# Matthew Foster

**Assistant Professor**

**Department:**
Physics and Astronomy

**Office Phone:** (713) 348-3922

**Website:** http://arxiv.org/find/grp_physics/1/au:+foster_matthew_s/0/1/0/all/0/1

### Research Areas

### Research Description

Prof. Foster studies theoretical condensed matter physics, with a focus on the effects of disorder and interactions in low-dimensional systems, and in particular Anderson localization and metal-insulator transitions. He works on Dirac materials including graphene, topological insulators and superconductors. He has also done work on non-equilibrium quantum dynamics relevant to ultracold atomic matter.

Most recently, Foster’s group has made significant contributions to the theory of bulk topological superconductors. These are predicted to host gapless Majorana fermion surface states with exotic properties. By treating the effects of disorder exactly using conformal field theory and that of interactions via different controlled expansions, they have shown that the low-temperature spin and thermal surface conductivities should be topologically quantized to universal values at low temperature. Surface transport measurements may therefore provide a “smoking gun” for bulk topological superconductivity, which is a 3D analog of the 2D quantum Hall effect.

In another recent work, Foster and collaborators have shown that a non-equilibrium topological BCS superfluid can be realized in an ultracold atomic gas. Trapped 2D fermion gases such as 6Li and 40K tuned close to a p-wave Feshbach resonance were expected to exhibit ground state topological superfluidity, but these were found to be experimentally unstable due to parasitic losses. They discovered that one can induce several non-equilibrium superfluid states if weakly interacting atoms are brought suddenly close (quenched) to such a Feshbach resonance, in the time before the instability kicks in. These include a Floquet topological superconductor. Exploiting the integrability of the problem, Foster and collaborators obtained exact results for the out-of-equilibrium dynamics of the order parameter (“Higgs mode”) and system topology.

### biography

Foster was born and raised in North Dakota. He obtained his Bachelors of Engineering (summa cum laude) in electrical engineering from the Cooper Union for the Advancement of Science and Art in NY, NY, and his Ph.D. in physics from the University of California, Santa Barbara. He was a post-doc at Columbia and Rutgers Universities in NY and NJ before joining Rice in 2012. Foster is a recipient of a 2014 Alfred P. Sloan Foundation Research Fellowship.

## Selected Publications

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

**“Surface transport coefficients for three-dimensional topological superconductors,”**

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

**“Quench-Induced Floquet Topological p-Wave Superfluids,” **

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

**3. ****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)**

**4. 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)**

**5. ****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)**

**6. ****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)**

**7. ****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)**

**8. ****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)**

**9. ****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)**

**10. ****M. S. Foster and I. L. Aleiner,**

**"Slow imbalance relaxation and thermoelectric transport in graphene,"**

**Phys. Rev. B 79, 085415 (2009)**

**11. ****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"**