Found 30 papers in cond-mat We review the recent advances and current challenges in the field of strong
spin-orbit coupled Kitaev materials, with a particular emphasis on the physics
beyond the exactly-solvable Kitaev spin liquid point. To that end, we give a
comprehensive overview of the most relevant exchange interactions in $d^5$ and
$d^7$ iridates and similar compounds, an exposition of their microscopic
origin, and a systematic attempt to map out the most interesting correlated
regimes of the multi-dimensional parameter space, guided by powerful symmetry
and duality transformations as well as by insights from wide-ranging analytical
and numerical studies. We also survey recent exciting results on quasi-1D
models and discuss their relevance to higher-dimensional models. Finally, we
highlight some of the key questions in the field as well as future directions.
Exceptional bound (EB) states represent an unique new class of robust bound
states protected by the defectiveness of non-Hermitian exceptional points.
Conceptually distinct from the more well-known topological states and
non-Hermitian skin states, they were recently discovered as a novel source of
negative entanglement entropy in the quantum entanglement context. Yet, EB
states have been physically elusive, being originally interpreted as negative
probability eigenstates of the propagator of non-Hermitian Fermi gases. In this
work, we show that EB states are in fact far more ubiquitous, also arising
robustly in broad classes of systems whether classical or quantum. This hinges
crucially on a newly-discovered spectral flow that rigorously justifies the EB
nature of small candidate lattice systems. As a highlight, we present their
first experimental realization through an electrical circuit, where they
manifest as prominent stable resonant voltage profiles. Our work brings a
hitherto elusive but fundamentally distinctive quantum phenomenon into the
realm of classical metamaterials, and provides a novel pathway for the
engineering of robust modes in otherwise sensitive systems.
Parafermion zero modes can be trapped in the domain walls of quantum Hall
edges proximitized by superconductors and ferromagnets. The $\nu = 1/3$
fractional quantum Hall side strip arising due to edge reconstruction of a $\nu
= 1$ edge doubles the number of topological sectors such that each of them is
$Z_{2} \times Z_{2}$ degenerate. The many-body spectrum displays a $4\pi$
Josephson periodicity, with the states in each $Z_{2}$ being energetically
decoupled. Signatures of the new states appear in the fractional Josephson
current when the edge velocities are taken to be different.
We study an unique form of metallic ferromagnetism in which orbital moments
surpasses the role of spin moments in shaping the overall magnetization. This
system emerges naturally upon doping a topologically non-trivial Chern band in
the recently identified quarter metal phase of rhombohedral trilayer graphene.
Our comprehensive scan of the density-interlayer potential parameter space
reveals an unexpected landscape of orbital magnetization marked by two sign
changes and a line of singularities. The sign change originates from an intense
Berry curvature concentrated close to the band-edge, and the singularity arises
from a topological Lifshitz transition that transform a simply connected Fermi
sea into an annular Fermi sea. Importantly, these variations occur while the
groundstate order-parameter (i.e.~valley and spin polarization) remains
unchanged. This unconventional relationship between the order parameter and
magnetization markedly contrasts traditional spin ferromagnets, where spin
magnetization is simply proportional to the groundstate spin polarization via
the gyromagnetic ratio. We compute energy and magnetization curves as functions
of collective valley rotation to shed light on magnetization dynamics and to
expand the Stoner-Wohlfarth magnetization reversal model. We provide
predictions on the magnetic coercive field that can be readily tested in
experiments. Our results challenge established perceptions of magnetism,
emphasising the important role of orbital moments in two-dimensional materials
such as graphene and transition metal dichalcogenides, and in turn, expand our
understanding and potential manipulation of magnetic behaviors in these
systems.
