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Electrons in solids owe their properties to the periodic potential landscapes they experience. The advent of moir\'e lattices has revolutionized our ability to engineer such landscapes on nanometer scales, leading to numerous groundbreaking discoveries. Despite this progress, direct imaging of these electrostatic potential landscapes remains elusive. In this work, we introduce the Atomic Single Electron Transistor (SET), a novel scanning probe utilizing a single atomic defect in a van der Waals (vdW) material, which serves as an ultrasensitive, high-resolution potential imaging sensor. Built upon the quantum twisting microscope (QTM) platform, this probe leverages the QTM's distinctive capability to form a pristine, scannable 2D interface between vdW heterostructures. Using the Atomic SET, we present the first direct images of the electrostatic potential in one of the most canonical moir\'e interfaces: graphene aligned to hexagonal boron nitride. Our results reveal that this potential exhibits an approximate C6 symmetry, has minimal dependence on the carrier density, and has a substantial magnitude of ~60 mV even in the absence of carriers. Theoretically, the observed symmetry can only be explained by a delicate interplay of physical mechanisms with competing symmetries. Intriguingly, the magnitude of the measured potential significantly exceeds theoretical predictions, suggesting that current understanding may be incomplete. With a spatial resolution of 1 nm and a sensitivity to detect the potential of even a few millionths of an electron charge, the Atomic SET opens the door for ultrasensitive imaging of charge order and thermodynamic properties for a range of quantum phenomena, including various symmetry-broken phases, quantum crystals, vortex charges, and fractionalized quasiparticles.

A fundamental idea in wave mechanics is that propagation in a periodic medium can be described by Bloch waves whose conserved crystal momenta define their transformations when displaced by the set of discrete lattice translations. In ordered materials where incommensurate spatial periods compete, this general principle is rendered ineffective, often with dramatic consequences. Examples are crystals with broken symmetries from charge or spin density waves, quasiperiodic lattices that produce diffraction patterns with crystallographically forbidden point symmetries, and stacks of two-dimensional lattices with a relative rotation (twist) between layers. In special cases when there is a small difference between the competing periods, a useful work-around is a continuum description where a periodic long-wavelength field produces Bragg scattering that coherently mixes short-wavelength carrier waves. In this work, we advocate an alternative approach to study three-dimensional twisted crystals that replaces their spectrally congested momentum-space Bloch band structures with a representation using squeezed coherent states in a Fock space of free-particle vortex states. This reorganization of the Hilbert space highlights the crucial role of the Coriolis force in the equations of motion that leads to unconventional phase space dynamics and edge state structure generic to a family of complex crystals., Comment: 9 + 16 pages; 4 + 6 figures. Comments are very appreciated!

Magnetic superconductors manifest a fascinating interplay between their magnetic and superconducting properties. This becomes evident, for example, in the significant enhancement of the upper critical field observed in uranium-based superconductors, or the destruction of superconductivity well below the superconducting transition temperature $T_c$ in cobalt-doped NbSe$_2$. In this work, we argue that the Kondo interaction plays a pivotal role in governing these behaviors. By employing a periodic Anderson model, we study the Kondo effect in superconductors with either singlet or triplet pairing. In the regime of small impurity energies and high doping concentrations, we find the emergence of a Kondo resistive region below $T_c$. While a magnetic field suppresses singlet superconductivity, it stabilizes triplet pairing through the screening of magnetic impurities, inducing reentrant superconductivity at high fields. Moreover, introducing an antisymmetric spin-orbital coupling suppresses triplet superconductivity. This framework provides a unified picture to understand the observation of Kondo effect in NbSe$_2$ as well as the phase diagrams in Kondo superconductors such as UTe$_2$, and URhGe., Comment: 9 pages, 3 figures

In-plane magnetic fields offer a relatively unexplored opportunity to alter the band structure of stacks of 2D materials so that they exhibit desired physical properties. Here we show that an in-plane magnetic field combined with a transverse electric field can induce an insulator-metal (IM) transition in bilayer graphene. Our study of the magnetic response reveals that the orbital magnetic susceptibility changes from diamagnetic to paramagnetic around the transition point. We discuss several strategies to observe the IM transition, switch the diamagnetism, and more generally control the band structure of stacked 2D materials at experimentally accessible magnetic fields., Comment: 9 pages, 4 figures

