Theoretical Condensed-Matter Physics
Michael Lawler
Adjunct Professor of Physics
B.Sc., Engineering Physics, 1999, Queen's University. PhD., Physics, 2006, University of Illinois at Urbana-Champaign, Postdoctoral Fellow, University of Toronto, 2006-2008. Adjunct Professor, Physics. Cornell University, 2008 - present. Assistant Professor, Physics, State University of New York at Binghamton, 2008-present. John Bardeen Award for outstanding contributions to electronic materials, 2006. Signal Processing Engineer, Computing Devices Canada, 1998-1999. Software Engineer, Aluminum Canada, 1996-1997.
Research Areas
Condensed Matter Theory
Current Research
My primary interests lie in the field of strongly correlated condensed matter physics. In this field, we seek to gain an understanding of the behavior of many strongly interacting particles. This is a far from well understood subject. However, we are fortunately aided in our exploration of it by an intimate connection between experiment and theory. Below are some of the topics related to this phenomenon that form my particular interest.
Frustrated Quantum Mechanical Systems
The concept of frustration in the classical limit can be illustrated as follows. In the classical limit one can pretend that Heisenberg's uncertainty principle has been "turned off". Hence one can know the exact position and momentum of particles and also the precise direction their spins. These classical particles are then "frustrated" when they have many equal energy configurations so that Newton's law cannot tell us what they will do next. This can happen, for example, when interacting classical spins are placed on certain lattices such that there are many spin configurations, each of which minimize the total energy.
A central question in the field is what happens when we turn on Heisenberg's uncertainty principle in a classically frustrated system? The spins can no longer point in a specific direction and it turns out that the laws of quantum mechanics then help the spins decide what they want to do. Should this happen, then the spin system can actually be governed by the laws of quantum mechanics at a macroscopic scale.
Recently, experimentalists have fabricated a number of materials (Herbertsmithite, NIO, K-BETD, diamond lattice spinels, ...) that may shed much light on the above central question. For some time now, we have had theories of quantum spin liquids based on the emergence of either fermions or bosons interacting via gluons, photons or visons as the new particles describing an emergent exotic phase. With these new materials, we can finally compare such theories with experiment, a comparison bound to lead to a new understanding of strongly correlated systems.
Recent papers:
[1] "Gapless spin liquids on the three dimensional hyper-kagome lattice of Na4Ir3O8", MJL, Arun Paramekanti, Yong Baek Kim and Leon Balents, arXiv:0806.4395
[2] "Quantum order by disorder in frustrated diamond lattice antiferromagnets", Jean-Sebastien Bernier, MJL and Yong Baek Kim, arXiv:0801.0598 (to be published in Phys. Rev. Lett.)
Quantum Liquid Crystals
It stands to reason that increasing the strength of interactions between particles in a gas phase will cause them to want to crystalize, to form a solid phase. If the particles are electrons, Wigner discovered in 1931 that this indeed happens. However, a transition to a Wigner crystal phase need not happen directly, but could in principle happen through a series of intermediate phases each progressively more crystalline. Examples of such intermediate phases include the electron nematic phase, which spontaneously breaks rotational symmetry, and an electron smectic or stripe phase, which involves the formation of an array of one-dimensional electronic rivers.
While symmetry provides a guiding principle in the theory of quantum liquid crystals, it alone cannot characterize a quantum world. As such, the general theory is fundamentally incomplete. It is very exciting, therefore, to study quantum liquid crystals found in nature, such as the nematic states found in Sr3Ru2O7 and quantum Hall systems and the stripe phases in cuprate superconductors. An interesting question, for example, is what happens at a continuous phase transition between two quantum liquid crystals? Or, can the stripes in a stripe phase slide freely next to each other? Can electrons in quantum liquid crystals pair easily to form a superconductor? At the heart of these questions is the quantum nature of these new phases, and their answers rely on the deep connection between experiment and theory achievable in condensed matter physics.
Recent papers:
[1] "Fluctuating stripes in strongly correlated electron systems and the nematic-smectic quantum phase transition", Kai Sun, Benjamin Fregoso, MJL and Eduardo Fradkin, arXiv: 0805.3526 (to be published
in Phys. Rev. B)
[2] "Theory of the nodal nematic quantum phase transition in superconductors" Eun-Ah Kim, MJL, Paul Oreto, Eduardo Fradkin and Steven A. Kivelson, Phys. Rev. B 77, 184514 (2008)