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Strongly correlated Chern insulators in magic-angle twisted bilayer graphene
Interactions between electrons and the topology of their energy bands can create unusual quantum phases of matter. Most topological electronic phases appear in systems with weak electron–electron interactions. The instances in which topological phases emerge only as a result of strong interactions are rare and mostly limited to those realized in intense magnetic fields
1
. The discovery of flat electronic bands with topological character in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for strongly correlated topological phases
2
–
9
. Here we introduce a local spectroscopic technique using a scanning tunnelling microscope to detect a sequence of topological insulators in MATBG with Chern numbers
C
= ±1, ±2 and ±3, which form near filling factors of ±3, ±2 and ±1 electrons per moiré unit cell, respectively, and are stabilized by modest magnetic fields. One of the phases detected here (
C
= +1) was previously observed when the sublattice symmetry of MATBG was intentionally broken by a hexagonal boron nitride substrate, with interactions having a secondary role
9
. We demonstrate that strong electron–electron interactions alone can produce not only the previously observed phase, but also other unexpected Chern insulating phases in MATBG. The full sequence of phases that we observe can be understood by postulating that strong correlations favour breaking time-reversal symmetry to form Chern insulators that are stabilized by weak magnetic fields. Our findings illustrate that many-body correlations can create topological phases in moiré systems beyond those anticipated from weakly interacting models.
Strong electron–electron interactions in magic-angle twisted bilayer graphene can fundamentally change the topology of the system’s flat bands, producing a hierarchy of strongly correlated topological insulators in modest magnetic fields.
Journal Article
Continuous Mott transition in semiconductor moiré superlattices
The evolution of a Landau Fermi liquid into a non-magnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics
1
–
6
. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids
4
–
7
, exciton condensates
8
and unconventional superconductivity
1
. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice
9
–
22
, providing a unique opportunity to drive a metal–insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electrically tuning the effective interaction strength in MoTe
2
/WSe
2
moiré superlattices, we observe a continuous MIT at a fixed filling of one electron per unit cell. The existence of quantum criticality is supported by the scaling collapse of the resistance, a continuously vanishing charge gap as the critical point is approached from the insulating side, and a diverging quasiparticle effective mass from the metallic side. We also observe a smooth evolution of the magnetic susceptibility across the MIT and no evidence of long-range magnetic order down to ~5% of the Curie–Weiss temperature. This signals an abundance of low-energy spinful excitations on the insulating side that is further corroborated by the Pomeranchuk effect observed on the metallic side. Our results are consistent with the universal critical theory of a continuous Mott transition in two dimensions
4
,
23
.
The interaction strength in moiré superlattices is tuned to drive a continuous metal-to-insulator transition at a fixed electron density.
Journal Article
Fractional Chern insulators in magic-angle twisted bilayer graphene
Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue towards manipulating non-Abelian excitations. Early theoretical studies
1
–
7
have predicted their existence in systems with flat Chern bands and highlighted the critical role of a particular quantum geometry. However, FCI states have been observed only in Bernal-stacked bilayer graphene (BLG) aligned with hexagonal boron nitride (hBN)
8
, in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field. By contrast, magic-angle twisted BLG
9
–
12
supports flat Chern bands at zero magnetic field
13
–
17
, and therefore offers a promising route towards stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in magic-angle twisted BLG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically trivial charge density wave states. We demonstrate that, unlike the case of the BLG/hBN platform, the principal role of the weak magnetic field is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum geometry favourable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in flat moiré Chern bands.
A study using local compressibility measurements reports fractional Chern insulator states at low magnetic field in magic-angle twisted bilayer graphene, and establishes the applied magnetic field as a means to tune the Berry curvature distribution.
