Research synopsis
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My research in condensed matter physics concerns the properties of the materials that surround us in our everyday lives. Condensed matter physics focuses on how a large assembly of particles are affected by thermal energy and the interactions between particles. For example, as a kettle warms water it causes the constituent molecules to vibrate more and more vigorously. When a molecule's kinetic energy exceeds the attractive interaction between adjacent molecules the water boils, undergoing a liquid to vapor phase transition. This type of phenomenon is not unique to water; changing interactions between particles causes phase transitions in other many-body systems including ferromagnets and superconductors.
An important consideration when studying a condensed matter system is how the particles move relative to one another, particularly when on the verge of a phase transition. This can cause the system to display new cooperative behavior which can be markedly different from that of the separate constituent particles. Returning to the kettle, the water molecules' thermal energy causes them to move randomly, so the relative motion of any two molecules is on average independent. However, in systems near to a phase transition, with either short or long ranged interactions between particles, two distant particles will on average move together so as to become strongly correlated even though they are far apart. An everyday consequence of strong correlations is the formation of clouds. Since the widely separated water vapor molecules move together they can clump into regions of high density. When the high density regions are similar in size to the wavelength of light (many thousand times the average water vapor molecule separation), passing light is strongly scattered making the cloud appear white. A further increase in density causes water droplets to form which then leads to rain.
The collective behavior of particles discussed so far can be understood purely in terms of classical physics. However, intriguingly, this behavior finds a counterpart in the realm of quantum physics. Quantum mechanics introduces the concept of wave particle duality, meaning that every particle has a new effective length scale -- the de Broglie wavelength. When that length scale is less than the separation between adjacent particles their respective de Broglie wavelengths overlap so they become quantum degenerate, which dramatically alters the particles' behavior. One consequence is the Pauli exclusion principle that prevents electrons from occupying the same point in space therefore making materials solid.
Some interacting systems can be both strongly correlated and quantum degenerate. The coupling of quantum mechanics and strong correlations often leads to a rich range of new phenomena that are the subject of present-day research. The phenomena can be classed into two broad categories: Firstly, strong correlations can make widely used approximations invalid, so new theory must be developed to accurately describe the material. Secondly, the system could driven into a completely new phase of matter.
The traditional setting to explore many-body quantum phenomena has been electrons an a solid. The electrons interact with the long-range Coulomb force and are quantum degenerate at temperatures below ~30000°C, making this the prototypical condensed matter system. However, the complicated interplay between the electrons and the background lattice of atoms, and the extreme conditions demanded to observe novel phenomena creates additional obstacles when trying to study the fundamental phenomena. Instead, since a breakthrough in 1995, the possibility of using an gas of ultracold atoms has revolutionized many-body physics. An ultracold atomic gas provides unprecedented control over a many-body system. For example, an external magnetic field controls the relative energies of the orbiting electrons allowing the strength of atom-atom interactions to be varied. Atomic gases can now be used to address long-standing questions about the influence of strong correlations in the solid state.
My research is focused not only on the systems, but also improving the tools that scientists employ to study them. Specifically, I have proposed new algorithms used to improve the efficiency of the Quantum Monte Carlo technique and increase its applicability to new condensed matter systems. This research, along with a detailed description of the systems that I have studied are described in more detail below.
This project concerns an atomic gas containing two species of atoms,
one species is taken to represent up-spin electrons in a solid and the
second species to represent the down-spin electrons. Then, since the
atomic species are set up with differing number densities and cannot
interchange, the system has a fixed magnetic moment along one axis. If
it becomes energetically favorable for the atomic gas to become
ferromagnetic, the magnetic moment must form in-plane. This makes the
system unique compared to ferromagnetic phenomenon in solid-state
systems and has allowed new aspects of strongly correlated phases to
be investigated [G.J. Conduit &
B.D. Simons,
Phys. Rev. A 79, 053606 (2009)].
Following on from this work, this phase has recently been observed for the first time by the Ketterle group at MIT [G.B. Jo et al., Science 325, 1521 (2009)]. I have performed a detailed critique of this experiment [G.J. Conduit & B.D. Simons, Phys. Rev. Lett 103, 200403 (2009)] and shown that its results cannot be understood within the framework of an itinerant ferromagnet at equilibrium, but is instead better described by a dynamic process with a condensed phase of topological defects undergoing mutual annihilation. A second possibility is highlighted in the followup work [G.J. Conduit & E. Altman, Phys. Rev. A 83, 043618 (2011)] that introduces a new formalism to expose how the interaction strength is renormalized by three-body atom loss.
Recently, in cooperation with the Ketterle group at MIT we have been exploring the possibilities for the next generation of the experiment, in which the goal is to eliminate the three-body loss. The proposal [G.J. Conduit & E. Altman, Phys. Rev. A 82, 043603 (2010)] is to start the gas in a spin spiral and then watch the ferromagnetic domains grow. This system, with its minimal three-body losses, should provide more clear signatures of the ferromagnetic transition that the original experimental setup. A two-dimensional [G.J. Conduit, Phys. Rev. A 82, 043604 (2010)] or mass imbalanced system [C.W. von Keyserlingk & G.J. Conduit, Phys. Rev. A 83, 053625 (2011)] could reduce competing many-body instabilities and at the same time also reveal distinctive signatures of ferromagnetism.
