533 research outputs found

### Correlated spinless fermions on the honeycomb lattice revisited

We investigate the quantum many-body instabilities of the extended Hubbard
model for spinless fermions on the honeycomb lattice with repulsive
nearest-neighbor and 2nd nearest-neighbor density-density interactions. Recent
exact diagonalization and infinite density matrix renormalization group results
suggest that a putative topological Mott insulator phase driven by the 2nd
nearest-neighbor repulsion is suppressed, while other numerically exact
approaches support the topological Mott insulator scenario. In the present
work, we employ the functional renormalization group (fRG) for correlated
fermionic systems. Our fRG results hint at a strong suppression of the
scattering processes stabilizing the topological Mott insulator. From analyzing
the effects of fermionic fluctuations, we obtain a phase diagram which is the
result of the competition of various charge ordering instabilities.Comment: 9 pages, 8 figure

### Bond-ordered states and $f$-wave pairing of spinless fermions on the honeycomb lattice

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor
interactions are known to harbour a quantum critical point at half-filling,
with critical behaviour in the Gross-Neveu (chiral Ising) universality class.
The critical interaction strength separates a weak-coupling semimetallic regime
from a commensurate charge-density-wave phase. The phase diagram of this basic
model of correlated fermions on the honeycomb lattice beyond half-filling is,
however, less well established. Here, we perform an analysis of its many-body
instabilities using the functional renormalization group method with a basic
Fermi surface patching scheme, which allows us to treat instabilities in
competing channels on equal footing also away from half-filling. Between
half-filling and the van-Hove filling, the free Fermi surface is hole-like and
we again find a charge-density wave instability to be dominant at large
interactions. Moreover, its characteristics are those of the half-filled case.
Directly at the van-Hove filling the nesting property of the free Fermi surface
stabilizes a dimerized bond-order phase. At lower filling the free Fermi
surface becomes electron-like and a superconducting instability with $f$-wave
symmetry is found to emerge from the interplay of intra-unitcell repulsion and
collective fluctuations in the proximity to the charge-density wave
instability. We estimate the extent of the various phases and extract the
corresponding order parameters from the effective low-energy Hamiltonians.Comment: 11 pages, 11 figure

### Spin-Orbit Coupling and Magnetic Anisotropy in Iron-Based Superconductors

We determine theoretically the effect of spin-orbit coupling on the magnetic
excitation spectrum of itinerant multi-orbital systems, with specific
application to iron-based superconductors. Our microscopic model includes a
realistic ten-band kinetic Hamiltonian, atomic spin-orbit coupling, and
multi-orbital Hubbard interactions. Our results highlight the remarkable
variability of the resulting magnetic anisotropy despite constant spin-orbit
coupling. At the same time, the magnetic anisotropy exhibits robust universal
behavior upon changes in the bandstructure corresponding to different materials
of iron-based superconductors. A natural explanation of the observed
universality emerges when considering optimal nesting as a resonance
phenomenon. Our theory is also of relevance to other itinerant system with
spin-orbit coupling and nesting tendencies in the bandstructure.Comment: 15 pages, 9 figure

### Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model

We study the quantum many-body instabilities of the $t -J_{\mathrm{K}} -
J_{\mathrm{H}}$ Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a
minimal model for a doped spin-orbit Mott insulator. This spin-$1/2$ model is
believed to describe the magnetic properties of the layered transition-metal
oxide Na$_2$IrO$_3$. We determine the ground-state of the system with finite
charge-carrier density from the functional renormalization group (fRG) for
correlated fermionic systems. To this end, we derive fRG flow-equations adapted
to the lack of full spin-rotational invariance in the fermionic interactions,
here represented by the highly frustrated and anisotropic Kitaev exchange term.
Additionally employing a set of Ward identities for the Kitaev-Heisenberg
model, the numerical solution of the flow equations suggests a rich phase
diagram emerging upon doping charge carriers into the ground-state manifold
($\mathbb{Z}_2$ quantum spin liquids and magnetically ordered phases). We
corroborate superconducting triplet $p$-wave instabilities driven by
ferromagnetic exchange and various singlet pairing phases. For filling $\delta
> 1/4$, the $p$-wave pairing gives rise to a topological state with protected
Majorana edge-modes. For antiferromagnetic Kitaev and ferromagnetic Heisenberg
exchange we obtain bond-order instabilities at van Hove filling supported by
nesting and density-of-states enhancement, yielding dimerization patterns of
the electronic degrees of freedom on the honeycomb lattice. Further, our flow
equations are applicable to a wider class of model Hamiltonians.Comment: 24 pages, 18 figures, corresponds to journal versio

