16 research outputs found
Inherited and flatband-induced ordering in twisted graphene bilayers
The nature of the insulating and superconducting states in twisted bilayer
graphene systems is intensely debated. While many works seek for explanations
in the few flat bands near the Fermi level, theory and a number of experiments
suggest that nontwisted bilayer graphene systems do exhibit - or are at least
close to - an ordered, insulating ground state related to antiferromagnetic
ordering. Here we investigate in which ways this magnetic ordering scenario is
affected by the slight twisting between the layers. We find that at charge
neutrality the ordering tendencies of twisted systems interpolate between those
of untwisted AA and AB stacked bilayers at intermediate temperatures, while at
lower temperatures of the order of typical flat-band dispersion energies, the
ordering tendencies are even enhanced for the twisted systems. The preferred
order at charge neutrality still exhibits an antiferromagnetic spin
arrangement, with ordered moments alternating on the carbon-carbon bonds, with
an enveloping variation on the moir\'e scale. This ordering can be understood
as inherited from the untwisted systems. However, even in the RPA analysis, the
possible low-energy behaviors are quite versatile, and slight doping of one or
more electrons per moir\'e cell can take the system into a, potentially
flat-band induced, ferromagnetic phase.Comment: 8 pages, 9 figure
Functional renormalization group for a large moir\'e unit cell
Layers of two-dimensional materials arranged at a twist angle with respect to
each other lead to enlarged unit cells with potentially strongly altered band
structures, offering a new arena for novel and engineered many-body ground
states. For the exploration of these, renormalization group methods are an
appropriate, flexible tool that take into account the mutual influence of
competing tendencies. Here we show that, within reasonable, non-trivial
approximations, the functional renormalization group known from simpler
two-dimensional systems can be employed for the large-unit cell moir\'e
superlattices with more than 10.000 bands, remedying the need to employ ad hoc
restrictions to effective low-energy theories of a few bands and/or effective
continuum theories. This provides a description on the atomic scale, allowing
one to absorb available ab-initio information on the model parameters and
therefore lending the analysis a more concrete quantitative character. For the
case of twisted bilayer graphene models, we explore the leading ordering
tendencies depending on the band filling and the range of interactions. The
results indicate a delicate balance between distinct magnetically ordered
ground states, as well as the occurrence of a charge modulation within the
moir\'e unit cell for sufficiently non-local repulsive interaction.Comment: 9 pages, 8 figure
Spin-fluctuation-induced pairing in twisted bilayer graphene
We investigate the interplay of magnetic fluctuations and Cooper pairing in
twisted bilayer graphene from a purely microscopic model within a large-scale
tight-binding approach resolving the \AA ngstr\"om scale. For local onsite
repulsive interactions and using the random-phase approximation for spin
fluctuations, we derive a microscopic effective pairing interaction that we use
for self-consistent solutions of the Bogoliubov-de-Gennes equations of
superconductivity. We study the predominant pairing types as function of
interaction strength, temperature and band filling. For large regions of this
parameter space, we find chiral -wave pairing regimes, spontaneously
breaking time-reversal symmetry, separated by magnetic instabilities at integer
band fillings. Interestingly, the -wave pairing is strongly concentrated in
the AA regions of the moir\'e unit cell and exhibits phase windings of integer
multiples of around these superconducting islands, i.e. pinned vortices.
