Prof. Adam C. Durst
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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 -- acceptor-acceptor interactions in diluted magnetic semiconductors, radiation-induced magneto-transport in two-dimensional 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 d-wave superconducting state of the high-Tc 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 Bi2Se3. 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, "Low-temperature thermal transport at the interface of a topological insulator and a d-wave superconductor," Phys. Rev. B 91, 094519 (2015)], I considered the low-temperature thermal transport properties of the 2D proximity-induced superconducting state formed at the interface between a 3D strong topological insulator (TI) and a d-wave superconductor (dSC). Dirac Cones 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 interface-state 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, κ0, as a function of μ, as it is tuned through this transition. In the large and small μ limits, I obtained disorder-independent, closed-form expressions for κ0/T. The large μ expression is exactly half the value expected for a d-wave 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 well-defined manner.

In another recent paper [A. C. Durst, "Scattering states of a vortex in the proximity-induced superconducting state at the interface of a topological insulator and an s-wave superconductor," Phys. Rev. B 93, 064514 (2016)], I considered an isolated vortex in the two-dimensional proximity-induced superconducting state formed at the interface of a topological insulator and an s-wave superconductor (sSC). Prior calculations of the bound states of this system famously revealed a zero-energy 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 spin-momentum-locked massless Dirac form of the single-particle 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 two-channel problem with the vortex mixing particle-like and hole-like excitations. And as in the ordinary case, the same-channel differential cross section diverges in the forward direction due to the Aharonov-Bohm 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 particle-like or hole-like excitations are tuned through the Dirac point.

In a third recent paper [A. C. Durst, "Disorder-induced 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. Disorder The energy spectrum of the spherical TI surface is discrete, for a sphere of finite radius, and can be truncated by imposing a high-energy 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 = V0(θ,φ) + V(θ,φ)·σ, where V0 describes the spin-independent part of the disorder and the three components of V describe the spin-dependent part. I expand these four disorder functions in spherical harmonics and draw the expansion coefficients randomly from a four-dimensional, zero-mean 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 disorder-averaged density of states, ρ(E), by averaging over 200,000 different instantiations. Disorder broadens the Landau-level delta functions of the clean density of states into peaks that decay and merge together. If the spin-dependent term is dominant, these peaks split due to the breaking of the degeneracy between time-reversed partner states. Increasing disorder strength pushes states closer and closer to zero energy (the Dirac point), resulting in a low-energy density of states that becomes nonzero for sufficient disorder, typically approaching an energy-independent saturation value, for most classes of disorder. But for purely spin-dependent disorder with V either entirely out-of-surface or entirely in-surface, I identified intriguing disorder-induced features in the vicinity of the Dirac point. In the out-of-surface case, a new peak emerges at zero energy. In the in-surface case, one sees a symmetry-protected zero at zero energy, with ρ(E) increasing linearly toward nonzero-energy 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 acceptor-acceptor interactions in doped semiconductors. This work, discussed in a recent preprint [A. C. Durst, K. E. Castoria, and R. N. Bhatt, "Heitler-London model for acceptor-acceptor 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 Heitler-London model is used to describe acceptor-acceptor interactions. But due to valence band degeneracy and spin-orbit 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 acceptor-acceptor Heitler-London model using single-acceptor wave functions of the form proposed by Baldereschi and Lipari, which more accurately capture the physics of the acceptor states. We calculated the resulting acceptor-pair energy levels and found, in contrast to the two-level singlet-triplet splitting of the hydrogen molecule, a rich ten-level energy spectrum. Our results, computed as a function of inter-acceptor distance and spin-orbit coupling strength, suggest that acceptor-acceptor interactions can be qualitatively different from donor-donor interactions, and should therefore be relevant to the magnetic properties of a variety of p-doped semiconductor systems. Further insight was drawn by fitting numerical results to closed-form energy-level expressions obtained via an acceptor-acceptor 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 co-author 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, "Heitler-London model for acceptor-acceptor interactions in doped semiconductors," arXiv:1706.09841 (2017), under review at Phys. Rev. B

19.

 

A. C. Durst, "Disorder-induced 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 proximity-induced superconducting state at the interface of a topological insulator and an s-wave superconductor," Phys. Rev. B 93, 064514 (2016)

17.

 

A. C. Durst, "Low-temperature thermal transport at the interface of a topological insulator and a d-wave superconductor," Phys. Rev. B 91, 094519 (2015)

16.

 

S. Ganeshan, M. Kulkarni, and A. C. Durst, "Quasiparticle scattering from vortices in d-wave 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 d-wave 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 low-temperature thermal conductivity in d-wave superconductors," Phys. Rev. B 81, 054504 (2010)

12.

 

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

11.

 

A. C. Durst and S. Sachdev, "Low temperature quasiparticle transport in a d-wave 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 two-dimensional electron gas with microwaves," Science (Perspective) 304, 1752 (2004)

8.

 

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

7.

 

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

5.

 

A. C. Durst, A. Vishwanath, and P. A. Lee, "Weak-field thermal Hall conductivity in the mixed state of d-wave 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 d-wave 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, "Impurity-induced quasiparticle transport and universal-limit Wiedemann-Franz violation in d-wave superconductors," Phys. Rev. B 62, 1270 (2000)

1.

 

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

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