Magic angle twisted bilayer graphene (MATBG) has become one of the prominent
topics in Condensed Matter during the last few years, however, fully atomistic
studies of the interacting physics are missing. In this work, we study the
correlated insulator states of MATBG in the setting of a tight-binding model,
under a perpendicular magnetic field of $0$ and $26.5$ T, corresponding to zero
and one quantum of magnetic flux per unit cell. At zero field and for dopings
of two holes ($\nu=-2$) or two electrons ($\nu=+2$) per unit cell, the Kramers
intervalley coherent (KIVC) order is the ground state at the Hartree-Fock
level, although it is stabilized by a different mechanism to that in continuum
model. At charge neutrality, the spin polarized state is competitive with the
KIVC due to the on-site Hubbard energy. We obtain a strongly electron-hole
asymmetric phase diagram with robust insulators for electron filling and metals
for negative filling. In the presence of magnetic flux, we predict an insulator
with Chern number $-2$ for $\nu=-2$, a spin polarized state at charge
neutrality and competing insulators with Chern numbers $+2$ and $0$ at
$\nu=+2$. The stability of the $\nu=+2$ insulators is determined by the
screening environment, allowing for the possibility of observing a topological
phase transition.
We show that the matrix product state (MPS) provides a thermal quantum pure
state (TPQ) representation in equilibrium in two spatial dimensions over the
whole temperature range. We use the Kitaev honeycomb model as a prominent
example hosting a quantum spin liquid (QSL) ground state to target the two
specific-heat peaks previously solved nearly exactly using the free Majorana
fermionic description. Starting from the high-temperature random state, our
TPQ-MPS wrapping the cylinder precisely reproduces these peaks, showing that
the quantum many-body description based on spins can still capture the emergent
itinerant Majorana fermions in a ${\mathbb Z}_2$ gauge field. The truncation
process efficiently discards the high-energy states, eventually reaching the
long-range entangled topological state.
The breaking of a chemical bond is fundamental in most chemical reactions. To
understand chemical processes in heterogeneous catalysis or on-surface
polymerization the study of bond dissociation in molecules adsorbed on
crystalline surfaces is advantageous. Single molecule studies of bond breaking
can give details of the dissociation dynamics, which are challenging to obtain
in mole-scale ensemble experiments. Bond breaking in single adsorbed molecules
can be triggered using the energy of the tunnelling electrons in a scanning
tunnelling microscope (STM) at selected positions to investigate the
dissociation dynamics. Single bond dissociation dynamics has been deeply
investigated only in small molecules, but not in larger molecules that exhibit
distinct rotational degrees of freedom. Here, we use low temperature (7 K) STM
to dissociate a single bromine atom from an elongated molecule
(dibromo-terfluorene) adsorbed on a Ag(111) surface. This rod-like molecule
allows to clearly identify not only displacement of the reaction fragments, but
also their rotation. The results show that the molecular fragment binds to the
nearest silver atom and only further rotation is allowed. Moreover, the
excitation responsible for the bond breaking can propagate through the
molecular backbone to dissociate a bromine atom that is not located at the
pulse position. These results show the important role of the metal substrate in
conditioning the bond dissociation dynamics. Our results might allow to improve
the control of the synthesis of 2D materials and targeted engineering of
molecular architectures.
The joint effects of Kekul\'e lattice distortions and Rashba-type spin-orbit
coupling on the electronic properties of graphene are explored. We modeled the
position dependence of the Rashba energy term in a manner that allows its
seamless integration into the scheme introduced by Gamayun et al.[New J. Phys.
20, 023016 (2018)] to describe graphene with Kekul\'e lattice distortion.
Particularly for the Kekul\'e-Y texture, the effective low energy Dirac
Hamiltonian contains a new spin-valley locking term, in addition to the
well-known Rashba-induced momentum-pseudospin and spin-pseudospin couplings,
and the Kekul\'e-induced momentum-valley coupling term. We report on the
low-energy band structure and Landau level spectra of Rashba-spin-orbit-coupled
Kek-Y graphene, and propose an experimental scheme to discern between the
presence of Rashba spin-orbit coupling, Kek-Y lattice distortion, and both,
based on doping-dependent magnetotransport measurements.