Recently there has been a series of intriguing experimental observations
of electronic transport through disordered SC thin films,
which have yet to be satisfactory explained, chiefly because
there is no theory that can calculate the current, even
numerically, through a disordered superconductor, based
on a microscopic model. We have developed a new formalism to calculate the exact current flow,
that starts from a microscopic model, and accounts for both the phase
and amplitude fluctuations in the superconducting order parameter [G.J. Conduit & Y. Meir,
Phys. Rev. B 84, 064513 (2011)].
Moreover we can plot maps of the local current flow,
distinguishing between the super and normal current,
and map the local chemical potential, which allows us to identify the weak links in the
sample, and diagnose the microscopic origin of the observed phenomena.
Having validated the formalism against well-established phenomena
in mesoscopic systems, we then use it to analyze two unexplained experimental
phenomena.
In our first application [G.J. Conduit & Y. Meir, arXiv:1107.1246] we address recent observations that have revealed the emergence of an unusual normal phase when a magnetic flux threads an ultra-thin superconducting cylinder [Liu et al., Science 294, 2332 (2001)]. Moreover, with increasing temperature, the resistance rises in a series of abrupt jumps. It is demonstrated that phase fluctuations lead to the sequential breakdown of local superconducting phase correlations, resulting in the formation of normal weak links, which give rise to the emergence of the normal phase in a stepwise manner.
Secondly, a recent experiment [Sambandamurthy et al., Phys. Rev. Lett. 92, 107005 (2004)] measured the resistance of a disordered superconductor connected between two metallic leads as a magnetic field tunes the system from the normal into purely superconducting state. In the intermediate phase when the sample contained puddles of superconducting regions embedded within a normal material, the resistance was a factor of ~10000 higher than when in either the normal or superconducting states. We have used our new formalism to explore the microscopic mechanism behind this counter-intuitive phenomenon.
The generality of the formalism developed to describe ferromagnetism
in an ultracold atom gas [G.J. Conduit &
B.D. Simons,
Phys. Rev. A 79, 053606 (2009)], enables it to be applied
to also study novel behavior in the solid state system. The formalism
predicts a new spatially varying ferromagnetic phase that should
preempt the ferromagnetic phase transition in some materials
[G.J. Conduit, A.G. Green &
B.D. Simons, Phys. Rev. Lett. 103,
207201 (2009)]. To verify the robustness of our results we also
developed a novel technique within the accurate ab initio
Quantum Monte Carlo method which provided strong evidence for the
formation of the phase. This study should go towards resolving
questions raised by recent experimental results.
An interesting phase in a superconductor is an inhomogeneous superconducting state whose energy gap varies sinusoidally across the sample. Understanding this phase will further our knowledge about superconductivity in the effort to develop room temperature superconductors. In the solid state this inhomogeneous phase is destroyed by unavoidable impurities so has never been experimentally studied. However, atomic gases contain no impurities so put investigators in the unique position to study this inhomogeneous phase. Also, they allow the additional experimental probes that the gas can be composed of two or more different species of atom with different masses or in variable proportions. The first project [G.J. Conduit, P.H. Conlon & B.D. Simons, Phys. Rev. A 77, 053617 (2008)] examined the stability and properties of such an inhomogeneous phase whose verification is under way by experimental collaborators at Duke University. As a follow-up to the project, in response to a request from collaborators, the collective modes of a two-dimensional superfluid with both population and mass imbalance have been calculated [in preparation].
For freely moving particles, kinetic energy increases with momentum and so has a single minimum. However, in many semiconductors such as silicon, interactions of electrons with the ionic lattice mean that the single electron energy has several minima as a function of momentum. Assuming that there is a large number of minima allows an exact analytical treatment, unlike other current models of semiconductors. The new formalism [G.J. Conduit, Phys. Rev. B 78, 035111 (2008)] gives an exact expression for the total electron energy, and access to the electron dynamical response. Computational verification [G.J. Conduit & P.D. Haynes, Phys. Rev. B 78, 195310 (2008)] showed that the formalism has widespread applicability; this was demonstrated in two real-life systems: electron-hole droplets analytically, and quantum dots computationally.
Ferroelectricity is the spontaneous electric polarization of a material that can be reversed by the application of an external electric field. My research [G.J. Conduit & B.D. Simons, Phys. Rev. B 81, 024102 (2010)] focuses on the low temperature behavior of displacive ferroelectrics. Their properties are manifestly controlled by quantum fluctuations, and unlike electrons in a solid, do not suffer from disruption of the background lattice. This work should help ferroelectrics to in the future be recognized as a new textbook paradigm of quantum critical behavior.
Quantum Monte Carlo is a computational technique that gives an exact value for the ground state energy of an interacting many-body system, subject only to the fixed node approximation. It is probably the most accurate computational technique used in condensed matter physics today. My research has enabled the first Quantum Monte Carlo calculations on a textured ferromagnet [G.J. Conduit, A.G. Green & B.D. Simons, Phys. Rev. Lett. 103, 207201 (2009)], and the application of Monte Carlo methods to a many-flavor fermion system [G.J. Conduit & P.D. Haynes, Phys. Rev. B 78, 195310 (2008)]. During my work I have not only developed new techniques that enables Quantum Monte Carlo to be used on new systems, but I have also developed new general algorithms that will improve the efficiency of all Quantum Monte Carlo calculations [R.M. Lee, G.J. Conduit, N. Nemec, P. López Ríos & N.D. Drummond, Phys. Rev. E 83, 066706 (2011)].