### Interacting electrons on trilayer honeycomb lattices

Few-layer graphene systems come in various stacking orders. Considering
tight-binding models for electrons on stacked honeycomb layers, this gives rise
to a variety of low-energy band structures near the charge neutrality point.
Depending on the stacking order these band structures enhance or reduce the
role of electron-electron interactions. Here, we investigate the instabilities
of interacting electrons on honeycomb multilayers with a focus on trilayers
with ABA and ABC stackings theoretically by means of the functional
renormalization group. We find different types of competing instabilities and
identify the leading ordering tendencies in the different regions of the phase
diagram for a range of local and non-local short-ranged interactions. The
dominant instabilities turn out to be toward an antiferromagnetic spin-density
wave (SDW), a charge density wave and toward quantum spin Hall (QSH) order.
Ab-initio values for the interaction parameters put the systems at the border
between SDW and QSH regimes. Furthermore, we discuss the energy scales for the
interaction-induced gaps of this model study and put them into context with the
scales for single-layer and Bernal-stacked bilayer honeycomb lattices. This
yields a comprehensive picture of the possible interaction-induced ground
states of few-layer graphene.Comment: 12 pages, 12 figure

### Collective magnetic excitations of $C_{4}$ symmetric magnetic states in iron-based superconductors

We study the collective magnetic excitations of the recently discovered
$C_{4}$ symmetric spin-density wave states of iron-based superconductors with
particular emphasis on their orbital character based on an itinerant
multiorbital approach. This is important since the $C_{4}$ symmetric
spin-density wave states exist only at moderate interaction strengths where
damping effects from a coupling to the continuum of particle-hole excitations
strongly modifies the shape of the excitation spectra compared to predictions
based on a local moment picture. We uncover a distinct orbital polarization
inherent to magnetic excitations in $C_{4}$ symmetric states, which provide a
route to identify the different commensurate magnetic states appearing in the
continuously updated phase diagram of the iron-pnictide family.Comment: 5+7 pages, 3+2 figure

### Topological superconductivity in the extended Kitaev-Heisenberg model

We study superconducting pairing in the doped Kitaev-Heisenberg model by
taking into account the recently proposed symmetric off-diagonal exchange
$\Gamma$. By performing a mean-field analysis, we classify all possible
superconducting phases in terms of symmetry, explicitly taking into account
effects of spin-orbit coupling. Solving the resulting gap equations
self-consistently, we map out a phase diagram that involves several
topologically nontrivial states. For $\Gamma<0$, we find a competition between
a time-reversal symmetry breaking chiral phase with Chern number $\pm1$ and a
time-reversal symmetric nematic phase that breaks the rotational symmetry of
the lattice. On the other hand, for $\Gamma \geq 0$ we find a time-reversal
symmetric phase that preserves all the lattice symmetries, thus yielding
clearly distinguishable experimental signatures for all superconducting phases.
Both of the time-reversal symmetric phases display a transition to a
$\mathbb{Z}_2$ non-trivial phase at high doping levels. Finally, we also
include a symmetry-allowed spin-orbit coupling kinetic energy and show that it
destroys a tentative symmetry protected topological order at lower doping
levels. However, it can be used to tune the time-reversal symmetric phases into
a $\mathbb{Z}_2$ non-trivial phase even at lower doping

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