Journal Article
Topological insulator laser: Experiments
Ideas based on topology, initially developed in mathematics to describe the properties of geometric space under deformations, are now finding application in materials, electronics, and optics. The main driver is topological protection, a property that provides stability to a system even in the presence of defects. Harari et al. outline a theoretical proposal that carries such ideas over to geometrically designed laser cavities. The lasing mode is confined to the topological edge state of the cavity structure. Bandres et al. implemented those ideas to fabricate a topological insulator laser with an array of ring resonators. The results demonstrate a powerful platform for developing new laser systems. Science , this issue p. eaar4003 , p. eaar4005 Lasing is observed in an edge mode of a designed optical topological insulator. Physical systems exhibiting topological invariants are naturally endowed with robustness against perturbations, as manifested in topological insulators—materials exhibiting robust electron transport, immune from scattering by defects and disorder. Recent years have witnessed intense efforts toward exploiting these phenomena in photonics. Here we demonstrate a nonmagnetic topological insulator laser system exhibiting topologically protected transport in the cavity. Its topological properties give rise to single-mode lasing, robustness against defects, and considerably higher slope efficiencies compared to the topologically trivial counterparts. We further exploit the properties of active topological platforms by assembling the system from S -chiral microresonators, enforcing predetermined unidirectional lasing without magnetic fields. This work paves the way toward active topological devices with exciting properties and functionalities.
Journal Article
Evidence for unconventional superconductivity in twisted bilayer graphene
The emergence of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors
1
–
4
, as described by the Bardeen–Cooper–Schrieffer (BCS) theory. However, recent studies have shown that superconductivity persists even when Coulomb interactions are partially screened
5
,
6
. This suggests that pairing in MATBG might be conventional in nature and a consequence of the large density of states of its flat bands. Here we combine tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope to observe several key experimental signatures of unconventional superconductivity in MATBG. We show that the tunnelling spectra below the transition temperature
T
c
are inconsistent with those of a conventional
s
-wave superconductor, but rather resemble those of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunnelling gap
Δ
T
, which far exceeds the mean-field BCS ratio (with 2
Δ
T
/
k
B
T
c
~ 25), and the gap
Δ
AR
extracted from Andreev reflection spectroscopy (2
Δ
AR
/
k
B
T
c
~ 6). The tunnelling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase. Moreover, the pseudogap and superconductivity are both absent when MATBG is aligned with hexagonal boron nitride. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.
A study combining tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope provides evidence for unconventional superconductivity in magic-angle twisted bilayer graphene.
Journal Article
Magic in twisted transition metal dichalcogenide bilayers
The long-wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe
2
, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles
θ
< 4
∘
, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, we predict the realization of a generalized Kane-Mele model with a topological flat band, interaction-driven Haldane insulator, and Mott insulators at the filling of one hole per moiré unit cell. The combination of flat dispersion and uniformity of Berry curvature near the magic angle holds promise for realizing fractional quantum anomalous Hall effect at fractional filling. We also identify twist angles favorable for quantum spin Hall insulators and interaction-induced quantum anomalous Hall insulators at other integer fillings.
The e moiré superlattice in twisted 2D structures becomes a highly tunable platform of strongly correlated electron systems. Here, the authors predict rich physics at small twist angles in twisted transition metal dichalcogenide bilayers, including a magic angle for flat band, interaction-driven Haldane insulator, fractional quantum anomalous Hall effect and quantum spin Hall insulators.
Journal Article
A quantized microwave quadrupole insulator with topologically protected corner states
A quantized quadrupole topological insulator composed of capacitively coupled microwave resonators has corner states that are protected by bulk topology and exhibit exceptional robustness against edge deformation.
Topological corner states
The properties of many materials with topological band structures can be understood in terms of a quantization of the electric polarization. A new class of higher-order topological insulators has recently been predicted by considering a quantization of higher-order polarizations. Christopher Peterson
et al.
now use a metamaterial composed of coupled microwave resonators to demonstrate such a system experimentally: a quantized quadrupole topological insulator that has corner states that are protected by topology. By deforming one of the edges from the topological to the trivial regime, they show that these corner states move inward to the corners of the newly generated boundaries, confirming that they are protected by the topology of the bulk. Such demonstrations not only provide evidence of a unique form of robustness, but also show that reconfigurable microwave circuits are a promising platform for exploring exotic topological phases of matter.