In our previous work, we synthesized a metal/2D material heterointerface
consisting of $L1_0$-ordered iron-palladium (FePd) and graphene (Gr) called
FePd(001)/Gr. This system has been explored by both experimental measurements
and theoretical calculations. In this study, we focus on a heterojunction
composed of FePd and multilayer graphene referred to as
FePd(001)/$m$-Gr/FePd(001), where $m$ represents the number of graphene layers.
We perform first-principles calculations to predict their spin-dependent
transport properties. The quantitative calculations of spin-resolved
conductance and magnetoresistance (MR) ratio (150-200%) suggest that the
proposed structure can function as a magnetic tunnel junction in spintronics
applications. We also find that an increase in $m$ not only reduces conductance
but also changes transport properties from the tunneling behavior to the
graphite $\pi$-band-like behavior. Furthermore, we examine the impact of
lateral displacements (sliding) at the interface and find that the spin
transport properties remain robust despite these changes; this is the advantage
of two-dimensional material hetero-interfaces over traditional insulating
barrier layers such as MgO.
We report the quantum transport properties of the $\alpha$-Sn films grown on
CdTe (001) substrates by molecular beam epitaxy. The $\alpha$-Sn films are
doped with phosphorus to tune the Fermi level and access the bulk state. Clear
Shubnikov-de Haas oscillations can be observed below 30 K and a nontrivial
Berry phase has been confirmed. A nearly spherical Fermi surface has been
demonstrated by angle-dependent oscillation frequencies. In addition, the sign
of negative magnetoresistance which is attributed to the chiral anomaly has
also been observed. These results provide strong evidence of the
three-dimensional Dirac semimetal phase in $\alpha$-Sn.
The functionality of atomic quantum emitters is intrinsically linked to their
host lattice coordination. Structural distortions that spontaneously break the
lattice symmetry strongly impact their optical emission properties and
spin-photon interface. Here we report on the direct imaging of charge
state-dependent symmetry breaking of two prototypical atomic quantum emitters
in mono- and bilayer MoS$_2$ by scanning tunneling microscopy (STM) and
non-contact atomic force microscopy (nc-AFM). By substrate chemical gating
different charge states of sulfur vacancies (Vac$_\text{S}$) and substitutional
rhenium dopants (Re$_\text{Mo}$) can be stabilized. Vac$_\text{S}^{-1}$ as well
as Re$_\text{Mo}^{0}$ and Re$_\text{Mo}^{-1}$ exhibit local lattice distortions
and symmetry-broken defect orbitals attributed to a Jahn-Teller effect (JTE)
and pseudo-JTE, respectively. By mapping the electronic and geometric structure
of single point defects, we disentangle the effects of spatial averaging,
charge multistability, configurational dynamics, and external perturbations
that often mask the presence of local symmetry breaking.
Comprehending nonequilibrium electron-phonon dynamics at the microscopic
level and at the short time scales is one of the main goals in condensed matter
physics. Effective temperature models and time-dependent Boltzmann equations
are standard techniques for exploring and understanding nonequilibrium state
and the corresponding scattering channels. However, these methods consider only
the time evolution of carrier occupation function, while the self-consistent
phonon dressing in each time instant coming from the nonequilibrium population
is ignored, which makes them less suitable for studying ultrafast phenomena
where softening of the phonon modes plays an active role. Here, we combine
ab-initio time-dependent Boltzmann equations and many-body phonon self-energy
calculations to investigate the full momentum- and mode-resolved nonadiabatic
phonon renormalization picture in the MoS$_2$ monolayer under nonequilibrium
conditions. Our results show that the nonequilibrium state of photoexcited
MoS$_2$ is governed by multi-valley topology of valence and conduction bands
that brings about characteristic anisotropic electron-phonon thermalization
paths and the corresponding phonon renormalization of strongly-coupled modes
around high-symmetry points of the Brillouin zone. As the carrier population is
thermalized towards its equilibrium state, we track in time the evolution of
the remarkable phonon anomalies induced by nonequilibrium and the overall
enhancement of the phonon relaxation rates. This work shows potential
guidelines to tailor the electron-phonon relaxation channels and control the
phonon dynamics under extreme photoexcited conditions.
