**Dr. Gunnar Þorgilsson**

Position: Assistant Professor

Website: http://www.ru.is/haskolinn/starfsfolk/gunnarth

# Research projects

- Spin and charge transport at nanoscale
- Methods of computational physics

# Publication

Anna Sitek, Gunnar Thorgilsson, Vidar Gudmundsson and Andrei Manolescu.

**Multi-domain electromagnetic absorption of triangular quantum rings**.*Nanotechnology*27, 225202 (2016).

Abstract We present a theoretical study of the unielectronic energy spectra, electron localization, and optical absorption of triangular core–shell quantum rings. We show how these properties depend on geometric details of the triangle, such as side thickness or corners’ symmetry. For equilateral triangles, the lowest six energy states (including spin) are grouped in an energy shell, are localized only around corner areas, and are separated by a large energy gap from the states with higher energy which are localized on the sides of the triangle. The energy levels strongly depend on the aspect ratio of the triangle sides, i.e., thickness/length ratio, in such a way that the energy differences are not monotonous functions of this ratio. In particular, the energy gap between the group of states localized in corners and the states localized on the sides strongly decreases with increasing the side thickness, and then slightly increases for thicker samples. With increasing the thickness the low-energy shell remains distinct but the spatial distribution of these states spreads. The behavior of the energy levels and localization leads to a thickness-dependent absorption spectrum where one transition may be tuned in the THz domain and a second transition can be tuned from THz to the infrared range of electromagnetic spectrum. We show how these features may be further controlled with an external magnetic field. In this work the electron–electron Coulomb repulsion is neglected.

URL arXiv, DOI BibTeX@article{0957-4484-27-22-225202, author = "Anna Sitek and Gunnar Thorgilsson and Vidar Gudmundsson and Andrei Manolescu", title = "Multi-domain electromagnetic absorption of triangular quantum rings", journal = "Nanotechnology", volume = 27, number = 22, pages = 225202, url = "http://stacks.iop.org/0957-4484/27/i=22/a=225202", year = 2016, doi = "10.1088/0957-4484/27/22/225202", arxiv = "http://arxiv.org/abs/1511.05596", abstract = "We present a theoretical study of the unielectronic energy spectra, electron localization, and optical absorption of triangular core–shell quantum rings. We show how these properties depend on geometric details of the triangle, such as side thickness or corners’ symmetry. For equilateral triangles, the lowest six energy states (including spin) are grouped in an energy shell, are localized only around corner areas, and are separated by a large energy gap from the states with higher energy which are localized on the sides of the triangle. The energy levels strongly depend on the aspect ratio of the triangle sides, i.e., thickness/length ratio, in such a way that the energy differences are not monotonous functions of this ratio. In particular, the energy gap between the group of states localized in corners and the states localized on the sides strongly decreases with increasing the side thickness, and then slightly increases for thicker samples. With increasing the thickness the low-energy shell remains distinct but the spatial distribution of these states spreads. The behavior of the energy levels and localization leads to a thickness-dependent absorption spectrum where one transition may be tuned in the THz domain and a second transition can be tuned from THz to the infrared range of electromagnetic spectrum. We show how these features may be further controlled with an external magnetic field. In this work the electron–electron Coulomb repulsion is neglected." }

G Thorgilsson, G Viktorsson and S I Erlingsson.

**Recursive Greenʼs function method for multi-terminal nanostructures**.*Journal of Computational Physics*261, 256 - 266 (2014).

Abstract Abstract We present and review an efficient method to calculate the retarded Greenʼs function in multi-terminal nanostructures; which is needed in order to calculate the conductance through the system and the local particle densities within it. The method uses the recursive Greenʼs function method after the discretized Hamilton matrix has been properly partitioned. We show that this method, the circular slicing scheme, can be modified to accommodate multi-terminal systems as well as the traditional two-terminal systems. Furthermore, we show that the performance and robustness of the circular slicing scheme is on par with other advanced methods and is well suited for large variety of multi-terminal geometries. We end by giving an example of how the method can be used to calculate transport in a non-trivial multi-terminal geometry.

