

Unlocking Transition for Modulated Surfaces and Quantum Hall Stripes

We develop a sine-Gordon model of layered systems of two-dimensional modulated surfaces and one dimensional stripes, and demonstrate that these systems can undergo a Kosterlitz-Thouless transition in which the modulations unlock as a result of thermal or quantum fluctuations, respectively. The unlocked phase is interpreted as an anisotropic crystal in which soliton-antisoliton pairs proliferate. The properties of such a state for modulated stripes in quantum Hall systems and its possible relevance to recent anomalies in transport data are discussed.

cond-mat.mes-hall↗

Electromagnetic Response of a Pinned Wigner Crystal

A microscopic model for analyzing the microwave absorption properties of a pinned, two-dimensional Wigner crystal in a strong perpendicular magnetic field is developed. The method focuses on excitations within the lowest Landau level, and corresponds to a quantum version of the harmonic approximation. For pure systems (no disorder), the method reproduces known results for the collective mode density of states of this system, and clearly identifies the origin of previously unexplained structure in this quantity. The application of the method to a simple diagonal disorder model uncovers a surprising result: a sharp (delta-function) response at zero temperature that is consistent with recent experiments. A simple spin lattice model is developed that reproduces the results of the quantum harmonic approximation, and shows that the sharp response is possible because the size scale $L_c$ of patches moving together in the lowest frequency collective mode is extremely large compared to the sample size for physically relevant parameters. This result is found to be a direct repercussion of the long-range nature of the Coulomb interaction. Finally, the model is used to analyze different disorder potentials that may pin the Wigner crystal, and it is argued that interface disorder is likely to represent the dominant pinning source for the system. A simple model of the interface is shown to reproduce some of the experimental trends for the magnetic field dependence of the pinning resonance.

cond-mat.mes-hall↗

Skymrion lattice melting in the quantum Hall system

The melting and magnetic disordering of the skyrmion lattice in the quantum Hall system at filling factor $ν\approx 1$ are studied. A Berezinskii-Kosterlitz-Thouless renormalization group theory is employed to describe the coupled magnetic and translational degrees of freedom. The non-trivial magnetic properties of the skyrmion system stem from the in-plane components of the non-collinear magnetization in the vicinity of skyrmions, which are described by an antiferromagnetic XY model. In a Coulomb gas formulation the `particles' are the topological defects of the XY model (vortices) and of the lattice (dislocations and disclinations). The latter frustrate the antiferromagnetic order and acquire fractional vorticity in order to minimize their energy. We find a number of melting/disordering scenarios for various lattice types. While these results do not depend on a particular model, we also consider a simple classical model for the skyrmion system. It results in a rich T=0 phase diagram. We propose that the triangular and square skyrmion lattices are generically separated by a centered rectangular phase in the quantum Hall system.

cond-mat.mes-hall↗

Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field

We propose a new ground state trial wavefunction for a two-dimensional Wigner crystal in a strong perpendicular magnetic field. The wavefunction includes Laughlin-Jastrow correlations between electron pairs, and may be interpreted as a crystal state of composite fermions or composite bosons. Treating the power $m$ of the Laughlin-Jastrow factor as a variational parameter, we use quantum Monte Carlo simulations to compute the energy of these new states. We find that our wavefunctions have lower energy than existing crystalline wavefunctions in the lowest Landau level. Our results are consistent with experimental observations of the filling factor at which the transition between the fractional quantum Hall liquid and the Wigner crystal occurs for electron systems. Exchange contributions to the wavefunctions are estimated quantitatively and shown to be negligible for sufficiently small filling factors.

cond-mat.mes-hall↗

Peak Effect and the Transition from Elastic to Plastic Depinning

We demonstrate for the first time an observation of the peak effect in simulations of magnetic vortices in a superconductor. The shear modulus $c_{66}$ of the vortex lattice is tuned by adding a fictitious {attractive} short range potential to the usual long-range repulsion between vortices. The peak effect is found to be most pronounced in low densities of pinning centers, and is always associated with a transition from elastic to plastic depinning. The simulations suggest in some situations that over a range of values of $c_{66}$ the production of lattice defects by a driving force enhances the pinning of the lattice.

cond-mat.supr-con↗

A critical comparison of classical field theory and microscopic wavefunctions for skyrmions in quantum Hall ferromagnets

We report on a study of the classical field theory description of charged skyrmions in quantum Hall ferromagnets. The appropriate field theory is a non-linear $σ$ model generalized to include Coulomb and Zeeman interaction terms. We have tested the range of validity of the classical field theory by comparing with microscopic descriptions of the single skyrmion state based on the Hartree-Fock approximation, exact diagonalization calculations, and many-body trial wavefunctions. We find that the field theory description is accurate for skyrmions with moderate spin quantum numbers ($\gtrsim 10$) although, as expected, it fails qualitatively for small spin quantum numbers.

cond-mat.mes-hall↗

Collective Excitations, NMR, and Phase Transitions in Skyrme Crystals

At Landau level filling factors near nu =1, quantum Hall ferromagnets form a Skyrme crystal state with quasi-long-range translational and non-collinear magnetic order. We develop an effective low energy theory which explains the presence in these systems of magnetic excitations at low energies below the Larmor gap (Delta) and which predicts a dramatic enhancement of the nuclear spin relaxation rate by a factor of 1000. The effective theory predicts a rich set of quantum and classical phase transitions. Based in part on accurate time-dependent Hartree-Fock calculations of the ordered state collective excitation spectrum, we discuss aspects of the T-nu-Delta crystal phase diagram.