We will study a class of system composed of interacting quantum dots (QDs)
placed in contact with a hot and cold thermal baths subjected to a
non-conservative driving worksource. Despite their simplicity, these models
showcase an intricate array of phenomena, including pump and heat engine
regimes as well as a discontinuous phase transition. We will look at three
distinctive topologies: a minimal and beyond minimal (homogeneous and
heterogeneous interaction structures). The former case is represented by stark
different networks ("all-to-all" interactions and only a central interacting to
its neighbors) and present exact solutions, whereas homogeneous and
heterogeneous structures have been analyzed by numerical simulations. We find
that the topology plays a major role on the thermodynamic performance if the
individual energies of the quantum dots are small, in part due to the presence
of first-order phase-transitions. If the individual energies are large, the
topology is not important and results are well-described by a system with
all-to-all interactions.
Topological insulators have been extended to higher-order versions that
possess topological hinge or corner states in lower dimensions. However, their
robustness against disorder is still unclear. Here, we theoretically
investigate the phase transitions of three-dimensional (3D) chiral second-order
topological insulator (SOTI) in the presence of disorders. Our results show
that, by increasing disorder strength, the nonzero densities of states of side
surface and bulk emerge at critical disorder strengths of $W_{S}$ and $W_{B}$,
respectively. The spectral function indicates that the bulk gap is only closed
at one of the $R_{4z}\mathcal{T}$-invariant points, i.e., $\Gamma_{3}$. The
closing of side surface gap or bulk gap is ascribed to the significant decrease
of the elastic mean free time of quasi-particles. Because of the localization
of side surface states, we find that the 3D chiral SOTI is robust at an
averaged quantized conductance of $2e^{2}/h$ with disorder strength up to
$W_{B}$. When the disorder strength is beyond $W_{B}$, the 3D chiral SOTI is
then successively driven into two phases, i.e., diffusive metallic phase and
Anderson insulating phase. Furthermore, an averaged conductance plateau of
$e^{2}/h$ emerges in the diffusive metallic phase.
Recently, quantum anomalous Hall state at odd integer filling in moir\'e
stacked MoTe$_2$/WSe$_2$ has been convincingly interpreted as a topological
Mott insulator state appearing due to strong interactions in {\it band} basis
[arXiv:2210.11486]. In this work, we aim to analyze the formation of a
topological Mott insulator due to interactions in {\it orbital} basis instead,
being more natural for systems where interactions originate from the character
of $f$ or $d$ orbitals rather than band flatness. For that reason, we study an
odd-integer filled Anderson lattice model incorporating odd-parity
hybridization between orbitals with different degrees of correlations
introduced in the Hatsugai-Kohmoto spirit. We demonstrate that a topological
Mott insulating state can be realized in a considered model only when weak
intra- and inter-orbital correlations involving dispersive states are taken
into account. Interestingly, we find that all topological transitions between
trivial and $\mathbb{Z}_2$ topological Mott insulating phases are not
accompanied by a spectral gap closing, consistently with a phenomenon called
{\it first-order topological transition}. Instead, they are signaled by a kink
developed in spectral function at one of the time reversal invariant momenta.
We believe that our approach can provide insightful phenomenology of
topological Mott insulators in spin-orbit coupled $f$ or $d$ electron systems.
