**Dr. Sigurður Ingi Erlingsson**

Position: Associate Professor

Website: http://www.ru.is/starfsfolk/sie

# Research projects

- Topological insulators
- Resonant flurescence in quantum dots

The focus of my reseach is theoretical condensed matter physics. I've worked on the effects of hyperfine interaction on spin dynamics in GaAs quantum dots. The role played by the Rashba spin-orbit interaction in transport in semiconductor nanostructure is something I've studied for a few years now. In order to highlight the role played by the the spin-orbit interaction I've worked on multiterminal systems (the spin-Hall effect) and transport throught periodic potential in a two terminal setup. I've also working on novel interface phenomena in magnetotransport in metallic spin-valve systems using resistor network model. More recently I've started working on topological isulators.

# Publication

Joanna M Zajac and Sigurdur I Erlingsson.

**Temperature dependency of resonance fluorescence from InAs/GaAs quantum dots: Dephasing mechanisms**.*Phys. Rev. B*94, 035432 (July 2016).

Abstract We report a study on temperature-dependent resonant fluorescence from InAs/GaAs quantum dots. We combined spectral and temporal measurements in order to identify sources of dephasing. In the spectral domain, we observed temperature-dependent broadening of the zero-phonon line as 0.3 ?eV/K, and a temperature-dependent phonon broadband. Time-resolved autocorrelation measurements revealed temperature-dependent spin pumping times between T$_1$$_,$$_s$=6 ns (4 K) and 0.5 ns (15 K). These results are compared against theoretical modeling with a master equation for a four-level system coupled to phonon and spin baths. We explained the results by phonon-mediated hole-spin scattering between two excited states, with the piezophonons as a dominant mechanism.

URL, DOI BibTeX@article{PhysRevB.94.035432, title = "Temperature dependency of resonance fluorescence from InAs/GaAs quantum dots: Dephasing mechanisms", author = "Zajac, Joanna M. and Erlingsson, Sigurdur I.", journal = "Phys. Rev. B", volume = 94, issue = 3, pages = 035432, numpages = 7, year = 2016, month = "Jul", publisher = "American Physical Society", doi = "10.1103/PhysRevB.94.035432", url = "http://link.aps.org/doi/10.1103/PhysRevB.94.035432", abstract = "We report a study on temperature-dependent resonant fluorescence from InAs/GaAs quantum dots. We combined spectral and temporal measurements in order to identify sources of dephasing. In the spectral domain, we observed temperature-dependent broadening of the zero-phonon line as 0.3 ?eV/K, and a temperature-dependent phonon broadband. Time-resolved autocorrelation measurements revealed temperature-dependent spin pumping times between T$_1$$_,$$_s$=6 ns (4 K) and 0.5 ns (15 K). These results are compared against theoretical modeling with a master equation for a four-level system coupled to phonon and spin baths. We explained the results by phonon-mediated hole-spin scattering between two excited states, with the piezophonons as a dominant mechanism." }

Andrei Manolescu, George Alexandru Nemnes, Anna Sitek, Tomas Orn Rosdahl, Sigurdur Ingi Erlingsson and Vidar Gudmundsson.

**Conductance oscillations of core-shell nanowires in transversal magnetic fields**.*Phys. Rev. B*93, 205445 (May 2016).

Abstract We analyze theoretically electronic transport through a core-shell nanowire in the presence of a transversal magnetic field. We calculate the conductance for a variable coupling between the nanowire and the attached leads and show how the snaking states, which are low-energy states localized along the lines of the vanishing radial component of the magnetic field, manifest their existence. In the strong-coupling regime they induce flux periodic, Aharonov-Bohm-like, conductance oscillations, which, by decreasing the coupling to the leads, evolve into well-resolved peaks. The flux periodic oscillations arise due to interference of the snaking states, which is a consequence of backscattering at either the contacts with leads or magnetic or potential barriers in the wire.