The theory of electric polarization in crystals defines the dipole moment of an insulator in terms of a Berry phase (geometric phase) associated with its electronic ground state
1
,
2
. This concept not only solves the long-standing puzzle of how to calculate dipole moments in crystals, but also explains topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator
3
,
4
and the quantum spin Hall insulator
5
,
6
,
7
, as well as quantized adiabatic pumping processes
8
,
9
,
10
. A recent theoretical study has extended the Berry phase framework to also account for higher electric multipole moments
11
, revealing the existence of higher-order topological phases that have not previously been observed. Here we demonstrate experimentally a member of this predicted class of materials—a quantized quadrupole topological insulator—produced using a gigahertz-frequency reconfigurable microwave circuit. We confirm the non-trivial topological phase using spectroscopic measurements and by identifying corner states that result from the bulk topology. In addition, we test the critical prediction that these corner states are protected by the topology of the bulk, and are not due to surface artefacts, by deforming the edges of the crystal lattice from the topological to the trivial regime. Our results provide conclusive evidence of a unique form of robustness against disorder and deformation, which is characteristic of higher-order topological insulators.
Journal Article
Bulk–disclination correspondence in topological crystalline insulators
Most natural and artificial materials have crystalline structures from which abundant topological phases emerge
1
–
6
. However, the bulk–edge correspondence—which has been widely used in experiments to determine the band topology from edge properties—is inadequate in discerning various topological crystalline phases
7
–
16
, leading to challenges in the experimental classification of the large family of topological crystalline materials
4
–
6
. It has been theoretically predicted that disclinations—ubiquitous crystallographic defects—can provide an effective probe of crystalline topology beyond edges
17
–
19
, but this has not yet been confirmed in experiments. Here we report an experimental demonstration of bulk–disclination correspondence, which manifests as fractional spectral charge and robust bound states at the disclinations. The fractional disclination charge originates from the symmetry-protected bulk charge patterns—a fundamental property of many topological crystalline insulators (TCIs). Furthermore, the robust bound states at disclinations emerge as a secondary, but directly observable, property of TCIs. Using reconfigurable photonic crystals as photonic TCIs with higher-order topology, we observe these hallmark features via pump–probe and near-field detection measurements. It is shown that both the fractional charge and the localized states emerge at the disclination in the TCI phase but vanish in the trivial phase. This experimental demonstration of bulk–disclination correspondence reveals a fundamental phenomenon and a paradigm for exploring topological materials.
It is experimentally shown that topological states exist at crystallographic defects in the bulk and that disclination defects trap fractional charges characteristic of topological crystalline insulators.
Journal Article
Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice
Studies of two-dimensional electron systems in a strong magnetic field revealed the quantum Hall effect
1
, a topological state of matter featuring a finite Chern number
C
and chiral edge states
2
,
3
. Haldane
4
later theorized that Chern insulators with integer quantum Hall effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (ABC-TLG/hBN) moiré superlattice provides an attractive platform with which to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent, electrically tunable Chern number
5
,
6
. Here we report the experimental observation of a correlated Chern insulator in an ABC-TLG/hBN moiré superlattice. We show that reversing the direction of the applied vertical electric field switches the moiré minibands of ABC-TLG/hBN between zero and finite Chern numbers, as revealed by large changes in magneto-transport behaviour. For topological hole minibands tuned to have a finite Chern number, we focus on quarter filling, corresponding to one hole per moiré unit cell. The Hall resistance is well quantized at
h
/2
e
2
(where
h
is Planck’s constant and
e
is the charge on the electron), which implies
C
= 2, for a magnetic field exceeding 0.4 tesla. The correlated Chern insulator is ferromagnetic, exhibiting substantial magnetic hysteresis and a large anomalous Hall signal at zero magnetic field. Our discovery of a
C
= 2 Chern insulator at zero magnetic field should open up opportunities for discovering correlated topological states, possibly with topological excitations
7
, in nearly flat and topologically nontrivial moiré minibands.
A topological Chern insulating state is reported to emerge from strong correlations in flat moiré bands in a graphene superlattice and by applying a vertical electric field the Chern number is switched.
Journal Article