Mexican-hat-shaped quartic dispersion manifests itself in certain families of
single-layer twodimensional hexagonal crystals such as compounds of groups
III-VI and groups IV-V as well as elemental crystals of group V. Quartic band
forms the valence band edge in various of these structures, and some of the
experimentally confirmed structures are GaS, GaSe, InSe, SnSb and blue
phosphorene. Here, we numerically investigate strictly-one-dimensional (1D) and
quasi-one dimensional (Q1D) nanoribbons with quartic dispersion and
systematically study the effects of Anderson disorder on their transport
properties with the help of a minimal tight-binding model and Landauer
formalism. We compare the analytical expression for the scaling function with
simulation data to deduce about the domains of diffusion and localization
regimes. In 1D, it is shown that conductance drops dramatically at the quartic
band edge compared to a quadratic band. As for the Q1D nanoribbons, a set of
singularities emerge close to the band edge, which suppress conductance and
lead to short mean-free-paths and localization lengths. Interestingly, wider
nanoribbons can have shorter mean-free-paths because of denser singularities.
However, the localization lengths do not necessarily follow the same trend. The
results display the peculiar effects of quartic dispersion on transport in
disordered systems.
We present experimental and theoretical results on formation of quantum
vortices in a laser beam propagating in a nonlinear medium. Topological
constrains richer that the mere conservation of vorticity impose an elaborate
dynamical behavior to the formation and annihilation of vortex/anti-vortex
pairs. We identify two such mechanisms, both described by the same fold-Hopf
bifurcation. One of them is particularly efficient although it is not observed
in the context of liquid helium films or stationary linear systems because it
relies on the finite compressibility and on the non-stationnarity of the fluid
of light we consider.
We study the intrinsic spin Hall effect of a Dirac Hamiltonian system with
ferromagnetic exchange coupling, a minimal model combining relativistic
spin-orbit interaction and ferromagnetism. The energy bands of the Dirac
Hamiltonian are split after introducing a Stoner-type ferromagnetic ordering
which breaks the spherical symmetry of pristine Dirac model. The totally
antisymmetric spin Hall conductivity (SHC) tensor becomes axially anisotropic
along the direction of external electric field. Interestingly, the anisotropy
does not vanish in the asymptotic limit of zero magnetization. We show that the
ferromagnetic ordering breaks the spin degeneracy of the eigenfunctions and
modifies the selection rules of the interband transitions for the intrinsic
spin Hall effect. The difference in the selection rule between the pristine and
the ferromagnetic Dirac phases causes the anisotropy of the SHC, resulting in a
discontinuity of the SHC as the magnetization, directed orthogonal to the
electric field, is reduced to zero in the ferromagnetic Dirac phase and enters
the pristine Dirac phase.
We study the interplay of lattice, spin and orbital degrees of freedom in a
two-dimensional model system: a flat square lattice of Te atoms on a Au(100)
surface. The atomic structure of the Te monolayer is determined by scanning
tunneling microscopy (STM) and quantitative low-energy electron diffraction
(LEED-IV). Using spin- and angle-resolved photoelectron spectroscopy (ARPES)
and density functional theory (DFT), we observe a Te-Au interface state with
highly anisotropic Rashba-type spin-orbit splitting at the X point of the
Brillouin zone. Based on a profound symmetry and tight-binding analysis, we
show how in-plane square lattice symmetry and broken inversion symmetry at the
Te-Au interface together enforce a remarkably anisotropic orbital Rashba effect
which strongly modulates the spin splitting.
Experimental investigation of the interplay of dualities, generalized
symmetries, and topological defects is an important challenge in condensed
matter physics and quantum materials. A simple model exhibiting this physics is
the transverse-field Ising model, which can host a noninvertible topological
defect that performs the Kramers-Wannier duality transformation. When acting on
one point in space, this duality defect imposes the duality twisted boundary
condition and binds a single Majorana zero mode. This Majorana zero mode is
unusual as it lacks localized partners and has an infinite lifetime, even in
finite systems. Using Floquet driving of a closed Ising chain with a duality
defect, we generate this Majorana zero mode in a digital quantum computer. We
detect the mode by measuring its associated persistent autocorrelation function
using an efficient sampling protocol and a compound strategy for error
mitigation. We also show that the Majorana zero mode resides at the domain wall
between two regions related by a Kramers-Wannier duality. Finally, we highlight
the robustness of the isolated Majorana zero mode to integrability and
symmetry-breaking perturbations. Our findings offer an experimental approach to
investigating exotic topological defects in Floquet systems.
