# Project

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## Effects of strong spin-orbit coupling in noncentrosymmetric two-dimensional metals

 English title Effects of strong spin-orbit coupling in noncentrosymmetric two-dimensional metals Mudry Christopher 129540 Project funding (Div. I-III) Paul Scherrer Institut Paul Scherrer Institute - PSI Condensed Matter Physics 01.07.2010 - 30.06.2013 153'499.00
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### Keywords (4)

unconventional superconductivity; spin-orbit interaction; superconductivity; quantum magnetism

### Lay Summary (English)

Lay summary
One of the greatest triumphs of Dirac was to predict the value taken by the Land\'e $g$ factor that controls the Zeeman interaction between the spin of a free electron and an applied magnetic field.Another consequence of the Dirac equation is the prediction of a spin-orbit coupling between the spin of an electron and its angular momentum, when it orbits around a central potential.The closer the orbit of the electron is to the origin of the central potential, the stronger this effect.The spin-orbit coupling is, of course, essential to explain atomic spectra, in particular when the atomic number $Z$ is large.Electrons confined to a quasi-two-dimensional geometry as occurs at the interfaces between semiconductors, Mott insulators, or as occurs on the surface of three-dimensional bulk crystals can be exposed to a strong spin-orbit coupling, since there is no inversion symmetry perpendicular to the plane.The low-dimensionality also favors interaction effects and fluctuation-driven phenomena. Compared to the literature dedicated to the instabilities of a two-dimensional metal without spin-orbit coupling, there is relatively little theoretical work done on the instabilities of a \textit{correlated two-dimensional metal with strong spin-orbit coupling}.The goal of this project is to go beyond the single-particle approximation and to explore the competing instabilities of noncentrosymmetric quasi-two-dimensional metals, with an emphasis on the superconducting and magnetic instabilities that are driven by the subtle interplay between \textit{strong} spin-orbit couplings and \textit{strong} fluctuations induced by electron-phonon and electron-electron interactions.
 Direct link to Lay Summary Last update: 21.02.2013

### Responsible applicant and co-applicants

Name Institute
 Mudry Christopher Paul Scherrer Institut

### Employees

Name Institute
 Neupert Titus Physik-Institut Universität Zürich

### Publications

Publication
Neupert Titus, Sigrist Manfred (2012), Coexistence of Ferromagnetism and Superconductivity in Noncentrosymmetric Materials with Cubic Symmetry, in JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN , 80, 114712.
Landolt Gabriel, Eremeev Sergey V., Koroteev Yury M., et al. (2012), Disentanglement of Surface and Bulk Rashba Spin Splittings in Noncentrosymmetric BiTeI, in PHYSICAL REVIEW LETTERS, 109 , 116403.
Neupert T, Santos L, Chamon C, Mudry C (2012), Elementary formula for the Hall conductivity of interacting systems, in PHYSICAL REVIEW B , 86, 165133.
Grushin AG, Neupert T, Chamon C, Mudry C (2012), Enhancing the stability of a fractional Chern insulator against competing phases, in Phys. Rev. B, 86, 205125.
Biswas PK, Luetkens H, Neupert T, et al (2012), Evidence for superconductivity with broken time-reversal symmetry in locally noncentrosymmetric SrPtAs, in PHYSICAL REVIEW B, 87, 180503.
Neupert Titus, Santos Luiz, Ryu Shinsei, et al. (2012), Noncommutative geometry for three-dimensional topological insulators, in PHYSICAL REVIEW B, 86, 035125.
Neupert T, Santos L, Ryu S, Chamon C, Mudry C (2012), Topological Hubbard Model and Its High-Temperature Quantum Hall Effect, in PHYSICAL REVIEW LETTERS, 108(4), 046806-1-046806-5.
Neupert Titus, Santos Luiz, Chamon Claudio, et al. (2011), Fractional Quantum Hall States at Zero Magnetic Field, in PHYSICAL REVIEW LETTERS , 106, 236804.
Neupert T, Santos L, Ryu S, Chamon C, Mudry C (2011), Fractional topological liquids with time-reversal symmetry and their lattice realization, in PHYSICAL REVIEW B, 84(16), 165107-1-165107-13.
Santos L, Neupert T, Ryu SS, Chamon C, Mudry C (2011), Time-reversal symmetric hierarchy of fractional incompressible liquids, in PHYSICAL REVIEW B, 84(16), 165138-1-165138-11.
Neupert Titus, Onoda Shigeki, Furusaki Akira (2010), Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall, in PHYSICAL REVIEW LETTERS, 105 , 206404.
Neupert T, Chamon C, Mudry C, How to Measure the Quantum Geometry of Bloch Bands, in PHYSICAL REVIEW B.
Arahata E, Neupert T, Sigrist M, Spin Currents and Spontaneous Magnetization at Twin Boundaries of Noncentrosymmetric Superconductors, in PHYSICAL REVIEW B.

