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Scholarly Interest Report
         
Matthew Foster
Assistant Professor
Assistant Professor of Physics and Astronomy
 
e-mail:Matthew.Foster@rice.edu
 
  • B.E. Electrical Engineering (2000) Cooper Union for the Advancement of Science and Art, New York, NY
  • Ph.D. Physics (2006) University of California, Santa Barbara, Santa Barbara, CA
 
Primary Department
   Department of Physics and Astronomy
Picture
 
Websites
 Papers on arXiv
 Talks and lectures
 
Research Areas
 Theoretical condensed matter physics. In particular, the effects of disorder and interactions in low-dimensional systems. Anderson localization and metal-insulator transitions. Dirac materials including graphene, topological insulators and superconductors. Non-equilibrium quantum dynamics. Applications of quantum field theory, renormalization group, and exact (symmetry-based) methods such as conformal field theory.
 

Disorder, interactions, and dynamics

 

 

One theme of my research involves the effects of disorder in condensed matter systems. For solid state materials, disorder is ubiquitous and typically unavoidable, taking the form of randomly-distributed impurity atoms, dopants, or structural defects. Perfect crystallinity is an ideal sought by materials growers and taught as the foundation for solid state physics; a concern is that the electronic properties of disordered materials may depend sensitively upon the details of the impurity distribution (which varies from sample to sample). Yet a remarkable and deep feature of quantum mechanics is that disordered systems fall into only ten symmetry classes. Physical properties at low temperatures are largely determined by the class, independent of the details of the disorder, as long as interparticle interactions are sufficiently weak.


Disorder induces complex interference patterns in electronic wavefunctions. These can induce strong effects that dominate low-temperature materials properties, such as insulating behavior due to Anderson localization. For a conducting phase, spatial fluctuations in the electronic local density of states exhibit an intricate structure governed by multifractal statistics. The latter also arise in the characterization of strange attractors and other complex phenomena. In many low-dimensional quantum systems, topology plays a crucial role regulating the influence of disorder. Recent experimental breakthroughs in graphene and 3D topological insulators provide a new theatre for localization physics, because disorder-induced quantum interference occurs along an exposed 2D surface that can be probed locally (e.g. by STM).


Another interest is the combination of electronic inhomogeneity, interparticle interactions, and interaction-mediated collective phenomena such as superconductivity and magnetism. These ingredients arise in strongly correlated materials, in low-dimensional systems like graphene, and also in "synthetic" environments such as ultracold atoms in optical lattices.


I am also interested in dynamics, in particular the far-from-equilibrium evolution of well-isolated many-body systems. Ultracold atoms and ultrafast spectroscopy techniques allow the probing of fully quantum coherent many body dynamics. Goals include shedding light upon the boundary between quantum and (effectively) classical behaviors, and understanding the emergence of dissipation and thermalization in the absence of an external heat bath.


In my research I employ mainly analytical techniques including field theory, renormalization group, and non-perturbative methods (bosonization, CFT, etc.).

 
Selected Publications
 Refereed articles
 

M. S. Foster, H.-Y. Xie, Y.-Z. Chou,

"Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors,"

Phys. Rev. B 89, 155140 (2014)

 
 

M. S. Foster, V. Gurarie, M. Dzero, E. A. Yuzbashyan,

"Quench-Induced Floquet Topological p-Wave Superfluids,"

Phys. Rev. Lett. 113, 076403 (2014)

 
 

Y.-Z. Chou and M. S. Foster,

"Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene,"

Phys. Rev. B 89, 165136 (2014)

 
 

M. S. Foster, M. Dzero, V. Gurarie, E. A. Yuzbashyan,

"Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium,"

Phys. Rev. B 88, 104511 (2013)

 
 

M. S. Foster,

"Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder,"

Phys. Rev. B 85, 085122 (2012)

 
 

M. S. Foster and E. A. Yuzbashyan,

"Interaction-mediated surface state instability in disordered three-dimensional topological superconductors with spin SU(2) symmetry,"

Phys. Rev. Lett. 109, 246801 (2012)

 
 

M. S. Foster, T. C. Berkelbach, D. R. Reichman, and E. A. Yuzbashyan,
"Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in an XXZ chain,"
Phys. Rev. B 84, 085146 (2011)

 
 

M. S. Foster, E. A. Yuzbashyan, and B. L. Altshuler,
"Quantum quench in one dimension: Coherent inhomogeneity amplification and ‘supersolitons’,"
Phys. Rev. Lett. 105, 135701 (2010)

 
 

M. S. Foster and I. L. Aleiner,
"Slow imbalance relaxation and thermoelectric transport in graphene,"
Phys. Rev. B 79, 085415 (2009)

 
 

M. S. Foster, S. Ryu, and A. W. W. Ludwig,
"Termination of typical wavefunction multifractal spectra at the Anderson metal-insulator transition: Field theory description using the functional renormalization group,"
Phys. Rev. B 80, 075101 (2009); Selected for a “Viewpoint” in Physics, Physics 2, 66 (2009)

 
 

M. S. Foster and A. W. W. Ludwig,
"Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping"
Phys. Rev. B 77, 165108 (2008)

 
 

M. S. Foster and I. L. Aleiner,
"Graphene via large N: A renormalization group study,"
Phys. Rev. B 77, 195413 (2008)

 
 

M. S. Foster and A. W. W. Ludwig,
"Interaction effects on 2D fermions with random hopping,"
Phys. Rev. B 73, 155104 (2006)

 
 

M. S. Foster and A. W. W. Ludwig,
"Metal-insulator transition in Hubbard-like models with random hopping,"
Phys. Rev. B 74, 241102(R) (2006)