The behavior of the topological index, characterizing the properties of
superconducting phases of quasi-two-dimensional systems with nontrivial
topology, is investigated depending on the temperature and parameters of the
effective non-Hermitian Hamiltonian. For this purpose, a method of calculating
the topological index, based on a self-consistent functional-integral theory,
is proposed. The method makes it possible to take into account thermal
fluctuations and study the behavior of the topological index as a function of
temperature and Hamiltonian parameters. The chiral d+id superconducting phase
of a quasi-two-dimensional model with effective attraction between the
electrons located at the nearest sites of a triangular lattice is considered.
It is shown that the characteristic features in the energy dependence of the
self-energy part, which arise when thermal fluctuations are taken into account,
have a structure that does not lead to a change in the topological properties
of the system. It is found that thermal fluctuations, as well as an increase in
effective attraction in this system, contribute to the expansion of the
temperature region, in which the value of the topological index is close to the
integer C1=-2.
Quantum cooperativity is evident in light-matter platforms where quantum
emitter ensembles are interfaced with confined optical modes and are coupled
via the ubiquitous electromagnetic quantum vacuum. Cooperative effects can find
applications, among other areas, in topological quantum optics, in quantum
metrology or in quantum information. This tutorial provides a set of
theoretical tools to tackle the behavior responsible for the onset of
cooperativity by extending open quantum system dynamics methods, such as the
master equation and quantum Langevin equations, to electron-photon interactions
in strongly coupled and correlated quantum emitter ensembles. The methods are
illustrated on a wide range of current research topics such as the design of
nanoscale coherent light sources, highly-reflective quantum metasurfaces or low
intracavity power superradiant lasers. The analytical approaches are developed
for ensembles of identical two-level quantum emitters and then extended to more
complex systems where frequency disorder or vibronic couplings are taken into
account. The relevance of the approach ranges from atoms in optical lattices to
quantum dots or molecular systems in solid-state environments.
We show that the most generic form of spin-singlet superconducting order
parameter for chiral fermions is of the $\Delta_s+i\gamma^5\Delta_5$ where
$\Delta_s$ is the usual order parameter and $\Delta_5$ is the pseudo-scalar
order parameter. After factoring out the $U(1)$ phase $e^{i\phi}$, this form of
superconductivity admits yet additional complex structure in the plane of
$(\Delta_s,\Delta_5)$. The polar angle $\chi$ in this plane dubbed chiral angle
will be locked to the $U(1)$ phase $\phi$. We propose a synthetic setup based
on stacking of topological insulators (TIs) and superconductors (SCs).
Alternatively flux biasing the superconductors with a fluxes $\pm\Phi$ leads to
$\Delta_5=\Delta_0 \sin(\chi)$, where $\Delta_0$ is the superconducting order
parameter of the SC layers, and the chiral angle $\chi=\Phi/\Phi_0$ is directly
given by the flux $\Phi$ in units of the flux quantum $\Phi_0=h/(2e)$. This can
be used as a building block to construct a two-dimensional Josephson array. In
this setup $\chi$ will be a background field defining a pseudoscalar $\Delta_5$
that can be tuned to desired configuration. While in a uniform background field
$\Delta_5$ the dynamics of $\phi$ is given by standard XY model and its
associated vortices, a {\em staggered} background $\pm\Delta_5$ (or
equivalently $\chi$ and $\chi+\pi$ in alternating lattice sites) creates a new
set of minima for the $\phi$ field that will support half-vortex excitations.
An isolated single synthetic "half-vortex" in the $\chi$ field in an otherwise
uniform background will bind a $\phi$-half-vortex. This is similar to the way a
p-wave superconducting vortex core binds a Majorana fermion.
