Evidence of the fractional quantum spin Hall effect in moiré MoTe2.

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities1-6. So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0 = e2/h (with e and h denoting the electron charge and Planck's constant, respectively)7-14. Here we report transport evidence of a fractional QSH insulator in 2.1° twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands15,16. At filling factor ν = 3 of the moiré valence bands, each edge contributes a conductance 3 2 G 0 with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Furthermore, at ν = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G0, 2G0 and 3G0, respectively. Our results open up the possibility of realizing time-reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moiré materials17-19.

Thermodynamic evidence of fractional Chern insulator in moiré MoTe2.

Chern insulators, which are the lattice analogues of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices1-3. Until now, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field3-8, whereas fractional Chern insulators have been reported in only graphene-based systems under a finite magnetic field9,10. The emergence of semiconductor moiré materials11, which support tunable topological flat bands12,13, provides an opportunity to realize fractional Chern insulators13-16. Here we report thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor ν = 1 and 2/3, the system is incompressible and spontaneously breaks time-reversal symmetry. We show that they are integer and fractional Chern insulators, respectively, from the dispersion of the state in the filling factor with an applied magnetic field. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for the demonstration of quantized fractional Hall conductance and anyonic excitation and braiding17 in semiconductor moiré materials.

Gate-tunable heavy fermions in a moiré Kondo lattice.

The Kondo lattice-a matrix of local magnetic moments coupled through spin-exchange interactions to itinerant conduction electrons-is a prototype of strongly correlated quantum matter1-4. Usually, Kondo lattices are realized in intermetallic compounds containing lanthanide or actinide1,2. The complex electronic structure and limited tunability of both the electron density and exchange interactions in these bulk materials pose considerable challenges to studying Kondo lattice physics. Here we report the realization of a synthetic Kondo lattice in AB-stacked MoTe2/WSe2 moiré bilayers, in which the MoTe2 layer is tuned to a Mott insulating state, supporting a triangular moiré lattice of local moments, and the WSe2 layer is doped with itinerant conduction carriers. We observe heavy fermions with a large Fermi surface below the Kondo temperature. We also observe the destruction of the heavy fermions by an external magnetic field with an abrupt decrease in the Fermi surface size and quasi-particle mass. We further demonstrate widely and continuously gate-tunable Kondo temperatures through either the itinerant carrier density or the Kondo interaction. Our study opens the possibility of in situ access to the phase diagram of the Kondo lattice with exotic quantum criticalities in a single device based on semiconductor moiré materials2-9.

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 physics1-6. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids4-7, exciton condensates8 and unconventional superconductivity1. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice9-22, 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 MoTe2/WSe2 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 dimensions4,23.

Quantum Oscillations in Graphene Using Surface Acoustic Wave Resonators.

Surface acoustic waves (SAWs) provide a contactless method for measuring wave-vector-dependent conductivity. This technique has been used to discover emergent length scales in the fractional quantum Hall regime of traditional, semiconductor-based heterostructures. SAWs would appear to be an ideal match for van der Waals heterostructures, but the right combination of substrate and experimental geometry to allow access to the quantum transport regime has not yet been found. We demonstrate that SAW resonant cavities fabricated on LiNbO_{3} substrates can be used to access the quantum Hall regime of high-mobility, hexagonal boron nitride encapsulated, graphene heterostructures. Our work establishes SAW resonant cavities as a viable platform for performing contactless conductivity measurements in the quantum transport regime of van der Waals materials.

van der Waals π Josephson Junctions.

Proximity-induced superconductivity in a ferromagnet can induce Cooper pairs with a finite center-of-mass momentum and stabilize Josephson junctions (JJs) with π phase difference in superconductor-ferromagnet-superconductor heterostructures. The emergence of two-dimensional layered superconducting and magnetic materials promises a new platform for realizing π JJs with atomically sharp interfaces. Here we demonstrate a thickness-driven 0-π transition in JJs made of NbSe2 (an Ising superconductor) and Cr2Ge2Te6 (a ferromagnetic semiconductor). By systematically increasing the Cr2Ge2Te6 weak link thickness, we observe a vanishing supercurrent at a critical thickness of ∼8 nm, followed by a re-entrant supercurrent. Near the critical thickness, we further observe unusual supercurrent interference patterns with vanishing critical current around zero in-plane magnetic field. They signify the formation of 0-π JJs (with both 0 and π regions), likely induced by the nanoscale magnetic domains in Cr2Ge2Te6.

