arXiv subjects

H. A. Fertig

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

At least 91 records · Page 5Linked to original sources

arXiv2004

Quantum Depinning Transition of Quantum Hall Stripes

We examine the effect of disorder on the electromagnetic response of quantum Hall stripes using an effective elastic theory to describe their low-energy dynamics, and replicas and the Gaussian variational method to handle disorder effects. Within our model we demonstrate the existence of a depinning transition at a critical partial Landau level filling factor $Δν_c$. For $Δν<Δν_c$, the pinned state is realized in a replica symmetry breaking (RSB) solution, and the frequency-dependent conductivities in both perpendicular and parallel to the stripes show resonant peaks. These peaks shift to zero frequency as $Δν\to Δν_c$. For $Δν\geΔν_c$, we find a {\em partial RSB (PRSB)} solution in which there is free sliding only along the stripe direction. The transition is analogous to the Kosterlitz-Thouless phase transition.

cond-mat.mes-hall↗

arXiv2004

Dynamics of electrons in the quantum Hall bubble phases

In Landau levels N > 1, the ground state of the two-dimensional electron gas (2DEG) in a perpendicular magnetic field evolves from a Wigner crystal for small filling of the partially filled Landau level, into a succession of bubble states with increasing number of guiding centers per bubble as the filling increases, to a modulated stripe state near half filling. In this work, we show that these first-order phase transitions between the bubble states lead to measurable discontinuities in several physical quantities such as the density of states and the magnetization of the 2DEG. We discuss in detail the behavior of the collective excitations of the bubble states and show that their spectra have higher-energy modes besides the pinned phonon mode. The frequencies of these modes, at small wavevector k, have a discontinuous evolution as a function of filling factor that should be measurable in, for example, microwave absorption experiments.

cond-mat.mes-hall↗

arXiv2003

Vortex States of a Superconducting Film from a Magnetic Dot Array

Using Ginzburg-Landau theory, we find novel configurations of vortices in superconducting thin films subject to the magnetic field of a magnetic dot array, with dipole moments oriented perpendicular to the film. Sufficiently strong magnets cause the formation of vortex-antivortex pairs. In most cases, the vortices are confined to dot regions, while the antivortices can form a rich variety of lattice states. We propose an experiment in which the perpendicular component of the dot dipole moments can be tuned using an in-plane magnetic field. We show that in such an experiment the vortex-antivortex pair density shows broad plateaus as a function of the dipole strength. Many of the plateaus correspond to vortex configurations which break dot lattice symmetries. In some of these states, the vortex cores are strongly distorted. Possible experimental consequences are mentioned.

cond-mat.supr-con↗

arXiv2003

Spinning Holes in Semiconductors

The electron spin is emerging as a new powerful tool in the electronics and optics industries. Many proposed applications involve the creation of spin currents, which so far have proven to be difficult to produce in semiconductor environments. A new theoretical analysis shows this might be achieved using holes rather than electrons in semiconductors with significant spin-orbit coupling.

cond-mat.mes-hall↗

arXiv2003

Deconfinement and Dissipation in Quantum Hall "Josephson" Tunneling

The zero-bias tunneling resonance in quantum Hall bilayer systems is investigated via numerical simulations of the classical two dimensional XY model with a symmetry-breaking field. Disorder is included in the model, and is shown to nucleate strings of overturned spins proliferated through the system, with unpaired vortices and antivortices at their endpoints. This string glass state supports low energy excitations which lead to anomalously large dissipation in tunneling, as observed in experiment. The effect of an in-plane magnetic field is discussed.

cond-mat.mes-hall↗

arXiv2003

Vortex Deconfinement in the XY Model with a Magnetic Field

We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field, the vortices unbind as the magnetic field is lowered in a two-step process: strings of overturned spins first proliferate and then vortices unbind. The transitions are highly continuous but are not of the Kosterlitz-Thouless type. The unbound vortex fixed point is shown to inherit properties of the underlying lattice, in particular containing a set of nodal lines that reflect the lattice symmetry.