The spontaneous circulating current creates a distinctive magnetic field
pattern. This signature of the chiral pairing should be measurable by
state-of-the-art experimental techniques.Comment: 5 pages, 3 figure
Competition of Density Waves and Superconductivity in Twisted Tungsten Diselenide
Evidence for correlated insulating and superconducting phases around regions
of high density of states was reported in the strongly spin-orbit coupled
van-der Waals material twisted tungsten diselenide (tWSe). We investigate
their origin and interplay by using a functional renormalization group approach
that allows to describe superconducting and spin/charge instabilities in an
unbiased way. We map out the phase diagram as function of filling and
perpendicular electric field, and find that the moir\'e Hubbard model for
tWSe features mixed-parity superconducting order parameters with -wave
and topological -wave symmetry next to (incommensurate) density wave
states. Our work systematically characterizes competing interaction-driven
phases in tWSe beyond mean-field approximations and provides guidance for
experimental measurements by outlining the fingerprint of correlated states in
interacting susceptibilities.Comment: 7 pages, 3 figures, supplemental materia
Rashba spin-orbit coupling in the square lattice Hubbard model: A truncated-unity functional renormalization group study
The Rashba-Hubbard model on the square lattice is the paradigmatic case for
studying the effect of spin-orbit coupling, which breaks spin and inversion
symmetry, in a correlated electron system. We employ a truncated-unity variant
of the functional renormalization group which allows us to analyze magnetic and
superconducting instabilities on equal footing. We derive phase diagrams
depending on the strengths of Rasbha spin-orbit coupling, real second-neighbor
hopping and electron filling. We find commensurate and incommensurate magnetic
phases which compete with d-wave superconductivity. Due to the breaking of
inversion symmetry, singlet and triplet components mix; we quantify the mixing
of d-wave singlet pairing with f-wave triplet pairing.Comment: 9 pages, 7 figure
Collective charge excitations between moir\'e-minibands in twisted WSe2 bilayers from resonant inelastic light scattering
We establish low-temperature resonant inelastic light scattering (RILS)
spectroscopy as a tool to probe the formation of a series of moir\'e-bands in
twisted WSe2 bilayers by accessing collective inter-moir\'e-band excitations
(IMBE). We observe resonances in such RILS spectra at energies in agreement
with inter-moir\'e band (IMB) transitions obtained from an ab-initio based
continuum model. Transitions between the first and second IMB for a twist angle
of about 8{\deg} are reported and between first and second, third and higher
bands for a twist of about 3{\deg}. The signatures from IMBE for the latter
highlight a strong departure from parabolic bands with flat minibands
exhibiting very high density of states in accord with theory. These
observations allow to quantify the transition energies at the K-point where the
states relevant for correlation physics are hosted.Comment: 6 pages, 3 figures and SI with 5 pages and 3 SI figure
Moiré nematic phase in twisted double bilayer graphene
Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron–electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report the existence of three-fold rotational (C3) symmetry breaking in twisted double bilayer graphene. Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the magnitude of the rotational symmetry breaking does not depend on the degree of the heterostrain or the displacement field, being instead a manifestation of an interaction-driven electronic nematic phase. We show that the nematic phase is a primary order that arises from the normal metal state over a wide range of doping away from charge neutrality. Our modelling suggests that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moiré lattice.S.T. and A.N.P. acknowledge funding from Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. STM equipment support (A.N.P.) and 2D sample synthesis (Y.S.) were provided by the Air Force Office of Scientific Research via grant no. FA9550-16-1-0601. C.R.-V. acknowledges funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement no. 844271. A.R. acknowledges funding by the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT1249-19) and the Flatiron Institute, a division of the Simons Foundation. L.K., D.M.K. and A.R. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy-Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769 and Advanced Imaging of Matter (AIM) EXC 2056−390715994 and funding by the Deutsche Forschungsgemeinschaft (DFG) under RTG 1995, within the Priority Program SPP 2244 ‘2DMP’ and GRK 2247. A.R. acknowledges support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. H.O. is supported by the NSF MRSEC programme grant no. DMR-1420634. Tight-binding and fRG simulations were performed with computing resources granted by RWTH Aachen University under projects rwth0496 and rwth0589. R.S. and M.S.S. acknowledge support from the National Science Foundation under grant no. DMR-2002850. R.M.F. was supported by the DOE-BES under award no. DE-SC0020045. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001), JSPS KAKENHI (grant no. JP20H00354) and the CREST (grant no. JPMJCR15F3) JST.Peer reviewe