### Collaboration

Group / person Country
Types of collaboration
 RIKEN Japan (Asia)
 - in-depth/constructive exchanges on approaches, methods or results- Publication- Research Infrastructure
 University of Illinois at Urbana-Champaign United States of America (North America)
 - in-depth/constructive exchanges on approaches, methods or results- Publication
 Harvard University United States of America (North America)
 - in-depth/constructive exchanges on approaches, methods or results- Publication

### Scientific events

#### Self-organised

Title Date Place
 Probing Phase Transitions using Photons, Muons and Neutrons 13.08.2011 Institut Montana Zugerberg, Switzerland

### Awards

Title Year
 Swiss Physical Society (SPS) 2013 Prize in General Physics 2013
 Auszeichnung von Doktorarbeiten mit der ETH-Medaille 2013 2013
 Fellow of the American Physical Society 2010

### Abstract

One of the greatest triumphs of Dirac was to predictthe value taken by the Land\'e $g$ factorthat controls the Zeeman interactionbetween the spin of a free electron and an applied magnetic field.Another consequence of the Dirac equation is the predictionof a spin-orbit coupling between the spin of an electron and itsangular momentum, when it orbits around a central potential.The closer the orbit of the electron is to the origin of thecentral potential, the stronger this effect.The spin-orbit coupling is, of course, essential to explain atomic spectra,in particular when the atomic number $Z$ is large.The spin-orbit interaction between the electron's crystal momentum and its spin can also be all important in the band theory ofsolid state physics. In band theory,the single-particle electronic energy levels are labeled by Bloch bands$\varepsilon^{\ }_{n;\boldsymbol{k}}$, where$\hbar\boldsymbol{k}$ is the crystal momentum while the collective index$n$ denotes the band index that encodes all the crystalline symmetry indicesof a Bloch electron. These are related to the structure of the relevant atomic orbitals as well as thesymmetries obeyed by the system, and the spin-$1/2$ degree of freedom associatedto the electron's spin.In the absence of external symmetry breaking fields such as magnetic fields (that break the time reversal symmetry), the band degeneracy results from the spin degeneracy and from orbital degeneracies, i.e., it is $(2s+1)\times d^{\ }_{\mathrm{orb}}$ where $s=1/2$ and $d^{\ }_{\mathrm{orb}}$depends on the lattice momentum $\hbar\boldsymbol{k}$. Spin-orbit coupling can lead to the lifting of some of these degeneracies. An inversion-symmetric spin-orbit coupling (that results directly from the atomic orbitals)yields a particular rearrangement of the electronic bands thatturns spinor states into so-called pseudospinor states while still keeping a two-fold degeneracy of each momentum $\hbar\boldsymbol{k}$. A new situation arises for systems without inversion symmetry, such as noncentrosymmetric crystalline structures.Here the spin degeneracy for a given $\hbar\boldsymbol{k}$ is lifted by the so-called antisymmetric spin-orbit coupling.Electrons confined to a quasi-two-dimensional geometryas occurs at the interfaces between semiconductors,Mott insulators, or as occurs on the surface of three-dimensionalbulk crystals can be exposed to a strong spin-orbit coupling, since there is no inversion symmetry perpendicular to the plane.The low-dimensionality also favors interaction effects and fluctuation-driven phenomena. Compared to the literature dedicatedto the instabilities of a two-dimensional metal without spin-orbit coupling, there is relatively little theoretical work done on the instabilities of a \textit{correlated two-dimensional metal with strong spin-orbit coupling}. This is perhaps so because it is only recently that this theoretical problem has become relevant experimentally.The goal of this project is to go beyond the single-particleapproximation and to explore the competinginstabilities of noncentrosymmetric quasi-two-dimensional metals,with an emphasis on the superconducting and magnetic instabilitiesthat are driven by the subtle interplay between \textit{strong} spin-orbit couplings and \textit{strong} fluctuations induced by electron-phononand electron-electron interactions.Among the many experiments motivating this project are:\begin{itemize}\itemSpin- and angle-resolved photoemission spectroscopy on Bi$^{\ }_x$Pb$^{\ }_{1-x}$/Ag(111) surface alloy conducted at PSI by the group ofJ. Osterwalder from the University of Z\" urich.\itemTransport measurements of theLaAlO$^{\ }_{3}$/SrTiO$^{\ }_{3}$ interfaceby the group of J.-M. Triscone from the University of Geneva.\itemStudies of magnetoelectric multiferroic materialsby the group of M. Kenzelmann from PSI.\end{itemize}
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