47,054 research outputs found

### 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 Cu$_x$Bi$_2$Se$_3$ 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 $T_c$, 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 $J$
formed by Bloch electrons with angular momentum $j$ 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 PrOs$_4$Sb$_{12}$ and related materials as promising candidates
for non-unitary chiral superconductors hosting three-dimensional Majorana
fermions.Comment: 12 pages, 3 figures + appendices; published versio

### Volume integrals associated with the inhomegeneous Helmholtz equation. Part 2: Cylindrical region; rectangular region

Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

### Ising-like transitions in the O($n$) loop model on the square lattice

We explore the phase diagram of the O($n$) loop model on the square lattice
in the $(x,n)$ plane, where $x$ is the weight of a lattice edge covered by a
loop. These results are based on transfer-matrix calculations and finite-size
scaling. We express the correlation length associated with the staggered loop
density in the transfer-matrix eigenvalues. The finite-size data for this
correlation length, combined with the scaling formula, reveal the location of
critical lines in the diagram. For $n>>2$ we find Ising-like phase transitions
associated with the onset of a checkerboard-like ordering of the elementary
loops, i.e., the smallest possible loops, with the size of an elementary face,
which cover precisely one half of the faces of the square lattice at the
maximum loop density. In this respect, the ordered state resembles that of the
hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of
$n$ represents a softening of its particle-particle potentials. We also
determine critical points in the range $-2\leq n\leq 2$. It is found that the
topology of the phase diagram depends on the set of allowed vertices of the
loop model. Depending on the choice of this set, the $n>2$ transition may
continue into the dense phase of the $n \leq 2$ loop model, or continue as a
line of $n \leq 2$ O($n$) multicritical points

### Special transitions in an O($n$) loop model with an Ising-like constraint

We investigate the O($n$) nonintersecting loop model on the square lattice
under the constraint that the loops consist of ninety-degree bends only. The
model is governed by the loop weight $n$, a weight $x$ for each vertex of the
lattice visited once by a loop, and a weight $z$ for each vertex visited twice
by a loop. We explore the $(x,z)$ phase diagram for some values of $n$. For
$0<n<1$, the diagram has the same topology as the generic O($n$) phase diagram
with $n<2$, with a first-order line when $z$ starts to dominate, and an
O($n$)-like transition when $x$ starts to dominate. Both lines meet in an
exactly solved higher critical point. For $n>1$, the O($n$)-like transition
line appears to be absent. Thus, for $z=0$, the $(n,x)$ phase diagram displays
a line of phase transitions for $n\le 1$. The line ends at $n=1$ in an
infinite-order transition. We determine the conformal anomaly and the critical
exponents along this line. These results agree accurately with a recent
proposal for the universal classification of this type of model, at least in
most of the range $-1 \leq n \leq 1$. We also determine the exponent describing
crossover to the generic O($n$) universality class, by introducing topological
defects associated with the introduction of `straight' vertices violating the
ninety-degree-bend rule. These results are obtained by means of transfer-matrix
calculations and finite-size scaling.Comment: 19 pages, 11 figure

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