 
 Articles
 

H.-Y. Xie, Y.-Z. Chou, and M. S. Foster,

"Surface transport coefficients for three-dimensional topological superconductors,"

arXiv:1405.7730 (2014)

 
Presentations
 Invited Talks
 

"Topological protection, disorder, and interactions: Life and death at the surface of a topological superconductor"

University of California, Berkeley (2/2014, Berkeley, CA)

 
 

"Interaction-mediated surface state instability in dirty topological superconductors"

National High Magnetic Field Laboratory (5/2013, Tallahassee, Florida)

Texas A & M University (10/2013, College Station, TX)

 
 

"Quantum quench in p+ip superfluids: Non-equilibrium “topological” gapless states"

University of Colorado, Boulder (2/2013, Boulder, CO)

Boston University (3/2013, Boston, MA)

 
 

"Interaction-mediated surface state instability in dirty topological superconductors"

University of Oklahoma (9/2012, Norman, OK)

University of Illinois at Urbana-Champaign (11/2012, Champaign, IL)

Niels Bohr Institute (12/2012, Copenhagen, Denmark)

 
 

"Quantum quench in p+ip superfluids: Non-equilibrium 'topological gapless' state"

The Abdus Salam International Centre for Theoretical Physics (ICTP) (12/2012, Trieste, Italy)

 
 

"When Quantum Waves Crash upon Strange Shores: Splash Statistics in Disordered
Media, and Correlated Fronts Far from Equilibrium"

University of Chicago (1/2012, Chicago, IL)

University of Minnesota (1/2012, Minneapolis, MN)

Rice University (2/2012, Houston, TX)

 
 

"Knotted wavefunctions and Dirac surface states: Introducing topological insulators,"

Cooper Union for the Advancement of Science and Art (11/2010, New York, NY)

 
 

"Quantum quench in 1D: Fractionalization and supersolitons,"

University of California, Los Angeles (11/2010, Los Angeles, CA)

 
 

"Termination of typical wavefunction multifractal spectra at the Anderson metal-insulator
transition,"

Mesoscopic and strongly correlated electron systems workshop, Landau Institute for Theoretical Physics (6/2009, Chernogolovka, Russia)

 
 

"Competing Disorder and Coulomb Interaction Effects in Graphene via Large N,"

Brookhaven National Laboratory (2/2008, Upton, NY)

 
 

"Quantum Physics of Disordered and Chaotic Condensed Matter Systems,"

The Cooper Union for the Advancement of Science and Art (2/2006, New York, NY)

 
 Lectures
 

"Frontiers in disordered quantum systems: Dirac fermions, random matrix theory, non-linear sigma models,"

Blackboard Lectures in Condensed Matter Physics, Yeshiva University (7/2012, New York, NY)

 
 Other
 

"LDOS multifractal hunter's guide to dirty topological insulators,"

APS March Meeting (2/2012, Boston, MA)

 
 

"Slow imbalance relaxation and thermoelectric transport in graphene"

APS March Meeting (3/2009 Pittsburgh, PA)

 
 Workshops
 

"Topological protection, disorder, and interactions: Life and death at the surface of a topological superconductor"

Recent Progress and Perspectives in Scaling, Multifractality, Interactions, and Topological Effects Near Anderson Transitions (3/2014, MPIPKS Dresden, Germany)

 
 

"Far from equilibrium topological p-wave superfluids"

Topological Matter out of Equilibrium (3/2014, MPIPKS Dresden, Germany)

 
 

"Quantum quench in p+ip superfluids: Winding numbers and topological states far from equilibrium"

Tutorial lecture version

Hangzhou Workshop on Quantum Matter (4/2013, Hangzhou, China)

 
 

"Interaction-mediated surface state instability in dirty topological superconductors"

Topological Phenomena in Quantum Dynamics and Disordered Systems, BIRS Workshop (2/2013, Banff Center, Alberta, CA)

 
 

"'Supersolitons' in continuum and lattice quenches: Correlated quantum fronts far from equilibrium"

Frontiers of quantum condensed matter physics: light, matter and unusual devices out of equilibrium, CUNY (3/2012, New York, NY)

 
 

"Instability of “Protected” Surface Andreev States in 3D Class CI Dirty Topological Superconductors due to Interactions and Multifractality"

Complex quantum systems: Nonergodicity, glassiness and localization, Abdus Salam ICTP (8/2012, ICTP, Trieste, Italy)

 
 

"Quantum quench in 1D: Coherent inhomogeneity amplification and supersolitons,"

Dynamics of Strongly Correlated Quantum Systems workshop Abdus Salam ICTP (6/2010, Trieste, Italy)

 
 

"Interparticle interaction effects in quantum disordered systems with random hopping,"

Dynamics and Relaxation in Complex Quantum and Classical Systems and Nanostructures, Max Planck Institute for the Physics of Complex Systems (8/2006, Dresden, Germany)

 
Awards, Prizes, & Fellowships
 Alfred P. Sloan Foundation Research Fellowship, The Alfred P. Sloan Foundation (2014-2016)

 Graduate Division Fellowship , University of California, Santa Barbara (September 2004)

 John Cardy Award, Physics Department, University of California, Santa Barbara (June 2001)

 First Place (with Nader Zaki) for the paper "PsiOptik: an optical image processing system", Region I IEEE Student Paper Competition (June 2000)

 Graduate Research Fellowship, National Science Foundation (September 2000)

 Broida Fellowship, University of California, Santa Barbara (September 2000)