Electric octupole order in bilayer Rashba system

The odd-parity multipole is an emergent degree of freedom, leading to spontaneous inversion symmetry breaking. The odd-parity multipole order may occur by forming staggered even-parity multipoles in a unit cell. We focus on a locally noncentrosymmetric bilayer Rashba system, and study an odd-parity electric octupole order caused by the antiferro stacking of local electric quadrupoles. Analyzing the forward scattering model, we show that the electric octupole order is stabilized by a layer-dependent Rashba spin-orbit coupling. The roles of the spin-orbit coupling are clarified on the basis of the analytic formula of multipole susceptibility. The spin texture allowed in the D_2d point group symmetry and its magnetic response are revealed. Furthermore, we show that the parity-breaking quantum critical point appears in the magnetic field. The possible realization of the electric octupole order in bilayer high-T_c cuprate superconductors is discussed.

[1]  M. Casula,et al.  Rashba coupling amplification by a staggered crystal field , 2016, Nature Communications.

[2]  Y. Yanase,et al.  Superconductivity in magnetic multipole states , 2016, 1603.09440.

[3]  S. Matteo,et al.  Magnetic ground state of Sr 2 IrO 4 and implications for second-harmonic generation , 2016, 1603.04311.

[4]  V. I. Ivanov,et al.  Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate , 2015, Nature Physics.

[5]  Y. Yanase,et al.  Odd-parity superconductivity by competing spin-orbit coupling and orbital effect in artificial heterostructures , 2015, 1508.01333.

[6]  M. Sigrist,et al.  Topological Crystalline Superconductivity in Locally Noncentrosymmetric Multilayer Superconductors. , 2015, Physical review letters.

[7]  W. Metzner,et al.  Anomalous dynamical scaling from nematic and U(1)-gauge field fluctuations in two dimensional metals , 2015, 1503.05089.

[8]  Y. Motome,et al.  Spontaneous Multipole Ordering by Local Parity Mixing , 2015, 1502.00057.

[9]  L. Fu,et al.  Parity-Breaking Phases of Spin-Orbit-Coupled Metals with Gyrotropic, Ferroelectric, and Multipolar Orders. , 2015, Physical review letters.

[10]  E. M. Forgan,et al.  Field-tunable spin-density-wave phases in Sr3Ru2O7. , 2014, Nature materials.

[11]  Y. Yanase,et al.  Electric Octupole Order in Bilayer Ruthenate Sr3Ru2O7 , 2014, 1408.6936.

[12]  Timur K. Kim,et al.  Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor , 2014, Nature Physics.

[13]  A. Maharaj,et al.  Crisscrossed stripe order from interlayer tunneling in hole-doped cuprates , 2014, 1406.4154.

[14]  Y. Motome,et al.  Spontaneous Parity Breaking in Spin-Orbital Coupled Systems , 2014, 1406.2093.

[15]  E. Schierle,et al.  Resonant x-ray scattering study of charge-density wave correlations in YBa 2 Cu 3 O 6 + x , 2014, 1406.1595.

[16]  Y. Motome,et al.  Toroidal order in metals without local inversion symmetry , 2014, 1404.1156.

[17]  A. Zunger,et al.  Hidden spin polarization in inversion-symmetric bulk crystals , 2014, Nature Physics.

[18]  Y. Yanase.  Magneto-Electric Effect in Three-Dimensional Coupled Zigzag Chains , 2013, 1310.3920.

[19]  N. P. Armitage,et al.  Optical birefringence and dichroism of cuprate superconductors in the THz regime. , 2013, Physical review letters.

[20]  M. Sigrist,et al.  Parity-Mixed Superconductivity in Locally Non-centrosymmetric System , 2013, 1311.4660.

[21]  Yasuharu Nakamura,et al.  Multi-Orbital Superconductivity in SrTiO3 /LaAlO3 Interface and SrTiO3 Surface , 2013, 1307.2363.

[22]  Y. Yanase.  Electronic Structure and Noncentrosymmetric Superconductivitity in Three-Orbitalt2gModel with Spin-Orbit Coupling: Sr2RuO4near [001] Surface/Interface , 2013 .

[23]  C. Mazzoli,et al.  Momentum-dependent charge correlations in YBa2Cu3O6+δ superconductors probed by resonant X-ray scattering: evidence for three competing phases. , 2012, Physical review letters.