Imaging and control of critical fluctuations in two-dimensional magnets.

Strong magnetization fluctuations are expected near the thermodynamic critical point of a continuous magnetic phase transition. Such critical fluctuations are highly correlated and in principle can occur at any time and length scales1; they govern critical phenomena and potentially can drive new phases2,3. Although critical phenomena in magnetic materials have been studied using neutron scattering, magnetic a.c. susceptibility and other techniques4-6, direct real-time imaging of critical magnetization fluctuations remains elusive. Here we develop a fast and sensitive magneto-optical imaging microscope to achieve wide-field, real-time monitoring of critical magnetization fluctuations in single-layer ferromagnetic insulator CrBr3. We track the critical phenomena directly from the fluctuation correlations and observe both slowing-down dynamics and enhanced correlation length. Through real-time feedback control of the critical fluctuations, we further achieve switching of magnetic states solely by electrostatic gating. The ability to directly image and control critical fluctuations in 2D magnets opens up exciting opportunities to explore critical phenomena and develop applications in nanoscale engines and information science.

Manipulation of the van der Waals Magnet Cr2Ge2Te6 by Spin-Orbit Torques.

We report measurements of current-induced thermoelectric and spin-orbit torque effects within devices in which multilayers of the semiconducting two-dimensional van der Waals magnet Cr2Ge2Te6 (CGT) are integrated with Pt and Ta metal overlayers. We show that the magnetic orientation of the CGT can be detected accurately either electrically (using an anomalous Hall effect) or optically (using magnetic circular dichroism) with good consistency. The samples exhibit large thermoelectric effects, but nevertheless, the spin-orbit torque can be measured quantitatively using the angle-dependent second harmonic Hall technique. For CGT/Pt, we measure the spin-orbit torque efficiency to be similar to conventional metallic-ferromagnet/Pt devices with the same Pt resistivity. The interfacial transparency for spin currents is therefore similar in both classes of devices. Our results demonstrate the promise of incorporating semiconducting 2D magnets within spin-orbitronic and magneto-thermal devices.

Nonlinear anomalous Hall effect in few-layer WTe2.

The Hall effect occurs only in systems with broken time-reversal symmetry, such as materials under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE)1. Here we show a nonlinear AHE in a non-magnetic material under zero magnetic field, in which the Hall voltage depends quadratically on the longitudinal current2-6. We observe the effect in few-layer Td-WTe2, a two-dimensional semimetal with broken inversion symmetry and only one mirror line in the crystal plane. Our angle-resolved electrical measurements reveal that the Hall voltage maximizes (vanishes) when the bias current is perpendicular (parallel) to the mirror line. The observed effect can be understood as an AHE induced by the bias current, which generates an out-of-plane magnetization. The temperature dependence of the Hall conductivity further suggests that both the intrinsic Berry curvature dipole and extrinsic spin-dependent scatterings contribute to the observed nonlinear AHE.

An unusual continuous paramagnetic-limited superconducting phase transition in 2D NbSe 2.

Time reversal and spatial inversion are two key symmetries for conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity 1 . Breaking inversion symmetry can lead to mixed-parity Cooper pairing and unconventional superconducting properties1-5. Two-dimensional (2D) NbSe2 has emerged as a new non-centrosymmetric superconductor with the unique out-of-plane or Ising spin-orbit coupling (SOC)6-9. Here we report the observation of an unusual continuous paramagnetic-limited superconductor-normal metal transition in 2D NbSe2. Using tunelling spectroscopy under high in-plane magnetic fields, we observe a continuous closing of the superconducting gap at the upper critical field at low temperatures, in stark contrast to the abrupt first-order transition observed in BCS thin-film superconductors10-12. The paramagnetic-limited continuous transition arises from a large spin susceptibility of the superconducting phase due to the Ising SOC. The result is further supported by self-consistent mean-field calculations based on the ab initio band structure of 2D NbSe2. Our findings establish 2D NbSe2 as a promising platform to explore novel spin-dependent superconducting phenomena and device concepts 1 , such as equal-spin Andreev reflection 13 and topological superconductivity14-16.

