Two-dimensional Superfluid Research Articles

MONOLAYER CHARGED QUANTUM FILMS: A QUANTUM SIMULATION STUDY

We use path-integral Monte Carlo (PIMC) to study the effects of adding a long-range repulsive Coulomb interaction to the usual Van der Waals interaction between two atoms of a submonolayer quantum film such as helium on graphite or a pure two-dimensional superfluid. Such interactions frustrate or compete with the natural tendency of the system for phase separation namely to form a macroscopic liquid or solid phase. We find that as a function of the relative strength of the long-range repulsion, surface coverage and temperature, the system undergoes a series of transformations, including a triangular Wigner-like crystal of clusters, a charge stripe-ordered phase and a fluid phase. The goal of these studies is to understand the role of quantum fluctuations when such competing interactions appear together with formation of preexisting electron pairs as might be the case in cuprate superconductors.

Detecting the quantum zero-point motion of vortices in the cuprate superconductors

We explore the experimental implications of a recent theory of the quantum dynamics of vortices in two-dimensional superfluids proximate to Mott insulators. The theory predicts modulations in the local density of states in the regions over which the vortices execute their quantum zero-point motion. We use the spatial extent of such modulations in scanning tunnelling microscopy measurements [J.E. Hoffman, E.W. Hudson, K.M. Lang, V. Madhavan, S.H. Pan, H. Eisaki, S. Uchida, J.C. Davis, Science 295 (2002) 466] on the vortex lattice of Bi 2Sr 2CaCu 2O 8+ δ to estimate the inertial mass of a point vortex. We discuss other, more direct, experimental signatures of the vortex dynamics.

Coherence Network in the Quantum Hall Bilayer

Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an imperfect two-dimensional superfluidity, in which there is nearly dissipationless transport at nonvanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a coherence network induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropriate to describe the system as a vortex liquid. We demonstrate that the dynamics of the nodes of the network leads to a power law temperature dependence of the tunneling resistance, whereas thermally activated hops of vortices across the links control the counterflow resistance.

Magnus force in discrete and continuous two-dimensional superfluids

Motion of vortices in two-dimensional superfluids in the classical limit is studied by solving the Gross-Pitaevskii equation numerically on a uniform lattice. We find that, in the presence of a superflow directed along one of the main lattice periods, vortices move with the superflow on fine lattices but perpendicular to it on coarse ones. We interpret this result as a transition from the full Magnus force in a Galilean-invariant limit to vanishing effective Magnus force in a discrete system, in agreement with the existing experiments on vortex motion in Josephson junction arrays.

Path integral formulation of the tunneling dynamics of a superfluid Fermi gas in an optical potential

To describe the tunneling dynamics of a stack of two-dimensional fermionic superfluids in an optical potential, we derive an effective action functional from a path integral treatment. This effective action leads, in the saddle point approximation, to equations of motion for the density and the phase of the superfluid Fermi gas in each layer. In the strong coupling limit (where bosonic molecules are formed) these equations reduce to a discrete nonlinear Schrodinger equation, where the molecular tunneling amplitude is reduced for large binding energies. In the weak coupling (BCS) regime, we study the evolution of the stacked superfluids and derive an approximate analytical expression for the Josephson oscillation frequency in an external harmonic potential. Both in the weak and intermediate coupling regimes the detection of the Josephson oscillations described by our path integral treatment constitutes experimental evidence for the fermionic superfluid regime.

Generalized coherent-state derivation of time-dependent density-functional theory equations for superconductors

Equations of motion are derived for the normal and anomalous single-electron density matrices of a Fermi liquid using a time-dependent finite-temperature generalized coherent-state variational ansatz for the many-body density matrix. Self-consistent equations for the order parameter $\ensuremath{\Delta}$ allow us to investigate the interplay of the Coulomb repulsion and pairing attraction in homogeneous and inhomogeneous Fermi liquids with spontaneously broken symmetry such as high-temperature superconductors. The temperature of the Kosterlitz-Thouless transition to the two-dimensional superfluidity is calculated.