cond-mat.mes-hall↗

Signature of Quantum Hall Effect Skyrmions in Tunneling: A Theoretical Study

We present a theoretical study of the $I-V$ tunneling characteristic between two parallel two-dimensional electron gases in a perpendicular magnetic field when both are near filling factor $ν=1$. Finite-size calculations of the single-layer spectral functions in the spherical geometry and analytical expressions for the disk geometry in the thermodynamic limit show that the current in the presence of skyrmions reflects in a direct way their underlying structure. It is also shown that fingerprints of the electron-electron interaction pseudopotentials are present in such a current.

cond-mat.mes-hall↗

Harmonic Solid Theory of Photoluminescence in the High Field Two-Dimensional Wigner Crystal

Motivated by recent experiments on radiative recombination of two-dimensional electrons in acceptor doped GaAs-AlGaAs heterojunctions as well as the success of a harmonic solid model in describing tunneling between two-dimensional electron systems, we calculate within the harmonic approximation and the time dependent perturbation theory the line shape of the photoluminescence spectrum corresponding to the recombination of an electron with a hole bound to an acceptor atom. The recombination process is modeled as a sudden perturbation of the Hamiltonian for the in-plane degrees of freedom of the electron. We include in the perturbation, in addition to changes in the equilibrium positions of electrons, changes in the curvatures of the harmonically approximated potential. The computed spectra have line shapes similar to that seen in a recent experiment. The spectral width, however, is roughly a factor of 3 smaller than that seen in experiment if one assumes a perfect Wigner crystal for the initial state state of the system, whereas a simple random disorder model yields a width a factor of 3 too large. We speculate on the possible mechanisms that may lead to better quantitative agreement with experiment.

cond-mat.str-el↗

Hartree-Fock Theory of Skyrmions in Quantum Hall Ferromagnets

We report on a study of the charged-skyrmion or spin-texture excitations which occur in quantum Hall ferromagnets near odd Landau level filling factors. Particle-hole symmetry is used to relate the spin-quantum numbers of charged particle and hole excitations and neutral particle-hole pair excitations. Hartree-Fock theory is used to provide quantitative estimates of the energies of these excitations and their dependence on Zeeman coupling strength, Landau level quantum numbers, and the thicknesses of the two-dimensional electron layers. For the case of $ν$ near three we suggest the possibility of first order phase transitions with increasing Zeeman coupling strength from a many skyrmion state to one with many maximally spin-polarized quasiparticles.

cond-mat.mes-hall↗

Internal Excitations and Dissipative Damping of Quantum Hall Skyrmions

We propose an intrinsic maximum speed for dissipationless E cross B drift of Skyrmion quasiparticles in quantum Hall ferromagnets. When this speed is exceeded, Skyrmions can radiate spin-waves by making internal excitations which allow total spin to be conserved. Our proposal is illustrated by a time-dependent Hartree-Fock approximation calculation of the excitation spectrum for a Skyrmion bound to an impurity.

cond-mat↗

Theory of Phonon Shakeup Effects on Photoluminescence from the Wigner Crystal in a Strong Magnetic Field

We develop a method to compute shakeup effects on photoluminescence from a strong magnetic field induced two-dimensional Wigner crystal. Only localized holes are considered. Our method treats the lattice electrons and the tunneling electron on an equal footing, and uses a quantum-mechanical calculation of the collective modes that does not depend in any way on a harmonic approximation. We find that shakeup produces a series of sidebands that may be identified with maxima in the collective mode density of states, and definitively distinguishes the crystal state from a liquid state in the absence of electron-hole interaction. In the presence of electron-hole interaction, sidebands also appear in the liquid state coming from short-range density fluctuations around the hole. However, the sidebands in the liquid state and the crystal state have different qualitative behaviors. We also find a shift in the main luminescence peak, that is associated with lattice relaxation in the vicinity of a vacancy. The relationship of the shakeup spectrum with previous mean-field calculations is discussed.

cond-mat↗

Skyrmions without Sigma Models in Quantum Hall Ferromagnets

We report on a microscopic theory of the Skyrmion states which occur in the quantum Hall regime. The theory is based on the identification of Skyrmion states in this system with zero-energy eigenstates of a hard-core model Hamiltonian. We find that for $N_ϕ$ orbital states in a Landau level, a set of Skyrmions states with orbital degeneracy $N_ϕ-K$ and spin quantum number $S = N/2 -K$ exists for each nonnegative integer $K$. The energetic ordering of states with different $K$ depends on the interaction potential.

cond-mat↗

Skyrme Crystal In A Two-Dimensional Electron Gas

The ground state of a two-dimensional electron gas at Landau level filling factors near $ν=1$ is a Skyrme crystal with long range order in the positions and orientations of the topologically and electrically charged elementary excitations of the $ν=1$ ferromagnetic ground state. The lowest energy Skyrme crystal is a square lattice with opposing postures for topological excitations on opposite sublattices. The filling factor dependence of the electron spin-polarization, calculated for the square lattice Skyrme crystal, is in excellent agreement with recent experiments.

cond-mat↗