Research
Theoretical Condensed Matter Physics
I am a theoretical condensed matter physicist. Quite generally, I am interested in the physics of complex materials in which interactions, disorder, and engineered nanostructure yield new phases of matter, exotic quasiparticles, and collective phenomena that cannot be understood in terms of established paradigms. Such phenomena are testaments to the complex elegance of nature and yet the same effects can often be harnessed for the development of future technology.
Though I have worked on a variety of problems throughout my career to date  acceptoracceptor interactions in diluted magnetic semiconductors, radiationinduced magnetotransport in twodimensional electron systems, Bloch oscillations in optical lattices with controlled aperiodicity  I have spent the majority of my time studying the physics of massless Dirac fermions in condensed matter systems. This work began during my graduate studies at MIT, under the supervision of Patrick Lee. Back then, the system of interest was the dwave superconducting state of the highT_{c} cuprates, and the massless Dirac fermions were the Bogoliubov quasiparticles excited in the vicinity of the gap nodes. Today, the physics of massless Dirac fermions is seen in many condensed matter systems, from graphene to the surface states of topological insulators like Bi_{2}Se_{3}. My recent work, undertaken while I have been a faculty member in the Department of Physics and Astronomy at Hofstra University, has focused on the latter.
In one recent paper [A. C. Durst, "Lowtemperature thermal transport at the interface of a topological insulator and a dwave superconductor," Phys. Rev. B 91, 094519 (2015)], I considered the lowtemperature thermal transport properties of the 2D proximityinduced superconducting state formed at the interface between a 3D strong topological insulator (TI) and a dwave superconductor (dSC).
This system is a playground for studying massless Dirac fermions, as they enter both as quasiparticles of the dSC and as surface states of the TI. For TI surface states with a single Dirac point, the four nodes in the interfacestate quasiparticle excitation spectrum coalesce into a single node as the chemical potential, μ, is tuned from above the impurity scattering rate to below. I calculated, via Kubo formula, the universal limit (T → 0) thermal conductivity, κ_{0}, as a function of μ, as it is tuned through this transition. In the large and small μ limits, I obtained disorderindependent, closedform expressions for κ_{0}/T. The large μ expression is exactly half the value expected for a dwave superconductor, a demonstration of the sense in which the TI surface topological metal is half of an ordinary 2D electron gas. Numerical results for intermediate μ illustrate the nature of the transition between these limits, which depends on disorder in a welldefined manner.
In another recent paper [A. C. Durst, "Scattering states of a vortex in the proximityinduced superconducting state at the interface of a topological insulator and an swave superconductor," Phys. Rev. B 93, 064514 (2016)], I considered an isolated vortex in the twodimensional proximityinduced superconducting state formed at the interface of a topological insulator and an swave superconductor (sSC). Prior calculations of the bound states of this system famously revealed a zeroenergy state that is its own conjugate, a Majorana fermion bound to the vortex core. I calculated, not the bound states, but the scattering states of this system, and asked how the spinmomentumlocked massless Dirac form of the singleparticle Hamiltonian, inherited from the TI surface, affects the cross section for scattering Bogoliubov quasiparticles from the vortex. As in the case of an ordinary superconductor, this is a twochannel problem with the vortex mixing particlelike and holelike excitations. And as in the ordinary case, the samechannel differential cross section diverges in the forward direction due to the AharonovBohm effect, resulting in an infinite total cross section but finite transport and skew cross sections. I calculated the transport and skew cross sections numerically, via a partial wave analysis, as a function of both quasiparticle excitation energy and chemical potential. Novel effects emerge as particlelike or holelike excitations are tuned through the Dirac point.
In a third recent paper [A. C. Durst, "Disorderinduced density of states on the surface of a spherical topological insulator," Phys. Rev. B 93, 245424 (2016)], I considered a topological insulator of spherical geometry and numerically investigated the influence of disorder on the density of surface states.