URL arXiv, DOI BibTeX@article{Thorgilsson2014256, title = "Recursive Greenʼs function method for multi-terminal nanostructures", journal = "Journal of Computational Physics", volume = 261, number = 0, pages = "256 - 266", year = 2014, note = "", issn = "0021-9991", doi = "10.1016/j.jcp.2013.12.054", url = "http://www.sciencedirect.com/science/article/pii/S0021999114000096", author = "G. Thorgilsson and G. Viktorsson and S.I. Erlingsson", keywords = "Multi-terminal nanostructures", abstract = "Abstract We present and review an efficient method to calculate the retarded Greenʼs function in multi-terminal nanostructures; which is needed in order to calculate the conductance through the system and the local particle densities within it. The method uses the recursive Greenʼs function method after the discretized Hamilton matrix has been properly partitioned. We show that this method, the circular slicing scheme, can be modified to accommodate multi-terminal systems as well as the traditional two-terminal systems. Furthermore, we show that the performance and robustness of the circular slicing scheme is on par with other advanced methods and is well suited for large variety of multi-terminal geometries. We end by giving an example of how the method can be used to calculate transport in a non-trivial multi-terminal geometry.", arxiv = "http://arxiv.org/abs/1305.7363" }

Gunnar Thorgilsson, Carlos J Egues, Daniel Loss and Sigurdur I Erlingsson.

**Rashba spin orbit interaction in a quantum wire superlattice**.*Phys. Rev. B*85, 045306 (January 2012).

Abstract In this work, we study the effects of a longitudinal periodic potential on a parabolic quantum wire defined in a two-dimensional electron gas with Rashba spin-orbit interaction. For an infinite wire superlattice we find, by direct diagonalization, that the energy gaps are shifted away from the usual Bragg planes due to the Rashba spin-orbit interaction. Interestingly, our results show that the location of the band gaps in energy can be controlled via the strength of the Rashba spin-orbit interaction. We have also calculated the charge conductance through a periodic potential of a finite length via the nonequilibrium Green's function method combined with the Landauer formalism. We find dips in the conductance that correspond well to the energy gaps of the infinite wire superlattice. From the infinite wire energy dispersion, we derive an equation relating the location of the conductance dips as a function of the (gate controllable) Fermi energy to the Rashba spin-orbit coupling strength. We propose that the strength of the Rashba spin-orbit interaction can be extracted via a charge conductance measurement.

URL arXiv PDF, DOI BibTeX@article{PhysRevB.85.045306, title = "Rashba spin orbit interaction in a quantum wire superlattice", author = "Thorgilsson, Gunnar and Egues, J. Carlos and Loss, Daniel and Erlingsson, Sigurdur I.", journal = "Phys. Rev. B", volume = 85, issue = 4, pages = 045306, numpages = 8, year = 2012, month = "Jan", doi = "10.1103/PhysRevB.85.045306", url = "http://link.aps.org/doi/10.1103/PhysRevB.85.045306", publisher = "American Physical Society", abstract = "In this work, we study the effects of a longitudinal periodic potential on a parabolic quantum wire defined in a two-dimensional electron gas with Rashba spin-orbit interaction. For an infinite wire superlattice we find, by direct diagonalization, that the energy gaps are shifted away from the usual Bragg planes due to the Rashba spin-orbit interaction. Interestingly, our results show that the location of the band gaps in energy can be controlled via the strength of the Rashba spin-orbit interaction. We have also calculated the charge conductance through a periodic potential of a finite length via the nonequilibrium Green's function method combined with the Landauer formalism. We find dips in the conductance that correspond well to the energy gaps of the infinite wire superlattice. From the infinite wire energy dispersion, we derive an equation relating the location of the conductance dips as a function of the (gate controllable) Fermi energy to the Rashba spin-orbit coupling strength. We propose that the strength of the Rashba spin-orbit interaction can be extracted via a charge conductance measurement.", pdf = "http://www.researchgate.net/publication/51952398_Rashba_spin_orbit_interaction_in_a_quantum_wire_superlattice", arxiv = "http://arxiv.org/abs/1111.1534" }

Halldor Gudfinnur Svavarsson, JaeWoong Yoon, SeokHo Song and Robert Magnusson.

**Fabrication of Large Plasmonic Arrays of Gold Nanocups Using Inverse Periodic Templates**.*Plasmonics*6, 741-744 (2011).

Abstract A facile procedure to fabricate large arrays of highly ordered metal nanocups, 250 nm in diameter, is reported. The nanostructure is generated from periodic photoresist templates created by holographic laser interference lithography. A subsequent gold deposition and a peeling-off step respectively results in a large area of hemispherical nano-indentations or nanocups. A wide range of coating materials can be used, and the dimensions and periodicity of the structure are easily controlled. The structure’s ability to support localized surface plasmon polaritons was manifested by reflectance spectroscopy. A good correlation between experimental data and calculated data was observed.