[24]  K. Held,et al.  Theory of spin-orbit coupling at LaAlO 3 /SrTiO 3 interfaces and SrTiO 3 surfaces , 2012, 1209.4705.

[25]  M. Sigrist,et al.  Pair-density wave states through spin-orbit coupling in multilayer superconductors , 2012, 1210.0315.

[26]  G. M. De Luca,et al.  Long-Range Incommensurate Charge Fluctuations in (Y,Nd)Ba2Cu3O6+x , 2012, Science.

[27]  E. M. Forgan,et al.  Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67 , 2012, Nature Physics.

[28]  S. A. Grigera,et al.  Quantum criticality and the formation of a putative electronic liquid crystal in Sr3Ru2O7 , 2012, 1201.6639.

[29]  D. Maruyama,et al.  Locally Non-centrosymmetric Superconductivity in Multilayer Systems , 2011, 1111.4293.

[30]  M. Salmhofer,et al.  Functional renormalization group approach to correlated fermion systems , 2011, 1105.5289.

[31]  M. Sigrist,et al.  Non-Centrosymmetric Superconductors , 2012 .

[32]  M. Sigrist,et al.  Superconductivity and local noncentrosymmetricity in crystal lattices , 2011, 1108.4694.

[33]  Y. Maeno,et al.  Symmetry-breaking lattice distortion in Sr₃Ru₂O₇. , 2010, Physical review letters.

[34]  S. Sachdev,et al.  Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order , 2010, 1001.1153.

[35]  H. Yamase.  Spontaneous Fermi surface symmetry breaking in bilayer systems , 2009, 0907.4253.

[36]  M. Sigrist,et al.  Probing the d x 2 -y 2 -wave Pomeranchuk instability by ultrasound , 2009, 0907.2081.

[37]  Y. Kuramoto,et al.  Multipole Orders and Fluctuations in Strongly Correlated Electron Systems , 2009 .

[38]  H. Yamase.  Self-masking of spontaneous symmetry breaking in layer materials. , 2008, Physical review letters.

[39]  Nicola A. Spaldin,et al.  The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect , 2008 .

[40]  M. Sigrist,et al.  Superconductivity and Magnetism in Non-centrosymmetric System : Application to CePt_3Si(Condensed matter: electronic structure and electrical, magnetic, and optical properties) , 2008, 0805.2791.

[41]  Manfred,et al.  Superconductivity and Magnetism in Non-centrosymmetric System: Application to CePt3Si , 2008 .

[42]  M. Fiebig,et al.  Observation of ferrotoroidic domains , 2007, Nature.

[43]  H. Yamase.  Effect of magnetic field on spontaneous Fermi-surface symmetry breaking , 2007, 0705.4233.

[44]  A. Katanin,et al.  Van Hove Singularity and Spontaneous Fermi Surface Symmetry Breaking in Sr3Ru2O7 , 2007, cond-mat/0701628.

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

[46]  L. Dell'Anna,et al.  Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions , 2005, cond-mat/0507532.

[47]  V. Oganesyan,et al.  Mean-field theory for symmetry-breaking Fermi surface deformations on a square lattice , 2005, cond-mat/0502238.

[48]  Yong Baek Kim,et al.  Itinerant metamagnetism induced by electronic nematic order , 2004, cond-mat/0408004.

[49]  H. Yamase.  Excitation spectrum of d-wave Fermi surface deformation. , 2004, Physical review letters.

[50]  H. Kee,et al.  Formation of an electronic nematic phase in interacting fermion systems , 2004, cond-mat/0402565.

[51]  S. Andergassen,et al.  Soft fermi surfaces and breakdown of Fermi-liquid behavior. , 2003, Physical review letters.

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

[53]  E. Fradkin,et al.  Quantum theory of a nematic Fermi fluid , 2001, cond-mat/0102093.

[54]  T. M. Rice,et al.  Breakdown of the Landau-Fermi liquid in two dimensions due to umklapp scattering , 2001 .

[55]  H. Kohno,et al.  Instability toward Formation of Quasi-One-Dimensional Fermi Surface in Two-Dimensional t-J Model , 2000, 2104.10467.

[56]  Metzner,et al.  d-wave superconductivity and pomeranchuk instability in the two-dimensional hubbard model , 2000, Physical review letters.

[57]  W. Metzner,et al.  Renormalization-group analysis of the two-dimensional Hubbard model , 1999, cond-mat/9908471.

[58]  V. M. Dubovik,et al.  Toroid moments in electrodynamics and solid-state physics , 1990 .