Characterization of ZYX graphite for studies of two-dimensional [formula omitted] at ultra-low temperatures

So far, theoretically predicted two-dimensional (2D) superfluidity in monolayer 3 He has not been observed yet. This may be due to the smaller single crystalline size (≃10 nm) of Grafoil substrate than the expected superfluid coherence length (⩾100 nm) , or pair breaking caused by trapped atoms on substrate heterogeneity. To eliminate these problems, we have made an NMR sample cell using ZYX grade exfoliated graphite substrate. This substrate has at least 10 times larger crystalline size than Grafoil. NMR measurements are now under way to search for possible 2D and quasi 2D superfluidity in 3 He thin films.

Superfluidity of disordered Bose systems: numerical analysis of the Gross–Pitaevskii equation with random potential

We study the two-dimensional superfluidity of disordered Bose systems by analyzing the Gross–Pitaevskii equation with random potential. First, we obtain the ground state and calculate its superfluid density by the linear response theory. The superfluid density shows their remarkable dependence on the potential amplitude, the healing length and the density. Secondly, we apply the velocity field to the ground state to observe the breaking of superfluidity due to the excitation of vortex pairs above a critical velocity.

Scattering of acoustic waves by a superfluid vortex

The scattering of plane acoustic waves by a vortex in a two-dimensional superfluid is examined for small Mach number M. The solution is developed from a systematic expansion of the governing equations in three separate regions: an inner vortical region which scales as the healing length, an interaction region governed by irrotational hydrodynamics and an outer wave region. The solutions in the different regions are matched together. The leading-order scattered field occurs at O(M2δ) in the wave region, where δ is the small non-dimensional amplitude of the incoming acoustic wave. The far-field behaviour of the wave-region solution shows that a different form of the expansion is required in the forward scatter direction: this corresponds to the expression previously derived for the acoustic Magnus force.

The Landau–Ginzberg Theory for the Two-Dimensional Bose Gas

Using results from sheaf theory combined with the phenomenological theory of the two-dimensional superfluid, the precipitation of quantum vortices is shown to be the genesis of a macroscopic order parameter for a phase transition in two dimensions.

Phase transitions driven by vortices in two-dimensional superfluids and superconductors: From Kosterlitz-Thouless to first order

The Landau-Ginzburg-Wilson hamiltonian is studied for different values of the parameter $\lambda$ which multiplies the quartic term (it turns out that this is equivalent to consider different values of the coherence length $\xi$ in units of the lattice spacing $a$). It is observed that amplitude fluctuations can change dramatically the nature of the phase transition: for small values of $\lambda$ ($\xi/a > 0.7$), instead of the smooth Kosterlitz-Thouless transition there is a {\em first order} transition with a discontinuous jump in the vortex density $v$ and a larger non-universal drop in the helicity modulus. In particular, for $\lambda$ sufficiently small ($\xi/a \cong 1$), the density of bound pairs of vortex-antivortex below $T_c$ is so low that, $v$ drops to zero almost for all temperature $T<Tc$.

Recombination of spin polarized atomic hydrogen adsorbed on a dilute 3He-4He mixture

We have been searching for two-dimensional (2-D) superfluidity of spin-polarized atomic hydrogen (H↓) adsorbed on liquid helium surface. We have investigated H↓ adsorbed on 3 He- 4 He mixtures instead of pure 4 He because the thermal coupling of H↓ to the mixtures is stronger than 4 He, ESR at 129 GHz was carried out to detect H↓ at 4.5 T by using the Fabri-Perot confocal cavity with the cold spot located at the confocal point and thus the 2-D H↓ signal was effectively detected. We investigated the two-body bulk and surface recombination processes of H↓ on a 3 % 3 He 3 He- 4 He mixture film. From the analysis of the surface recombination process, we found the adsorption energy of H↓ was a 0.6 K for the mixture film in the temperature range between 120 mK and 250 mK, greater than the 0.3-0.4 K found previously for pure 3 He and a 67 % 3 He 3 He- 4 He mixture.