Switchable moiré potentials in ferroelectric WTe2/WSe2 superlattices.

Moiré materials with superlattice periodicity many times the atomic length scale have shown strong electronic correlations and band topology with unprecedented tunability. Non-volatile control of the moiré potentials could allow on-demand switching of superlattice effects but has remained challenging to achieve. Here we demonstrate the switching of the correlated and moiré band insulating states, and the associated nonlinear anomalous Hall effect, by the ferroelectric effect. This is achieved in a ferroelectric WTe2 bilayer of the Td structure with a centred-rectangular moiré superlattice induced by interfacing with a WSe2 monolayer of the H structure. The results can be understood in terms of polarization-dependent charge transfer between two WTe2 monolayers, in which the interfacial layer has a much stronger moiré potential depth; ferroelectric switching thus turns on and off the moiré insulating states. Our study demonstrates the potential for creating new functional moiré materials by incorporating intrinsic symmetry-breaking orders.

A tunable bilayer Hubbard model in twisted WSe2.

Moiré materials with flat electronic bands provide a highly controllable quantum system for studies of strong-correlation physics and topology. In particular, angle-aligned heterobilayers of semiconducting transition metal dichalcogenides with large band offset realize the single-band Hubbard model. Introduction of a new layer degree of freedom is expected to foster richer interactions, enabling Hund's physics, interlayer exciton condensation and new superconducting pairing mechanisms to name a few. Here we report competing electronic states in twisted AB-homobilayer WSe2, which realizes a bilayer Hubbard model in the weak interlayer hopping limit for holes. By layer-polarizing holes via a perpendicular electric field, we observe a crossover from an excitonic insulator to a charge-transfer insulator at a hole density of ν = 1 (in units of moiré density), a transition from a paramagnetic to an antiferromagnetic charge-transfer insulator at ν = 2 and evidence for a layer-selective Mott insulator at 1 < ν < 2. The unique coupling of charge and spin to external electric and magnetic fields also manifests a giant magnetoelectric response. Our results establish a new solid-state simulator for the bilayer Hubbard model Hamiltonian.

Enhanced photoresponse of a MoS2 monolayer using an AAO template.

Monolayer two-dimensional transition metal dichalcogenides (TMDs) with direct band gaps, such as MoS2, have received great attention from researchers due to their peculiar band structure and physical properties. However, their extremely small thickness (0.65 nm for MoS2) results in a critically low light absorption efficiency, thus limiting their optoelectronic applications. To achieve the enhancement of the light-matter interaction in MoS2, a resonant Al/AAO (anodic alumina oxide template)/MoS2 trilayer nanocavity structure was designed and implemented in the present study. In such a system, the appropriate change in pore size and pore depth of the AAO template via control of the growth conditions allows one to adjust the thickness and refractive index of the dielectric layer (AAO). This nanocavity structure provides a possible way to regulate the light-matter interaction of MoS2 film.

Enhanced valley splitting in monolayer WSe2 due to magnetic exchange field.

Exploiting the valley degree of freedom to store and manipulate information provides a novel paradigm for future electronics. A monolayer transition-metal dichalcogenide (TMDC) with a broken inversion symmetry possesses two degenerate yet inequivalent valleys, which offers unique opportunities for valley control through the helicity of light. Lifting the valley degeneracy by Zeeman splitting has been demonstrated recently, which may enable valley control by a magnetic field. However, the realized valley splitting is modest (∼0.2 meV T-1). Here we show greatly enhanced valley spitting in monolayer WSe2, utilizing the interfacial magnetic exchange field (MEF) from a ferromagnetic EuS substrate. A valley splitting of 2.5 meV is demonstrated at 1 T by magnetoreflectance measurements and corresponds to an effective exchange field of ∼12 T. Moreover, the splitting follows the magnetization of EuS, a hallmark of the MEF. Utilizing the MEF of a magnetic insulator can induce magnetic order and valley and spin polarization in TMDCs, which may enable valleytronic and quantum-computing applications.