URL arXiv, DOI BibTeX@article{PhysRevB.93.205445, title = "Conductance oscillations of core-shell nanowires in transversal magnetic fields", author = "Manolescu, Andrei and Nemnes, George Alexandru and Sitek, Anna and Rosdahl, Tomas Orn and Erlingsson, Sigurdur Ingi and Gudmundsson, Vidar", journal = "Phys. Rev. B", volume = 93, issue = 20, pages = 205445, numpages = 6, year = 2016, month = "May", publisher = "American Physical Society", doi = "10.1103/PhysRevB.93.205445", arxiv = "http://arxiv.org/abs/1601.01477", url = "http://link.aps.org/doi/10.1103/PhysRevB.93.205445", abstract = "We analyze theoretically electronic transport through a core-shell nanowire in the presence of a transversal magnetic field. We calculate the conductance for a variable coupling between the nanowire and the attached leads and show how the snaking states, which are low-energy states localized along the lines of the vanishing radial component of the magnetic field, manifest their existence. In the strong-coupling regime they induce flux periodic, Aharonov-Bohm-like, conductance oscillations, which, by decreasing the coupling to the leads, evolve into well-resolved peaks. The flux periodic oscillations arise due to interference of the snaking states, which is a consequence of backscattering at either the contacts with leads or magnetic or potential barriers in the wire." }

Sigurdur I Erlingsson, Andrei Manolescu and D C Marinescu.

**Asymmetric Landau bands due to spin–orbit coupling**.*Journal of Physics: Condensed Matter*27, 225303 (2015).

Abstract We show that the Landau bands obtained in a two-dimensional lateral semiconductor superlattice with spin–orbit coupling (SOC) of the Rashba/Dresselhaus type, linear in the electron momentum, placed in a tilted magnetic field, do not follow the symmetry of the spatial modulation. Moreover, this phenomenology is found to depend on the relative tilt of magnetic field and on the SOC type: (a) when only Rashba SOC exists and the magnetic field is tilted in the direction of the superlattice (b) Dresselhaus SOC exists and the magnetic field is tilted in the direction perpendicular to the superlattice. Consequently, measurable properties of the modulated system become anisotropic in a tilted magnetic field when the field is conically rotated around the z axis, at a fixed polar angle, as we demonstrate by calculating the resistivity and the magnetization.

URL arXiv, DOI BibTeX@article{0953-8984-27-22-225303, author = "Sigurdur I Erlingsson and Andrei Manolescu and D C Marinescu", title = "Asymmetric Landau bands due to spin–orbit coupling", journal = "Journal of Physics: Condensed Matter", volume = 27, number = 22, pages = 225303, url = "http://stacks.iop.org/0953-8984/27/i=22/a=225303", year = 2015, doi = "10.1088/0953-8984/27/22/225303", abstract = "We show that the Landau bands obtained in a two-dimensional lateral semiconductor superlattice with spin–orbit coupling (SOC) of the Rashba/Dresselhaus type, linear in the electron momentum, placed in a tilted magnetic field, do not follow the symmetry of the spatial modulation. Moreover, this phenomenology is found to depend on the relative tilt of magnetic field and on the SOC type: (a) when only Rashba SOC exists and the magnetic field is tilted in the direction of the superlattice (b) Dresselhaus SOC exists and the magnetic field is tilted in the direction perpendicular to the superlattice. Consequently, measurable properties of the modulated system become anisotropic in a tilted magnetic field when the field is conically rotated around the z axis, at a fixed polar angle, as we demonstrate by calculating the resistivity and the magnetization.", arxiv = "http://arxiv.org/abs/1504.04699" }

Sigurdur I Erlingsson and Carlos J Egues.

**All-electron topological insulator in InAs double wells**.*Phys. Rev. B*91, 035312 (January 2015).

Abstract We show that electrons in ordinary III-V semiconductor double wells with an in-plane modulating periodic potential and interwell spin-orbit interaction are tunable topological insulators (TIs). Here the essential TI ingredients, namely, band inversion and the opening of an overall bulk gap in the spectrum arise, respectively, from (i) the combined effect of the double-well even-odd state splitting \(\Delta\)SAS together with the superlattice potential and (ii) the interband Rashba spin-orbit coupling \(\eta\). We corroborate our exact diagonalization results with an analytical nearly-free-electron description that allows us to derive an effective Bernevig-Hughes-Zhang model. Interestingly, the gate-tunable mass gap M drives a topological phase transition featuring a discontinuous Chern number at \(\Delta\)SAS\(\sim\)5.4meV. Finally, we explicitly verify the bulk-edge correspondence by considering a strip configuration and determining not only the bulk bands in the nontopological and topological phases but also the edge states and their Dirac-like spectrum in the topological phase. The edge electronic densities exhibit peculiar spatial oscillations as they decay away into the bulk. For concreteness, we present our results for InAs-based wells with realistic parameters