cond-mat↗

arXiv2002

Deformation and Depinning of Superconducting Vortices from Artificial Defects: A Ginzburg-Landau Study

Using Ginzburg-Landau theory, we have performed detailed studies of vortices in the presence of artificial defect arrays, for a thin film geometry. We show that when a vortex approaches the vicinity of a defect, an abrupt transition occurs in which the vortex core develops a ``string'' extending to the defect boundary, while simultaneously the supercurrents and associated magnetic flux spread out and engulf the defect. Current induced depinning of vortices is shown to be dominated by the core string distortion in typical experimental situations. Experimental consequences of this unusual depinning behavior are discussed.

cond-mat.supr-con↗

arXiv2002

Probing Vortex Unbinding via Dipole Fluctuations

We develop a numerical method for detecting a vortex unbinding transition in a two-dimensional system by measuring large scale fluctuations in the total vortex dipole moment ${\vec P}$ of the system. These are characterized by a quantity $\cal F$ which measures the number of configurations in a simulation for which the either $P_x$ or $P_y$ is half the system size. It is shown that $\cal F$ tends to a non-vanishing constant for large system sizes in the unbound phase, and vanishes in the bound phase. The method is applied to the XY model both in the absence and presence of a magnetic field. In the latter case, the system size dependence of $\cal F$ suggests that there exist three distinct phases, one unbound vortex phase, a logarithmically bound phase, and a linearly bound phase.

cond-mat.stat-mech↗

arXiv2002

Commensurate-incommensurate transitions of quantum Hall stripe states in double-quantum-well systems

In higher Landau levels (N>0) and around filling factors nu =4N+1, a two-dimensional electron gas in a double-quantum-well system supports a stripe groundstate in which the electron density in each well is spatially modulated. When a parallel magnetic field is added in the plane of the wells, tunneling between the wells acts as a spatially rotating effective Zeeman field coupled to the ``pseudospins'' describing the well index of the electron states. For small parallel fields, these pseudospins follow this rotation, but at larger fields they do not, and a commensurate-incommensurate transition results. Working in the Hartree-Fock approximation, we show that the combination of stripes and commensuration in this system leads to a very rich phase diagram. The parallel magnetic field is responsible for oscillations in the tunneling matrix element that induce a complex sequence of transitions between commensurate and incommensurate liquid or stripe states. The homogeneous and stripe states we find can be distinguished by their collective excitations and tunneling I-V, which we compute within the time-dependent Hartree-Fock approximation.

cond-mat.mes-hall↗

arXiv2002

Deconfinement in the Two Dimensional XY Model

The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system supports two phase transitions, one in which closed strings proliferate, and a second in which vortices unbind. The transitions are shown to be dual to one another, and are remarkably continuous. Possible consequences for a variety of systems are discussed.

cond-mat.stat-mech↗

arXiv2001

Core Strings and Flux Spreading Near Pinning Centers

At the nucleus of a superconducting vortex is a small, circular region where superconductivity is destroyed. Like an atomic nucleus, this core may become deformed, and such distortions can have important consequences in non-equilibrium situations. Using Ginzburg-Landau theory, we have investigated this phenomenon for vortices in the presence of artificial defects. We show that when a vortex approaches the vicinity of a defect, an abrupt transition occurs in which the vortex core develops a "string" extending to the defect boundary, while simultaneously the supercurrents and associated magnetic flux spread out and engulf the defect. The energetics of stretching the string determines the pinning behavior of the vortex. Experimental consequences of these strings are discussed.

cond-mat.supr-con↗

arXiv2001

Dynamics of quantum Hall stripes in double-quantum-well systems

The collective modes of stripes in double layer quantum Hall systems are computed using the time-dependent Hartree-Fock approximation. It is found that, when the system possesses spontaneous interlayer coherence, there are two gapless modes, one a phonon associated with broken translational invariance, the other a pseudospin-wave associated with a broken U(1) symmetry. For large layer separations the modes disperse weakly for wavevectors perpendicular to the stripe orientation, indicating the system becomes akin to an array of weakly coupled one-dimensional XY systems. At higher wavevectors the collective modes develop a roton minimum associated with a transition out of the coherent state with further increasing layer separation. A spin wave model of the system is developed, and it is shown that the collective modes may be described as those of a system with helimagnetic ordering.