Synthetic dimensions provide a powerful approach for simulating condensed
matter physics in cold atoms and photonics, whereby a set of discrete degrees
of freedom are coupled together and re-interpreted as lattice sites along an
artificial spatial dimension. However, atomic experimental realisations have
been limited so far by the number of artificial lattice sites that can be
feasibly coupled along the synthetic dimension. Here, we experimentally realise
for the first time a very long and controllable synthetic dimension of atomic
harmonic trap states. To create this, we couple trap states by dynamically
modulating the trapping potential of the atomic cloud with patterned light. By
controlling the detuning between the frequency of the driving potential and the
trapping frequency, we implement a controllable force in the synthetic
dimension. This induces Bloch oscillations in which atoms move periodically up
and down tens of atomic trap states. We experimentally observe the key
characteristics of this behaviour in the real space dynamics of the cloud, and
verify our observations with numerical simulations and semiclassical theory.
This experiment provides an intuitive approach for the manipulation and control
of highly-excited trap states, and sets the stage for the future exploration of
topological physics in higher dimensions.
A multi-phase field model is employed to study the microstructural evolution
of an alloy undergoing liquid dealloying. The model proposed extends upon the
original approach of Geslin et al. to consider dealloying in the presence of
grain boundaries. The model is implemented using a semi-implicit time stepping
algorithm using spectral methods, which enables simulating large 2D and 3D
domains over long time-scales while still maintaining a realistic interfacial
thickness. The model is exercised to demonstrate a mechanism of coupled
grain-boundary migration to maintain equilibrium contact angles with this
topologically-complex solid-liquid interface during dealloying. This mechanism
locally accelerates dealloying by dissolving the less noble alloy metal from
(and rejecting the more noble metal into) the migrating grain boundary, thereby
enhancing the diffusion-coupled-growth of the liquid channel into the
precursor. The deeper corrosion channel at the migrating grain boundary
asymmetrically disrupts the ligament connectivity of the final dealloyed
structure, in qualitative agreement with published experimental observations.
It is shown that these grain boundary migration-assisted corrosion channels
form even for precursors with small amounts of the dissolving alloy species,
below the so-called \textit{parting limit}
In this work, we study the synergistic correlated states in two distinct
types of interacting electronic systems coupled by interlayer Coulomb
interactions. We propose that this scenario can be realized in a type of
Coulomb-coupled graphene-insulator heterostructures with gate tunable band
alignment. We find that, by virtue of the interlayer Coulomb coupling between
the interacting electrons in the two layers, electronic states that cannot be
revealed in either individual layer would emerge in a cooperative and
synergistic manner. Specifically, as a result of the band alignment, charge
carriers can be transferred between graphene and the substrate under the
control of gate voltages, which can yield a long-wavelength electronic crystal
at the surface of the substrate. This electronic crystal exerts a superlattice
Coulomb potential on the Dirac electrons in graphene, which generates subbands
with reduced non-interacting Fermi velocity. As a result, $e$-$e$ Coulomb
interactions within graphene would play a more important role, giving rise to a
gapped Dirac state at the charge neutrality point, accompanied by
interaction-enhanced Fermi velocity. Moreover, the superlattice potential can
give rise to topologically nontrivial subband structures which are tunable by
superlattice's constant and anisotropy. Reciprocally, the electronic crystal
formed in the substrate can be substantially stabilized in such coupled bilayer
heterostructure by virtue of the cooperative interlayer Coulomb coupling. We
further perform high-throughput first principles calculations to identify a
number of promising insulating materials as candidate substrates for graphene
to demonstrate these effects.
Topological materials have been a main focus of studies in the past decade
due to their protected properties that can be exploited for the fabrication of
new devices. Among them, Weyl semimetals are a class of topological semimetals
with non-trivial linear band crossing close to the Fermi level. The existence
of such crossings requires the breaking of either time-reversal or inversion
symmetry and is responsible for the exotic physical properties.