The energy spectrum of the spherical TI surface is discrete, for a sphere of finite radius, and can be truncated by imposing a highenergy cutoff at the scale of the bulk band gap. To this clean system I added a surface disorder potential of the most general Hermitian form, V = V_{0}(θ,φ) + V(θ,φ)·σ, where V_{0} describes the spinindependent part of the disorder and the three components of V describe the spindependent part. I expand these four disorder functions in spherical harmonics and draw the expansion coefficients randomly from a fourdimensional, zeromean Gaussian distribution. Different strengths and classes of disorder are realized by specifying the 4×4 covariance matrix. For each instantiation of the disorder, I solved for the energy spectrum via exact diagonalization. Then I computed the disorderaveraged density of states, ρ(E), by averaging over 200,000 different instantiations. Disorder broadens the Landaulevel delta functions of the clean density of states into peaks that decay and merge together. If the spindependent term is dominant, these peaks split due to the breaking of the degeneracy between timereversed partner states. Increasing disorder strength pushes states closer and closer to zero energy (the Dirac point), resulting in a lowenergy density of states that becomes nonzero for sufficient disorder, typically approaching an energyindependent saturation value, for most classes of disorder. But for purely spindependent disorder with V either entirely outofsurface or entirely insurface, I identified intriguing disorderinduced features in the vicinity of the Dirac point. In the outofsurface case, a new peak emerges at zero energy. In the insurface case, one sees a symmetryprotected zero at zero energy, with ρ(E) increasing linearly toward nonzeroenergy peaks. These striking features are explained in terms of the breaking (or not) of two chiral symmetries of the clean Hamiltonian.
I have also recently concluded a computational project studying acceptoracceptor interactions in doped semiconductors. This work, discussed in a recent preprint [A. C. Durst, K. E. Castoria, and R. N. Bhatt, "HeitlerLondon model for acceptoracceptor interactions in doped semiconductors," arXiv:1706.09841 (2017), under review at Phys. Rev. B], grew out of an unfinished aspect of my undergraduate thesis at Princeton with Ravin Bhatt, two decades ago, which recently became the undergraduate research project of Hofstra student Kyle Castoria. The interactions between acceptors in semiconductors are often treated in qualitatively the same manner as those between donors. Acceptor wave functions are taken to be approximately hydrogenic and the standard hydrogen molecule HeitlerLondon model is used to describe acceptoracceptor interactions. But due to valence band degeneracy and spinorbit coupling, acceptor states can be far more complex than those of hydrogen atoms, which brings into question the validity of this approximation. To address this issue, we developed an acceptoracceptor HeitlerLondon model using singleacceptor wave functions of the form proposed by Baldereschi and Lipari, which more accurately capture the physics of the acceptor states. We calculated the resulting acceptorpair energy levels and found, in contrast to the twolevel singlettriplet splitting of the hydrogen molecule, a rich tenlevel energy spectrum. Our results, computed as a function of interacceptor distance and spinorbit coupling strength, suggest that acceptoracceptor interactions can be qualitatively different from donordonor interactions, and should therefore be relevant to the magnetic properties of a variety of pdoped semiconductor systems. Further insight was drawn by fitting numerical results to closedform energylevel expressions obtained via an acceptoracceptor Hubbard model.
I am very proud of the achievements of the undergraduate students whose independent work I have supervised at Hofstra. Of the two who have since graduated, both have gone on to excellent graduate programs. Kyle Castoria, whose research I supervised for four semesters and one summer, is the coauthor of the acceptor interactions preprint discussed above, and will begin his Ph.D. this fall in the Department of Electrical Engineering at Princeton University. And Claire Weaver, for whom I supervised an independent study of crystal structure and electronic band theory as well as an internship at the CUNY ASRC NanoFabrication Facility, started her Ph.D. last year in the Materials Department at the University of California at Santa Barbara, and was awarded a prestigious National Defense Science & Engineering Graduate (NDSEG) Fellowship. It has been my privilege to work with these very talented students.
The above work has also earned me several accolades, for which I am quite grateful. In 2016, Hofstra awarded me the Lawrence A. Stessin Prize for Outstanding Scholarly Publications, an award presented to three junior faculty members per year, selected amongst all disciplines throughout the university. And in 2017, I was named a KITP Scholar by the Kavli Institute for Theoretical Physics, one of the premiere scientific institutes in the world.
Publications
20. 

