62 research outputs found
Multi- hexagonal spin density waves and dynamically generated spin-orbit coupling: time-reversal invariant analog of the chiral spin density wave
We study hexagonal spin-channel ("triplet") density waves with commensurate
-point propagation vectors. We first show that the three components of
the singlet charge density and charge-current density waves can be mapped to
multi-component nonzero angular momentum order in three dimensions ()
with cubic crystal symmetry. This one-to-one correspondence is exploited to
define a symmetry classification for triplet -point density waves using the
standard classification of spin-orbit coupled electronic liquid crystal phases
of a cubic crystal. Through this classification we naturally identify a set of
non-coplanar spin density and spin-current density waves: the chiral spin
density wave and its time-reversal invariant analog. These can be thought of as
and spin-orbit coupled isotropic -phase orders. In
contrast, uniaxial spin density waves are shown to correspond to
-phases. The non-coplanar triple- spin-current density wave realizes
a novel semimetal state with three flavors of four-component spin-momentum
locked Dirac cones, protected by a crystal symmetry akin to non-symmorphic
symmetry, and sits at the boundary between a trivial and topological insulator.
In addition, we point out that a special class of classical spin states,
defined as classical spin states respecting all lattice symmetries up to global
spin rotation, are naturally obtained from the symmetry classification of
electronic triplet density waves. These symmetric classical spin states are the
classical long-range ordered limits of chiral spin liquids.Comment: 14 + 4 pages, 5 + 0 figures; published versio
Interacting Dirac fermions under spatially alternating pseudo-magnetic field: Realization of spontaneous quantum Hall effect
Both topological crystalline insulators surfaces and graphene host
multi-valley massless Dirac fermions which are not pinned to a high-symmetry
point of the Brillouin zone. Strain couples to the low-energy electrons as a
time-reversal invariant gauge field, leading to the formation of pseudo-Landau
levels (PLL). Here we study periodic pseudo-magnetic fields originating from
strain superlattices. We study the low-energy Dirac PLL spectrum induced by the
strain superlattice and analyze the effect of various polarized states. Through
self-consistent Hartree-Fock calculations we establish that, due to the strain
superlattice and PLL electronic structure, a valley-ordered state spontaneously
breaking time-reversal and realizing a quantum Hall phase is favored, while
others are suppressed.Comment: 13 pages + 2 appendices, 9 figure
Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node
Motivated by the recent experiment indicating that superconductivity in the
doped topological insulator CuBiSe has an odd-parity pairing
symmetry with rotational symmetry breaking, we study the general class of
odd-parity superconductors with two-component order parameters in trigonal and
hexagonal crystal systems. In the presence of strong spin-orbit interaction, we
find two possible superconducting phases below , a time-reversal-breaking
(i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine
their relative energetics from the gap function in momentum space. The nematic
superconductor generally has a full quasi-particle gap, whereas the chiral
superconductor with a three-dimensional (3D) Fermi surface has point nodes with
lifted spin degeneracy, resulting in itinerant Majorana fermions in the bulk
and topological Majorana arcs on the surface.Comment: 4+ pages, 2 figures; 20 pages suppl mat + 4 figures; published
versio
Three-Dimensional Majorana Fermions in Chiral Superconductors
Through a systematic symmetry and topology analysis we establish that
three-dimensional chiral superconductors with strong spin-orbit coupling and
odd-parity pairing generically host low-energy nodal quasiparticles that are
spin-non-degenerate and realize Majorana fermions in three dimensions. By
examining all types of chiral Cooper pairs with total angular momentum
formed by Bloch electrons with angular momentum in crystals, we obtain a
comprehensive classification of gapless Majorana quasiparticles in terms of
energy-momentum relation and location on the Fermi surface. We show that the
existence of bulk Majorana fermions in the vicinity of spin-selective point
nodes is rooted in the non-unitary nature of chiral pairing in
spin-orbit-coupled superconductors. We address experimental signatures of
Majorana fermions, and find that the nuclear magnetic resonance (NMR) spin
relaxation rate is significantly suppressed for nuclear spins polarized along
the nodal direction as a consequence of the spin-selective Majorana nature of
nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial
topology and imply the presence of Majorana bound states on the surface that
form arcs in momentum space. We conclude by proposing the heavy fermion
superconductor PrOsSb and related materials as promising candidates
for non-unitary chiral superconductors hosting three-dimensional Majorana
fermions.Comment: 12 pages, 3 figures + appendices; published versio
Symmetry analysis of translational symmetry broken density waves: Application to hexagonal lattices in two dimensions
In this work we introduce a symmetry classification for electronic density waves which break translational symmetry due to commensurate wave-vector modulations. The symmetry classification builds on the concept of extended point groups: symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become “nonsymmorphic”-like elements. Multidimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of this work, we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple single- and two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional (2D) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multicomponent density waves corresponding to the commensurate M-point ordering vectors are worked out in detail. To show that our results generally apply to 2D hexagonal lattices, we develop a general low-energy SU(3) theory of (spinless) saddle-point electrons.NWO of the Netherland
Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene
Nematic superconductors possess unconventional superconducting order
parameters that spontaneously break rotational symmetry of the underlying
crystal. In this work we propose a mechanism for nematic superconductivity
stabilized by strong density wave fluctuations in two dimensions. While the
weak-coupling theory finds the fully gapped chiral state to be energetically
stable, we show that strong density wave fluctuations result in an additional
contribution to the free energy of a superconductor with multicomponent order
parameters, which generally favors nematic superconductivity. Our theory shades
light on the recent observation of rotational symmetry breaking in the
superconducting state of twisted bilayer graphene
- …