In this work we identify the full-Heusler compound InMnTi$_2$, as a
promising, easy to synthesize, $T$- and $I$-breaking Weyl semimetal. This
material exhibits several features that are comparatively more intriguing with
respect to other known Weyl semimetals: the distance between two neighboring
nodes is large enough to observe a wide range of linear dispersions in the
bands, and only one kind of such node's pairs is present in the Brillouin zone.
We also show the presence of Fermi arcs stable across a wide range of chemical
potentials. Finally, the lack of contributions from trivial points to the
low-energy properties makes the materials a promising candidate for practical
devices.
We analyze an analog of the $t$-$J$-$U$ model as applied to the description
of a single moir\'e flat band of twisted WSe$_2$ bilayer. To take into account
the correlation effects induced by a significant strength of the Coulomb
repulsion, we use the Gutzwiller approach and compare it with the results
obtained by the Hartree-Fock method. We discuss in detail the graduate
appearance of a two dome structure of the superconducting state in the phase
diagram by systematically increasing the Coulomb repulsion integral, $U$. The
two superconducting domes residing on both sides of a Mott insulating state can
be reproduced for a realistic parameter range in agreement with the available
experimental data. According to our analysis the paired state has a highly
unconventional character with a mixed $d+id$ (singlet) and $p-ip$ (triplet)
symmetry. Both components of the mixed paired state are of comparable
amplitudes. However, as shown here, a transition between pure singlet and pure
triplet pairing should be possible in the considered system by tuning the gate
voltage, which controls the magnitude of the valley-dependent spin-splitting in
the system.
We analyze the possible dynamical chiral symmetry breaking patterns taking
place within Weyl type of materials. Here, these systems are modeled by the
(2+1)-dimensional Gross-Neveu model with a tilt in the Dirac cone. The
optimized perturbation theory (OPT) is employed in order to evaluate the
effective potential at finite temperatures and chemical potentials beyond the
traditional large-$N$ limit. The nonperturbative finite-$N$ corrections
generated by the OPT method and its associated variational procedure show that
a first-order phase transition boundary, missed at large $N$, exists in the
regime of low temperatures and large chemical potentials. This result, which
represents our main finding, implies that one should hit a region of mixed
phases when exploring the low-temperature range. The associated first order
transition line, which starts at $T=0$, terminates at a tricritical point such
that the transitions taking place at high $T$ are of the second kind. In
particular, we discuss how the tilt in the Dirac cone affects the position of
the tricritical point as well as the values of critical temperature and
coexistence chemical potential among other quantities. Some experimental
implications and predictions are also briefly discussed.
In this work, we exhaust all the spin-space symmetries, which fully
characterize collinear, non-collinear, commensurate, and incommensurate spiral
magnetism, and investigate enriched features of electronic bands that respect
these symmetries. We achieve this by systematically classifying the so-called
spin space groups (SSGs) - joint symmetry groups of spatial and spin operations
that leave the magnetic structure unchanged. Generally speaking, they are
accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is
negligible (finite but weaker than the interested energy scale); but we also
show that specific SSGs could remain valid even in the presence of a strong
SOC. By representing the SSGs as O($N$) representations, we - for the first
time - obtain the complete classifications of 1421, 9542, and 56512 distinct
SSGs for collinear ($N=1$), coplanar ($N=2$), and non-coplanar ($N=3$)
magnetism, respectively. SSG not only fully characterizes the symmetry of spin
d.o.f., but also gives rise to exotic electronic states, which, in general,
form projective representations of magnetic space groups (MSGs). Surprisingly,
electronic bands in SSGs exhibit features never seen in MSGs, such as
nonsymmorphic SSG Brillouin zone (BZ), where SSG operations behave as glide or
screw when act on momentum and unconventional spin-momentum locking, which is
completely determined by SSG, independent of Hamiltonian details. To apply our
theory, we identify the SSG for each of the 1604 published magnetic structures
in the MAGNDATA database on the Bilbao Crystallographic Server. Material
examples exhibiting aforementioned novel features are discussed with emphasis.
We also investigate new types of SSG-protected topological electronic states
that are unprecedented in MSGs.

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