Images and Animations

All images and animations contained herein are copyright Curry Taylor and J.C. Davis, and they may not be used for any other purpose other than personal viewing without the explicit permission of either party. All images and animations here were created using POV-Ray.

Transport in a D-Wave Cuprate Superconductor: Analogy to Quantum Dot Experimental Techniques

A traditional quantum dot transport experiment is somewhat analagous to transport across the CuO2 plane of a cuprate d-wave superconductor. In a quantum dot transport experiment, two quantum dot reservoirs are separated by a small gated region which has an energy slightly higher than that of the two wells surrounding it. Each dot can be populated by a metal conductor, and the two conductors form electrodes which completes the circuit in the transport experiment. This can be viewed, instead, as a lattice of such dots, each connected to nearest neighbors by a gated coupling region. In turn, the oxygen orbitals of the CuO2 plane in a cuprate superconductor are analagous to these gated coupling areas, and the copper orbitals play the role of the charge-quantized dots.

Schematic Representation of Normal STM Tunneling in a BCS-like High-Tc Superconductor

In order to tunnel through the vacuum barrier, a quasiparticle must have sufficient energy. In "normal" STM tunneling, the tunneling current is sensitive only to fermionic quasiparticles, which are energetically electron-like and behave as if they have a charge of -e (at least as far as we know right now). As the tip scans the surface of the sample, it only normal quasiparticles may then be extracted from the surface density of states.

Schematic Representation of Josephson STM Tunneling in a BCS-like High-Tc Superconductor

In contrast, it is possible to reduce system noise and temperature far enough to create a Josephson current between a sample and a superconducting tip. In such a case, conventional quantum theory and experiment implies that such a probe would be sensitive to the bosonic quasiparticles present, and moreover, to the order parameter of the sample itself. Demonstrating this capability in a repeatable manner would revolutionize the field of cuprate studies with a high-precision STM.

Hole Moving Through an Antiferromagnet in the (1,0) direction.

Half-filled antiferromagnets are a phase of matter in which the electron on one particular microscopic site has spin opposed to that of all the electrons occupying neighboring sites. This microscopic effect makes motion inside the antiferromagnet difficult: the electron cannot move to its neighbor's site because the new state would have a larger energy than the previous state. If a hole (site with no electron) forms in the lattice, the electron still cannot move because the antiferromagnetic exchange energy would again be higher than that before the move. This precarious situation results in what is known as a Mott insulator. A system in such a state will not conduct any current. This animation shows how the motion of a hole in the (1,0) direction disrupts the normal cohesiveness of the antiferromagnetic order.

Hole Moving Through an Antiferromagnet in the (1,1) direction.

However, not all motions will result in antiferrogmagnetic frustration. A move in the (1,1) (diagonal) direction will not disrupt the antiferromagnetic order. Since this move (hop) requires a longer distance than a nearest-neighbor move, though, it is generally assumed that the move is less likely to occur.

Boson Cooling

A cartoonish animation of what happens to bosons when they cool to absolute zero temperature. The balls in the animation represent boson particles, and the circular sheets represent quantized energy levels. (I gave the system a quadratic potential energy profile for illustrative purposes, although some real systems such as quantum dots have almost quadratic potentials.) Bosons follow Bose-Einstein statistics (by maininition) which says that any number of particles are allowed to occupy any given energy level. However, due to thermal energy considerations, they will not all occupy the lowest energy level, and will distrubute themselves in a decaying exponential-like way with increasing energy. Once the temperature is lowered, however, all the particles want to get chummy and fall down into the lowest energy level. (This is not a closed system: energy can by lost to the environment. Nature will seek the lowest energy state whenever it has the opportunity to do so.) There are other, smaller, effects going on here, but this is a simple illustration of the mechanism.

Fermion Cooling

As above, a cartoonish animation of what happens to fermions they cool to absolute zero temperature. Fermions (for example, electrons) obey Fermi-Dirac statstics (by maininition), and therefore must obey the Pauli exclusion principle. The Pauli exclusion principle says that no two identical particles (fermions) in your system may have the same set of quantum numbers. In other words, for this system, no two particles can have the same energy and spin. (I am assuming there are no degenerate energy levels in this system.) Ultimately, then, each energy level can hold two fermions, since the two fermions may have opposing spins. When the temperature is reduced to zero for this system, not all the fermions can fall to the ground state.

Animation of Physics Today Cover

This is an associated animation that I made with the Physics Today Cover (see the Papers section) for more visual presentation. Once again, the top layer is often proportional to the local density of electronic states (LDOS), and the bottom layer is the integrated density of states, which typically shows atomic locations. If this animation is too large for you, try this smaller version.

Alternative Image for Checkerboard Paper Release

This was one of my alternative versions of the accompanying image which was to be released with the Ca2-xNaxCuO2Cl (NaCCOC) paper. This one is large, but the top LDOS-like layer is not actual data. Therefore, another version was chosen over this one eventually. In this version, I draw vertical green poles to delineate 4 lattice constants in the topograph. Comparing these sections to the top layer, we can see that the signal in the conductance map is not commensurate in an obvious way to that of the atomic corrugations. Or, at least, that was the original idea.

Ca2-xNaxCuO2Cl Structure

A cartoon animation of one unit cell (not a primitive cell) of the substance I study, Ca2-xNaxCuO2Cl. The copper-oxygen (CuO) planes, the mainining characteristic of the high-Tc cuprate superconductors, have yellow (Cu) and blue (O) atoms. The "more insulating", intervening layers in this substance have Ca (red) and Cl (green) atoms. When this substance is doped, Ca atoms will be substituted for the dopant, in our case, Na (would also be red). The bonding forces between two intervening layers of cuprates are much weaker (just a quasi Van der-Waals interaction) than than the bonding forces between a CuO layer and a neighboring intervening layer. This is why samples cleave so readily between intervening layers. I tried to represent (roughly) the relative radii (size) of each atom as known from its size when making simple bonds.