URL arXiv, DOI BibTeX@article{PhysRevB.91.035312, title = "All-electron topological insulator in InAs double wells", author = "Erlingsson, Sigurdur I. and Egues, J. Carlos", journal = "Phys. Rev. B", volume = 91, issue = 3, pages = 035312, numpages = 8, year = 2015, month = "Jan", publisher = "American Physical Society", doi = "10.1103/PhysRevB.91.035312", url = "http://link.aps.org/doi/10.1103/PhysRevB.91.035312", arxiv = "http://arxiv.org/abs/1312.2034", abstract = "We show that electrons in ordinary III-V semiconductor double wells with an in-plane modulating periodic potential and interwell spin-orbit interaction are tunable topological insulators (TIs). Here the essential TI ingredients, namely, band inversion and the opening of an overall bulk gap in the spectrum arise, respectively, from (i) the combined effect of the double-well even-odd state splitting \(\Delta\)SAS together with the superlattice potential and (ii) the interband Rashba spin-orbit coupling \(\eta\). We corroborate our exact diagonalization results with an analytical nearly-free-electron description that allows us to derive an effective Bernevig-Hughes-Zhang model. Interestingly, the gate-tunable mass gap M drives a topological phase transition featuring a discontinuous Chern number at \(\Delta\)SAS\(\sim\)5.4meV. Finally, we explicitly verify the bulk-edge correspondence by considering a strip configuration and determining not only the bulk bands in the nontopological and topological phases but also the edge states and their Dirac-like spectrum in the topological phase. The edge electronic densities exhibit peculiar spatial oscillations as they decay away into the bulk. For concreteness, we present our results for InAs-based wells with realistic parameters" }

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" }

Kristinn Torfason, Andrei Manolescu, Sigurdur I Erlingsson and Vidar Gudmundsson.

**Thermoelectric current and Coulomb-blockade plateaus in a quantum dot**.*Physica E: Low-dimensional Systems and Nanostructures*53, 178 - 185 (2013).

Abstract A Generalized Master Equation (GME) is used to study the thermoelectric currents through a quantum dot in both the transient and steady-state regime. The two semi-infinite leads are kept at the same chemical potential but at different temperatures to produce a thermoelectric current which has a varying sign depending on the chemical potential. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. We observe a saw-teeth like profile of the current alternating with plateaus of almost zero current. Our calculations go beyond the linear response with respect to the temperature gradient, but are compatible with known results for the thermopower in the linear response regime.

URL arXiv, DOI BibTeX@article{Torfason2013178, title = "Thermoelectric current and Coulomb-blockade plateaus in a quantum dot", journal = "Physica E: Low-dimensional Systems and Nanostructures", volume = 53, number = 0, pages = "178 - 185", year = 2013, note = "", issn = "1386-9477", doi = "10.1016/j.physe.2013.05.005", url = "http://www.sciencedirect.com/science/article/pii/S1386947713001689", author = "Kristinn Torfason and Andrei Manolescu and Sigurdur I. Erlingsson and Vidar Gudmundsson", abstract = "A Generalized Master Equation (GME) is used to study the thermoelectric currents through a quantum dot in both the transient and steady-state regime. The two semi-infinite leads are kept at the same chemical potential but at different temperatures to produce a thermoelectric current which has a varying sign depending on the chemical potential. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. We observe a saw-teeth like profile of the current alternating with plateaus of almost zero current. Our calculations go beyond the linear response with respect to the temperature gradient, but are compatible with known results for the thermopower in the linear response regime.", arxiv = "http://arxiv.org/abs/1303.3160" }

Karel Vborn, Goran Mihajlović, Axel Hoffmann and Sigurdur I Erlingsson.

**Magnetic field dependence of non-local lateral spin-valve signals beyond the Hanle effect**.*Journal of Physics: Condensed Matter*25, 216007 (2013).

Abstract We present a theoretical model of spin transport in metallic lateral valves that takes into account spin scattering on magnetic impurities. We show that the model agrees with recent experimental findings of increasing non-local spin signals by in-plane magnetic field, which is parallel to the injected spins. The increase arises due to reduction of conduction electron spin flips on magnetic impurities present at the metalferromagnet interfaces as they freeze out under application of the magnetic field.

URL, DOI BibTeX@article{0953-8984-25-21-216007, author = "Karel Vborn and Goran Mihajlović and Axel Hoffmann and Sigurdur I Erlingsson", title = "Magnetic field dependence of non-local lateral spin-valve signals beyond the Hanle effect", journal = "Journal of Physics: Condensed Matter", volume = 25, number = 21, pages = 216007, url = "http://stacks.iop.org/0953-8984/25/i=21/a=216007", doi = "10.1088/0953-8984/25/21/216007", year = 2013, abstract = "We present a theoretical model of spin transport in metallic lateral valves that takes into account spin scattering on magnetic impurities. We show that the model agrees with recent experimental findings of increasing non-local spin signals by in-plane magnetic field, which is parallel to the injected spins. The increase arises due to reduction of conduction electron spin flips on magnetic impurities present at the metalferromagnet interfaces as they freeze out under application of the magnetic field." }

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" }

G Mihajlović, S I Erlingsson, K Výborný, J E Pearson, S D Bader and A Hoffmann.

**Magnetic-field enhancement of nonlocal spin signal in Ni80Fe20/Ag lateral spin valves**.*Phys. Rev. B*84, 132407 (October 2011).

Abstract We observe a magnetic-field-induced enhancement of the nonlocal spin signal in Ni80Fe20/Ag lateral spin valves. The enhancement depends on the bias current polarity but not on the field direction. We present a theoretical model that explains our experimental results, taking into account the electron-spin relaxation of magnetic impurities. We find that the relaxation is about an order of magnitude weaker than Elliott-Yafet relaxation.

URL PDF, DOI BibTeX@article{PhysRevB.84.132407, title = "Magnetic-field enhancement of nonlocal spin signal in Ni80Fe20/Ag lateral spin valves", author = "Mihajlović, G. and Erlingsson, S. I. and V\'yborn\'y, K. and Pearson, J. E. and Bader, S. D. and Hoffmann, A.", journal = "Phys. Rev. B", volume = 84, issue = 13, pages = 132407, numpages = 4, year = 2011, month = "Oct", doi = "10.1103/PhysRevB.84.132407", url = "http://link.aps.org/doi/10.1103/PhysRevB.84.132407", publisher = "American Physical Society", abstract = "We observe a magnetic-field-induced enhancement of the nonlocal spin signal in Ni80Fe20/Ag lateral spin valves. The enhancement depends on the bias current polarity but not on the field direction. We present a theoretical model that explains our experimental results, taking into account the electron-spin relaxation of magnetic impurities. We find that the relaxation is about an order of magnitude weaker than Elliott-Yafet relaxation.", pdf = "http://unix12.fzu.cz/~vybornyk/physics/publ-download/lit/10.1103/PhysRevB.84.132407.pdf" }

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." }

Sigurdur I Erlingsson, Carlos J Egues and Daniel Loss.

**Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions**.*Phys. Rev. B*82, 155456 (October 2010).

Abstract We introduce an analytical approximation scheme to diagonalize parabolically confined two-dimensional (2D) electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and noncrossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength $k_R$ℓ of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the nth Landau-level gn factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

URL, DOI BibTeX@article{PhysRevB.82.155456, title = "Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions", author = "Erlingsson, Sigurdur I. and Egues, J. Carlos and Loss, Daniel", journal = "Phys. Rev. B", volume = 82, issue = 15, pages = 155456, numpages = 12, year = 2010, month = "Oct", doi = "10.1103/PhysRevB.82.155456", url = "http://link.aps.org/doi/10.1103/PhysRevB.82.155456", abstract = "We introduce an analytical approximation scheme to diagonalize parabolically confined two-dimensional (2D) electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and noncrossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength $k_R$ℓ of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the nth Landau-level gn factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.", publisher = "American Physical Society" }