URL, DOI BibTeX@article{, year = 2011, issn = "1557-1955", journal = "Plasmonics", volume = 6, number = 4, doi = "10.1007/s11468-011-9258-8", title = "Fabrication of Large Plasmonic Arrays of Gold Nanocups Using Inverse Periodic Templates", url = "http://dx.doi.org/10.1007/s11468-011-9258-8", publisher = "Springer US", keywords = "Nanocups; Periodic arrays; Nano-indented films; Plasmonics", author = "Svavarsson, Halldor Gudfinnur and Yoon, JaeWoong and Song, SeokHo and Magnusson, Robert", pages = "741-744", abstract = "A facile procedure to fabricate large arrays of highly ordered metal nanocups, 250 nm in diameter, is reported. The nanostructure is generated from periodic photoresist templates created by holographic laser interference lithography. A subsequent gold deposition and a peeling-off step respectively results in a large area of hemispherical nano-indentations or nanocups. A wide range of coating materials can be used, and the dimensions and periodicity of the structure are easily controlled. The structure’s ability to support localized surface plasmon polaritons was manifested by reflectance spectroscopy. A good correlation between experimental data and calculated data was observed.", language = "English" }

Gunnar Thorgilsson and Sigurdur I Erlingsson.

**Effects of scattering area shape on spin conductance in a four-terminal spin-Hall setup**.*Phys. Rev. B*82, 245308 (December 2010).

Abstract We study spin conductance in a ballistic and quasiballistic two-dimensional electron system with Rashba spin-orbit coupling. The system has a four-terminal geometry with round corners at the connection to the leads. It is found that by going from sharp corners to more round corners in the ballistic system the energy-depended spin conductance goes from being relatively flat to a curve showing a series of minima and maxima. It is also found that when changing the size of the terminal area by modifying the roundness of the terminal corners the maxima and minima in the transverse spin conductance are shifted in energy. This shift is due increased (decreased) energy for smaller (larger) terminal area. These results were also found to be reasonably stable in quasiballistic systems.

URL arXiv, DOI BibTeX@article{PhysRevB.82.245308, title = "Effects of scattering area shape on spin conductance in a four-terminal spin-Hall setup", author = "Thorgilsson, Gunnar and Erlingsson, Sigurdur I.", journal = "Phys. Rev. B", volume = 82, issue = 24, pages = 245308, numpages = 7, year = 2010, month = "Dec", doi = "10.1103/PhysRevB.82.245308", url = "http://link.aps.org/doi/10.1103/PhysRevB.82.245308", publisher = "American Physical Society", abstract = "We study spin conductance in a ballistic and quasiballistic two-dimensional electron system with Rashba spin-orbit coupling. The system has a four-terminal geometry with round corners at the connection to the leads. It is found that by going from sharp corners to more round corners in the ballistic system the energy-depended spin conductance goes from being relatively flat to a curve showing a series of minima and maxima. It is also found that when changing the size of the terminal area by modifying the roundness of the terminal corners the maxima and minima in the transverse spin conductance are shifted in energy. This shift is due increased (decreased) energy for smaller (larger) terminal area. These results were also found to be reasonably stable in quasiballistic systems.", arxiv = "http://arxiv.org/abs/1111.1529" }

Gunnar Thorgilsson and Sigurdur I Erlingsson.

**Transport in four-terminal semiconductor nanostructures with Rashba spin–orbit interaction**.*Physica Scripta*2010, 014014 (2010).

Abstract We studied spin transport in a four-terminal system with Rashba spin–orbit coupling. Using discretization, we convert the non-equilibrium Green's function equations into matrix equations, which are then solved using the recursive Green's function method. The calculations show that having round edges in the scattering region leads to a more regular spin polarization, indicating that the shape of the scattering region can be used as an additional control for spintronics applications.

URL BibTeX@article{1402-4896-2010-T141-014014, author = "Gunnar Thorgilsson and Sigurdur I Erlingsson", title = "Transport in four-terminal semiconductor nanostructures with Rashba spin–orbit interaction", journal = "Physica Scripta", volume = 2010, number = "T141", pages = 014014, url = "http://stacks.iop.org/1402-4896/2010/i=T141/a=014014", year = 2010, abstract = "We studied spin transport in a four-terminal system with Rashba spin–orbit coupling. Using discretization, we convert the non-equilibrium Green's function equations into matrix equations, which are then solved using the recursive Green's function method. The calculations show that having round edges in the scattering region leads to a more regular spin polarization, indicating that the shape of the scattering region can be used as an additional control for spintronics applications." }