Observation of a nematic quantum Hall liquid on the surface of bismuth

Relating interactions and nematicity The electronic system in a strongly correlated material can sometimes be less symmetrical than the underlying crystal lattice. This loss of symmetry, caused by interactions and dubbed electronic nematicity, has been observed in a number of exotic materials. However, establishing a direct connection between the interactions and nematicity is tricky. Feldman et al. used scanning tunneling microscopy to image the wave functions of electrons on the surface of bismuth placed in an external magnetic field. The exchange interactions in the material caused a loss of symmetry, which was reflected in the orientations of the electrons' elliptical orbits. Science, this issue p. 316 Scanning tunneling spectroscopy makes a direct connection between exchange interactions and electronic nematicity. Nematic quantum fluids with wave functions that break the underlying crystalline symmetry can form in interacting electronic systems. We examined the quantum Hall states that arise in high magnetic fields from anisotropic hole pockets on the Bi(111) surface. Spectroscopy performed with a scanning tunneling microscope showed that a combination of single-particle effects and many-body Coulomb interactions lift the six-fold Landau level (LL) degeneracy to form three valley-polarized quantum Hall states. We imaged the resulting anisotropic LL wave functions and found that they have a different orientation for each broken-symmetry state. The wave functions correspond to those expected from pairs of hole valleys and provide a direct spatial signature of a nematic electronic phase.

[1]  Jinlong Yang,et al.  Surface Landau levels and spin states in bismuth (111) ultrathin films , 2016, Nature Communications.

[2]  Kazuo Saito,et al.  Tight-binding theory of surface spin states on bismuth thin films , 2015, 1507.06783.

[3]  Fan Zhang,et al.  SU(3) Quantum Hall Ferromagnetism in SnTe. , 2015, Physical review letters.

[4]  S. Sondhi,et al.  Order by disorder and by doping in quantum Hall valley ferromagnets , 2014, 1411.3354.

[5]  Kamran Behnia,et al.  Angle dependence of the orbital magnetoresistance in bismuth , 2015, 1501.01584.

[6]  H. Takagi,et al.  Imaging the two-component nature of Dirac–Landau levels in the topological surface state of Bi2Se3 , 2014, Nature Physics.

[7]  M. Brando,et al.  Thermodynamic evidence for valley-dependent density of states in bulk bismuth. , 2014, Nature materials.

[8]  H. Eisaki,et al.  Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking , 2014, Science.

[9]  Huiwen Ji,et al.  One-dimensional topological edge states of bismuth bilayers , 2014, Nature Physics.

[10]  T. Taniguchi,et al.  Screening charged impurities and lifting the orbital degeneracy in graphene by populating Landau levels. , 2013, Physical review letters.

[11]  A. Millis,et al.  Visualization of electron nematicity and unidirectional antiferroic fluctuations at high temperatures in NaFeAs , 2013, Nature Physics.

[12]  B. E. Kane,et al.  Valley-degenerate two-dimensional electrons in the lowest Landau level , 2012, 1210.2386.

[13]  L. Urban,et al.  Design and performance of an ultra-high vacuum scanning tunneling microscope operating at dilution refrigerator temperatures and high magnetic fields. , 2013, The Review of scientific instruments.

[14]  S. Sondhi,et al.  Microscopic theory of a quantum Hall Ising nematic: Domain walls and disorder , 2013, 1304.4255.

[15]  A. Taleb-Ibrahimi,et al.  Giant anisotropy of spin-orbit splitting at the bismuth surface. , 2012, Physical review letters.

[16]  Kamran Behnia,et al.  Landau spectrum and twin boundaries of bismuth in the extreme quantum limit , 2012, Proceedings of the National Academy of Sciences.

[17]  Stephen D. Wilson,et al.  Visualizing Landau levels of Dirac electrons in a one-dimensional potential. , 2012, Physical review letters.

[18]  R. Wiesendanger,et al.  Robust nodal structure of Landau level wave functions revealed by Fourier transform scanning tunneling spectroscopy. , 2012, Physical review letters.

[19]  Kamran Behnia,et al.  Field-induced polarization of Dirac valleys in bismuth , 2011, Nature Physics.

[20]  K. Novoselov,et al.  Interaction-Driven Spectrum Reconstruction in Bilayer Graphene , 2011, Science.

[21]  T. Mashoff,et al.  Probing electron-electron interaction in quantum Hall systems with scanning tunneling spectroscopy. , 2010, Physical review letters.

[22]  P. First,et al.  Real-space mapping of magnetically quantized graphene states , 2010 .

[23]  P. McMahon,et al.  In-Plane Resistivity Anisotropy in an Underdoped Iron Arsenide Superconductor , 2010, Science.

[24]  S. Sondhi,et al.  Nematic valley ordering in quantum Hall systems , 2010, 1003.1978.

[25]  P. Canfield,et al.  Nematic Electronic Structure in the “Parent” State of the Iron-Based Superconductor Ca(Fe1–xCox)2As2 , 2010, Science.

[26]  Michael J. Lawler,et al.  Nematic Fermi Fluids in Condensed Matter Physics , 2009, 0910.4166.

[27]  R. Cava,et al.  Phase Transitions of Dirac Electrons in Bismuth , 2008, Science.

[28]  R. Wiesendanger,et al.  Quantum Hall transition in real space: from localized to extended states. , 2008, Physical review letters.

[29]  B. Keimer,et al.  Electronic Liquid Crystal State in the High-Temperature Superconductor YBa2Cu3O6.45 , 2008, Science.

[30]  Y. Maeno,et al.  Formation of a Nematic Fluid at High Fields in Sr3Ru2O7 , 2006, Science.

[31]  G. Bihlmayer,et al.  Role of spin-orbit coupling and hybridization effects in the electronic structure of ultrathin Bi films. , 2006, Physical review letters.

[32]  P. Hofmann,et al.  The surfaces of bismuth: Structural and electronic properties , 2006 .

[33]  M. Shayegan,et al.  Observation of quantum Hall "valley Skyrmions". , 2005, Physical review letters.

[34]  M. Shayegan,et al.  Giant low-temperature piezoresistance effect in AlAs two-dimensional electrons , 2004, cond-mat/0411741.

[35]  G. Bihlmayer,et al.  Strong spin-orbit splitting on bi surfaces. , 2004, Physical review letters.

[36]  Y. Ando,et al.  Electrical resistivity anisotropy from self-organized one dimensionality in high-temperature superconductors. , 2001, Physical review letters.

[37]  C. Ast,et al.  Fermi surface of Bi(111) measured by photoemission spectroscopy. , 2001, Physical review letters.

[38]  L. Pfeiffer,et al.  Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field , 1999, cond-mat/9903196.

[39]  K. West,et al.  Strongly Anisotropic Transport in Higher Two-Dimensional Landau Levels , 1998, cond-mat/9812025.

[40]  V. J. Emery,et al.  Electronic liquid-crystal phases of a doped Mott insulator , 1997, Nature.

[41]  Boris I Shklovskii,et al.  Coulomb gap and low temperature conductivity of disordered systems , 1975 .