Dynamic scaling for two-dimensional superconductors, Josephson-junction arrays, and superfluids

The value of the dynamic critical exponent $z$ is studied for two-dimensional superconducting, superfluid, and Josephson Junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find $z\simeq5.6\pm0.3$, a relatively large value indicative of non-diffusive dynamics. Universality of the scaling function is tested and confirmed for the thinnest samples. We discuss the validity of the dynamic scaling analysis as well as the previous studies of the Kosterlitz-Thouless-Berezinskii transition in these systems, the results of which seem to be consistent with simple diffusion ($z=2$). Further studies are discussed and encouraged.

Eigenstates of the Vorticity Operator: The Creation and Annihilation of Vortex States in Two Dimensions

A quantum mechanical description of vortices in two-dimensional superfluid 4 He films is presented. Single vortex creation and annihilation operators are defined and wavefunctions for these states are explicitly constructed.

Non-Abelian adiabatic phases in vortex dynamics. Magnus force in Fermi superfluids

The Magnus force acting on a vortex in a two-dimensional neutral Fermi superfluid is derived using the method of adiabatic phases. The large core contribution to this force is generated by the non-Abelian structure of the gauge potentials. The Abelian approximation yields a small hydrodynamic force sensitive to the bulk band structure.

Atomic hydrogen experiments at the onset of two-dimensional superfluidity

Adsorption of spin-polarized hydrogen gas H↓ at the surface of liquid4He was greatly enhanced by magnetically focusing H↓ atoms onto the 0.03 cm dia. tip of a Dy “needle”. Two-dimensional phase space densities up to σ(h 2/2πmkTs)>2 were detected atT s≈225 mK using recombination energy yield NMR.

Strong correlations in two-dimensional quantum fluids of4He and3He adsorbed on hectorite

Quantum fluids of4He and3He adsorbed on mesopores of Hectorite were studied by measuring the heat capacity down to 50mK. Phonon and roton-like heat capacities of the two-dimensional (2D) superfluid were observed as a function of the coverage. Comparisons with model calculations suggest a strong correlation between the4He adatoms of which an effective hard core diameter is 4–6A. At the coverage and temperatures corresponding to the superfluid, the3He adatoms show a large nuclear heat capacity probably due to a Fermi degeneracy. The temperature-linear region in the3He heat capacity is likely to be much lower than that expected for an ideal Fermi gas. Assuming a 2D Fermi liquid, the effective mass at the coverage of about 2 layers is estimated to be 2.5 times that of the3He atom.

Reactive effects of core fermion excitations on the inertial mass of a vortex

The time-dependent Schrodinger equation for a fermion two-dimensional super-fluid containing a moving vortex is solved using the adiabatic approximation. The expectation value of the linear momentum of the vortex is found dominated by core fermion excitations. The resulting inertial vortex mass, obtained in the adiabatic limit, is larger than the standard core mass by a factor of (kFξ,)2 where ξ, is the coherence length at T = 0. Anamalous velocity dependence of the mass, associated with the breakdown of the adiabatic approximation, is predicted.

Non-linear response to an external AC drive near the Kosterlitz Thouless phase transition

We discuss the effect of an external AC drive on the motion of vortices near the vortex unbinding transition in two-dimensional superfluids, and on the motion of the interface between a crystal and its melt at the roughening transition. Both belong to the Kosterlitz Thouless class of phase transitions. There are three length scales in the problem: the correlation length, a diffusion length which varies as ω − 1 2 and a length inversely related to the strength of the drive. A possible resonance experiment for helium crystals is discussed.

Finite-size scaling in two-dimensional superfluids.

Using the $x-y$ model and a non-local updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two dimensional superfluid on large-size square lattices $L \times L$ up to $400\times 400$. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of $L$ values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson Renormalization Group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments.