![Statement of Research
Jeremy Capps
Department of Physics and Astronomy
Clemson University
Current Research
My research projects have mostly focused on computationally investigating fully interacting
quantum systems endowed with spin-orbit interaction (SOI). To model physical electron sys-
tems more accurately, the Coulomb interaction and electronic screening effects are included in
the simulations. For Friedel oscillations, we begin by calculating analytically and numerically
the Lindhard polarization function Π(q, ω) to realize self-consistently [1] the charge-density
response function χ(q, ω) in the momentum-space of these systems. In the case of spin and
charge transport properties, we investigate the role of SOI in the realization of a magnetic
ordering lower in energy than the usual paramagnetic state, resulting in significant enhance-
ment of the Seebeck (charge and spin) coefficient for GaAs and InAs systems in the regime
of equal Rashba-Dresselhaus spin-orbit couplign strengths.
Friedel Oscillations
The spin-orbit interaction has played a vital role in the field of spintronics. The interaction,
which is a consequence of potential well inversion asymmetry (Rashba) or bulk inversion
asymmetry (Dresselhaus), results in a significant change in the single-particle energy spec-
trum as well as many static and dynamic properties. We have focused specifically on the
consequences of including a Rashba SO term in a lateral superlattice (LSL). The SO inter-
actions are very important in GaAs 2D systems. There is much interest in the LSL system
because of the recent experimental findings [2, 3] that there is robust spin-coupling on the
surface of Au(111) with vicinal cuts, or terraces, patterned periodically perpendicular to the
SL axis. The density of these terraces influences the behavior of the electron confinement.
Too few steps (lower terrace density) results in total electron confinement along the SL axis,
while a high terrace density results in total delocalization along the average surface.
To investigate the sustainable Friedel oscillations in the LSL system, one must consider
the static case of the density response function (ω = 0). Also, the impurity can be either
neutral or charged. The more interesting is the neutral case, where beating in the real-
space charge density oscillations is found [4]. This beating is traditionally found in systems
that exhibit both Rashba and Dresselhaus SO interactions. However, for the LSL system,
the geometry leads to periodic behavior in the energy spectrum. This, combined with the
constant impurity contribution in momentum-space, results in same beating behaviour. The
system was modeled as a series of delta-function potentials along the LSL axis. Delta-
functions were used because one deals with only one bound state, and the results are still
in good agreement with more sophisticated models, such as the Kronig-Penney model. The
real-space oscillations are calculated numerically via Fourier transform. It was concluded
1](https://image.slidesharecdn.com/09726711-d243-483a-a78f-0366f1c0d596-150504135809-conversion-gate02/85/ResearchStatementCapps2-1-320.jpg)
![that the amplitudes of oscillation are mostly sensitive to the lattice spacing between the
gates (∼30 − 50nm), but also dependent on the Rashba coupling strength itself [5].
Spin and Charge Transport in 2D Electron Systems
Currently I am focused on investigating enhanced spin and charge tranport in simple 2D
Fermi systems endowed with spin-orbit interaction. The degeneracy of opposite-spin elec-
trons in momentum-space indicate that a long-range magnetic ordering may exist that is
lower in energy than the usual paramagnetic state, namely that of the intinerant antiferro-
magnetic (IAF) state, which allows for continuous spin-rotation in momentum space, and
results in a gap at the previously degeneracy point. This was a fundamental idea behind the
spin-density waves first proposed by Overhauser in the 1960’s [6, 7]. A many-body calcula-
tion in the Hartree-Fock approximation verifies the existance of this IAF magnetic ordering,
which transitions to the usual paramagnetic state above a critical temperaure TC.
Full calculations of the gap in momentum-space are performed, allowing us to investigate
the effects of screening on the transition temperature, as well as construct the relation time
of the quasi-particles to be used in defining the charge and spin currents and conductances.
These expressions are used to directly calculate the spin and charge Seebeck transport coef-
ficient for the system in both GaAs and InAs [8, 9].
Future Research
In the future I intend to continue investigating 2D quantum systems that exhibit exotic
phenomena due to spin-orbit interactions. Extensions of my research would entail enhanced
transport properties in simple 2D Fermi systems. This includes calculating and simulating
thermoelectric properties of materials, specifically Seebeck coefficients along with thermal
and electrical conductivities, that may be used to further improve the efficiency of energy
scavenging technologies.
References
[1] C. Kukkonen, A. Overhauser, Phys. Rev. B, Vol. 20, Number 2 (1979)
[2] J. Lobo-Checa, F. Meier, J. Dil, T. Okuda, M. Corso, V. Petrov, M. Hengsberger, L.
Patthey, and J. Osterwalder, PRL 104, 187602 (2010)
[3] P. Sprunger, L. Petersen, E. Plummer, E. Laegsgaard, F. Besenbacher, Science 275,
1764 (1997)
[4] S. Badalyan, A. Matos-Abiague, G. Vignale, J. Fabian, Phys. Rev. B 81, 205314 (2010)
[5] J. Capps, D. Marinescu, C. Sosolik, M. Daniels, To be published by Edizioni della
Normale (Pisa, Italy) in a volume in honor of Gabriele F. Giuliani edited by M. Polini,
G. Vignale, V. Pellegrini, and J. K. Jain (2014) (Invited)
2](https://image.slidesharecdn.com/09726711-d243-483a-a78f-0366f1c0d596-150504135809-conversion-gate02/85/ResearchStatementCapps2-2-320.jpg)
![[6] Overhauser, A. W., Phys. Rev. Lett. 4, 9, 462-465 (1960)
[7] Overhauser, A. W., Phys. Rev. 128, 3, 1437-1452 (1962)
[8] D. C. Marinescu, Andrei Manolescu and Jeremy Capps, Proc. SPIE 9167, Spintronics
VII, 91671M (2014)
[9] Capps, Jeremy and Marinescu, D. C. and Manolescu, Andrei, Phys. Rev. B 91, 16,
165301 (2015)
3](https://image.slidesharecdn.com/09726711-d243-483a-a78f-0366f1c0d596-150504135809-conversion-gate02/85/ResearchStatementCapps2-3-320.jpg)
ResearchStatementCapps2
- 1. Statement of Research Jeremy Capps Department of Physics and Astronomy Clemson University Current Research My research projects have mostly focused on computationally investigating fully interacting quantum systems endowed with spin-orbit interaction (SOI). To model physical electron sys- tems more accurately, the Coulomb interaction and electronic screening effects are included in the simulations. For Friedel oscillations, we begin by calculating analytically and numerically the Lindhard polarization function Π(q, ω) to realize self-consistently [1] the charge-density response function χ(q, ω) in the momentum-space of these systems. In the case of spin and charge transport properties, we investigate the role of SOI in the realization of a magnetic ordering lower in energy than the usual paramagnetic state, resulting in significant enhance- ment of the Seebeck (charge and spin) coefficient for GaAs and InAs systems in the regime of equal Rashba-Dresselhaus spin-orbit couplign strengths. Friedel Oscillations The spin-orbit interaction has played a vital role in the field of spintronics. The interaction, which is a consequence of potential well inversion asymmetry (Rashba) or bulk inversion asymmetry (Dresselhaus), results in a significant change in the single-particle energy spec- trum as well as many static and dynamic properties. We have focused specifically on the consequences of including a Rashba SO term in a lateral superlattice (LSL). The SO inter- actions are very important in GaAs 2D systems. There is much interest in the LSL system because of the recent experimental findings [2, 3] that there is robust spin-coupling on the surface of Au(111) with vicinal cuts, or terraces, patterned periodically perpendicular to the SL axis. The density of these terraces influences the behavior of the electron confinement. Too few steps (lower terrace density) results in total electron confinement along the SL axis, while a high terrace density results in total delocalization along the average surface. To investigate the sustainable Friedel oscillations in the LSL system, one must consider the static case of the density response function (ω = 0). Also, the impurity can be either neutral or charged. The more interesting is the neutral case, where beating in the real- space charge density oscillations is found [4]. This beating is traditionally found in systems that exhibit both Rashba and Dresselhaus SO interactions. However, for the LSL system, the geometry leads to periodic behavior in the energy spectrum. This, combined with the constant impurity contribution in momentum-space, results in same beating behaviour. The system was modeled as a series of delta-function potentials along the LSL axis. Delta- functions were used because one deals with only one bound state, and the results are still in good agreement with more sophisticated models, such as the Kronig-Penney model. The real-space oscillations are calculated numerically via Fourier transform. It was concluded 1
- 2. that the amplitudes of oscillation are mostly sensitive to the lattice spacing between the gates (∼30 − 50nm), but also dependent on the Rashba coupling strength itself [5]. Spin and Charge Transport in 2D Electron Systems Currently I am focused on investigating enhanced spin and charge tranport in simple 2D Fermi systems endowed with spin-orbit interaction. The degeneracy of opposite-spin elec- trons in momentum-space indicate that a long-range magnetic ordering may exist that is lower in energy than the usual paramagnetic state, namely that of the intinerant antiferro- magnetic (IAF) state, which allows for continuous spin-rotation in momentum space, and results in a gap at the previously degeneracy point. This was a fundamental idea behind the spin-density waves first proposed by Overhauser in the 1960’s [6, 7]. A many-body calcula- tion in the Hartree-Fock approximation verifies the existance of this IAF magnetic ordering, which transitions to the usual paramagnetic state above a critical temperaure TC. Full calculations of the gap in momentum-space are performed, allowing us to investigate the effects of screening on the transition temperature, as well as construct the relation time of the quasi-particles to be used in defining the charge and spin currents and conductances. These expressions are used to directly calculate the spin and charge Seebeck transport coef- ficient for the system in both GaAs and InAs [8, 9]. Future Research In the future I intend to continue investigating 2D quantum systems that exhibit exotic phenomena due to spin-orbit interactions. Extensions of my research would entail enhanced transport properties in simple 2D Fermi systems. This includes calculating and simulating thermoelectric properties of materials, specifically Seebeck coefficients along with thermal and electrical conductivities, that may be used to further improve the efficiency of energy scavenging technologies. References [1] C. Kukkonen, A. Overhauser, Phys. Rev. B, Vol. 20, Number 2 (1979) [2] J. Lobo-Checa, F. Meier, J. Dil, T. Okuda, M. Corso, V. Petrov, M. Hengsberger, L. Patthey, and J. Osterwalder, PRL 104, 187602 (2010) [3] P. Sprunger, L. Petersen, E. Plummer, E. Laegsgaard, F. Besenbacher, Science 275, 1764 (1997) [4] S. Badalyan, A. Matos-Abiague, G. Vignale, J. Fabian, Phys. Rev. B 81, 205314 (2010) [5] J. Capps, D. Marinescu, C. Sosolik, M. Daniels, To be published by Edizioni della Normale (Pisa, Italy) in a volume in honor of Gabriele F. Giuliani edited by M. Polini, G. Vignale, V. Pellegrini, and J. K. Jain (2014) (Invited) 2
- 3. [6] Overhauser, A. W., Phys. Rev. Lett. 4, 9, 462-465 (1960) [7] Overhauser, A. W., Phys. Rev. 128, 3, 1437-1452 (1962) [8] D. C. Marinescu, Andrei Manolescu and Jeremy Capps, Proc. SPIE 9167, Spintronics VII, 91671M (2014) [9] Capps, Jeremy and Marinescu, D. C. and Manolescu, Andrei, Phys. Rev. B 91, 16, 165301 (2015) 3