A. C. Durst, K. E. Castoria, and R. N. Bhatt, "HeitlerLondon model for acceptoracceptor interactions in doped semiconductors," arXiv:1706.09841 (2017), under review at Phys. Rev. B 
19. 

A. C. Durst, "Disorderinduced density of states on the surface of a spherical topological insulator," Phys. Rev. B 93, 245424 (2016) 
18. 

A. C. Durst, "Scattering states of a vortex in the proximityinduced superconducting state at the interface of a topological insulator and an swave superconductor," Phys. Rev. B 93, 064514 (2016) 
17. 

A. C. Durst, "Lowtemperature thermal transport at the interface of a topological insulator and a dwave superconductor," Phys. Rev. B 91, 094519 (2015) 
16. 

S. Ganeshan, M. Kulkarni, and A. C. Durst, "Quasiparticle scattering from vortices in dwave superconductors. II. Berry phase contribution," Phys. Rev. B 84, 064503 (2011) 
15. 

M. Kulkarni, S. Ganeshan, and A. C. Durst, "Quasiparticle scattering from vortices in dwave superconductors. I. Superflow contribution," Phys. Rev. B 84, 064502 (2011) 
14. 

S. Walter, D. Schneble, and A. C. Durst, "Bloch oscillations in lattice potentials with controlled aperiodicity," Phys. Rev. A 81, 033623 (2010) 
13. 

P. R. Schiff and A. C. Durst, "Effect of coexisting order of various form and wave vector on lowtemperature thermal conductivity in dwave superconductors," Phys. Rev. B 81, 054504 (2010) 
12. 

P. R. Schiff and A. C. Durst, "Low temperature thermal conductivity in a dwave superconductor with coexisting charge order: Effect of selfconsistent disorder and vertex corrections," Physica C 469, 740 (2009) 
11. 

A. C. Durst and S. Sachdev, "Low temperature quasiparticle transport in a dwave superconductor with coexisting charge order," Phys. Rev. B 80, 054518 (2009) 
10. 

A. C. Durst, "Resistance is futile," Nature (News & Views) 442, 752 (2006) 
9. 

A. C. Durst and S. M. Girvin, "Cooking a twodimensional electron gas with microwaves," Science (Perspective) 304, 1752 (2004) 
8. 

A. C. Durst, S. Sachdev, N. Read, and S. M. Girvin, "Radiationinduced magnetoresistance oscillations in a 2D electron gas," Proceedings of the 13th International Winterschool on New Developments in Solid State Physics  LowDimensional Systems, Physica E 25, 198 (2004) 
7. 

A. C. Durst, S. Sachdev, N. Read, and S. M. Girvin, "Radiationinduced magnetoresistance oscillations in a 2D electron gas," Proceedings of the International Symposium Quantum Hall Effect: Past, Present and Future, edited by R. Haug and D. Weiss, Physica E 20, 117 (2003) 
6. 

A. C. Durst, S. Sachdev, N. Read, and S. M. Girvin, "Radiationinduced magnetoresistance oscillations in a 2D electron gas," Phys. Rev. Lett. 91, 086803 (2003) 
5. 

A. C. Durst, A. Vishwanath, and P. A. Lee, "Weakfield thermal Hall conductivity in the mixed state of dwave superconductors," Phys. Rev. Lett. 90, 187002 (2003) 
4. 

A. C. Durst and P. A. Lee, "Microwave conductivity due to scattering from extended linear defects in dwave superconductors," Phys. Rev. B 65, 094501 (2002) 
3. 

A. C. Durst, R. N. Bhatt, and P. A. Wolff, "Bound magnetic polaron interactions in insulating doped diluted magnetic semiconductors," Phys. Rev. B 65, 235205 (2002) 
2. 

A. C. Durst and P. A. Lee, "Impurityinduced quasiparticle transport and universallimit WiedemannFranz violation in dwave superconductors," Phys. Rev. B 62, 1270 (2000) 
1. 

P. A. Wolff, R. N. Bhatt, and A. C. Durst, "Polaronpolaron interactions in diluted magnetic semiconductors," J. Appl. Phys. 79, 5196 (1996) 