cond-mat.mes-hall↗

arXiv2001

London equation studies of thin-film superconductors with a triangular antidot lattice

We report on a study of vortex pinning in nanoscale antidot defect arrays in the context of the London Theory. Using a wire network model, we discretize the array with a fine mesh, thereby providing a detailed treatment of pinning phenomena. The use of a fine grid has enabled us to examine both circular and elongated defects, patterned in the form of a rhombus. The latter display pinning characteristics superior to circular defects constructed with the similar area. We calculate pinning potentials for defects containing zero and single quanta, and we obtain a pinning phase diagram for the second matching field, $H = 2 Φ_{o}$.

cond-mat.supr-con↗

arXiv2001

Hamiltonian Theory of the Composite Fermion Wigner Crystal

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the excitation gaps of the Wigner Crystal states. We find that the Wigner Crystal states near $ν=1/5$ are quantitatively well described as crystals of Composite Fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.

cond-mat.mes-hall↗

arXiv2000

Electrostatic Attraction of Coupled Wigner Crystals: Finite Temperature Effects

In this paper, we present a unified physical picture for the electrostatic attraction between two coupled planar Wigner crystals at finite (but below their melting) temperature. At very low temperatures, we find a new regime where the attraction, arising from the long-wavelength excitation of the plasmon mode, scales with the interplanar distance $d$ as $d^{-2}$. At higher temperatures, our calculation agrees with known results. Furthermore, we analyze the temperature dependence of the short-ranged attraction arising from ``structural'' correlations and argue that thermal fluctuations drastically reduce the strength of this attraction.

cond-mat.soft↗

arXiv2000

Landau Level Mixing and Skyrmion Stability in Quantum Hall Ferromagnets

We present a Hartree-Fock study that incorporates the effects of Landau level mixing and screening due to filled levels into the computation of energies and states of quasiparticles in quantum Hall ferromagnets. We use it to construct a phase diagram for skyrmion stability as a function of magnetic field and Zeeman coupling strengths. We find that Landau level mixing tends to favor spin-polarized quasiparticles, while finite thickness corrections favor skyrmions. Our studies show that skyrmion stability in high Landau levels is very sensitive to the way in which electron-electron interactions are modified by finite thickness, and indicate that it is crucial to use models with realistic short distance behavior to get qualitatively correct results. We find that recent experimental evidence for skyrmions in higher Landau levels cannot be explained within our model.

cond-mat.mes-hall↗

arXiv2000

Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory

The density of an atom in a state of well-defined angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and Local Density Approximations, generally violate this feature. We analyze, by means of perturbation theory, the degree of this violation and show that it is small. The correct symmetry of the density can be assured by a constrained-search formulation without significantly altering the calculated energies. We compare our procedure to the (different) common practice of spherically averaging the self-consistent potential. Kohn-Sham density functional theory with the exact exchange-correlation potential has the correct finite spherical harmonic content in its density; but the corresponding exact single particle potential and wavefunctions contain an infinite number of spherical harmonics.

cond-mat.mtrl-sci↗

arXiv2000

Stability of the Smectic Quantum Hall State: A Quantitative Study

We present an effective elastic theory which {\em quantitatively} describes the stripe phase of the two-dimensional electron gas in high Landau levels ($N\geq2$). The dynamical matrix is obtained with remarkably high precision from the density-density correlation function in the time-dependent Hartree-Fock approximation. A renormalization group analysis shows that at T=0, as the partial filling factor $Δν\equivν-\lfloorν\rfloor$ moves away from 1/2, the anisotropic conducting state may undergo quantum phase transitions: stripes may get pinned along their conducting direction by disorder, or may lock into one another to form a two-dimensional crystal. The model predicts values of $Δν$ for each transition. The transitions should be reflected in the temperature dependence of the dissipative conductivity.

cond-mat.mes-hall↗