Moire superlattices formed in van der Waals heterostructures due to twisting, lattice mismatch and strain present an opportunity for creating novel metamaterials with unique properties not present in the individual layers themselves. Ferroelectricity for example, arises due to broken inversion symmetry in twisted and strained bilayers of 2D semiconductors with stacking domains of alternating out-of-plane polarization. However, understanding the individual contributions of twist and strain to the formation of topological polar nanostructures remains to be established and has proven to be experimentally challenging. Inversion symmetry breaking has been predicted to give rise to an in-plane component of polarization along the domain walls, leading to the formation of a network of topologically non-trivial merons (half-skyrmions) that are Bloch-type for twisted and Neel-type for strained systems. Here we utilise angle-resolved, high-resolution vector piezoresponse force microscopy (PFM) to spatially resolve polarization components and topological polar nanostructures in marginally twisted bilayer WSe2, and provide experimental proof for the existence of topologically non-trivial meron/antimeron structures. We observe both Bloch-type and Neel-type merons, allowing us to differentiate between moire superlattices formed due to twist or heterogeneous strain. This first demonstration of non-trivial real-space topology in a twisted van der Waals heterostructure opens pathways for exploring the connection between twist and topology in engineered nano-devices.

In sufficiently clean materials where electron-electron interactions are strong compared to momentum-relaxing scattering processes, electron transport resembles the flow of a viscous fluid. We study hydrodynamic electron transport across density interfaces (n-n junctions) in a 2DEG in the Corbino geometry. From numerical simulations in COMSOL using realistic parameters, we show that we can produce tunable viscous layers at the density interface by varying the density ratio of charge carriers. We quantitatively explain this observation with simple analytic expressions together with boundary conditions at the interface. We also show signatures of these viscous layers in the magnetoresistance. Breaking down viscous and ohmic contributions, we find that when outer radial region of the Corbino has higher charge density compared to the inner region, the viscous layers at the interface serve to suppress the magneto-resistance produced by momentum-relaxing scattering. Conversely, the magneto-resistance is enhanced when the inner region has higher density than the outer. Our results add to the repertoire of techniques for engineering viscous electron flows, which hold a promise for applications in future electronic devices.

For twisted bilayer graphene close to magic angle, we show that the effects of lattice relaxation and the Hartree interaction both become simultaneously important. Including both effects in a continuum theory reveals a Lifshitz transition to a Fermi surface topology that supports both a ``heavy fermion" pocket and an ultraflat band ($\approx 8~{\rm meV}$) that is pinned to the Fermi energy for a large range of fillings. We provide analytical and numerical results to understand the narrow ``magic angle range" that supports this pinned ultraflat band and make predictions for its experimental observation. We believe that the bands presented here are accurate at high temperature and provide a good starting point to understand the myriad of complex behaviour observed in this system.

By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moir\'e materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted WSe$_2$ bilayers using large-scale molecular dynamics simulations. Our theory is valid in graphene bilayers for twist angles $\theta \gtrsim 1^\circ$, and in twisted transition metal dichalcogenides for $\theta \gtrsim 4^\circ$. We also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

Electrons in quantum matter behave like a fluid when the quantum-mechanical carrier-carrier scattering dominates over other relaxation mechanisms. By combining a microscopic treatment of electron-electron interactions within the random phase approximation with a phenomenological Navier-Stokes like equation, we predict that in the limit of high temperature and strong Coulomb interactions, both monolayer and bilayer graphene exhibit a universal behavior in dynamic viscosity. We find that the dynamic viscosity to entropy density ratio for bilayer graphene is closer to the holographic bound suggesting that such a bound might be observable in a condensed matter system. We discuss how this could be observed experimentally using a magnetoconductance measurements in a Corbino geometry for a realistic range of temperature and carrier density.

The microscopic pairing mechanism for superconductivity in magic-angle twisted bilayer graphene remains an open question. Recent experimental studies seem to rule out a purely electronic mechanism due to the insensitivity of the critical superconducting temperature to either a highly doped screening layer or the proximity to a metallic screening gate. In this theoretical work, we explore the role of external screening layers on the superconducting properties of twisted bilayer graphene within a purely electronic mechanism. Consistent with the experimental observations, we find that the critical temperature is unaffected by screening unless the screening layer is closer than 3 nanometers from the superconductor. Thus, the available transport data is not in contradiction with a plasmon-mediated mechanism. We also investigate other properties of this plasmon-mediated superconductivity including signatures in the tunneling density of states as probed in spectroscopy experiments., Comment: 13 pages and 7 figures

Moir\'e-pattern based potential engineering has become an important way to explore exotic physics in a variety of two-dimensional condensed matter systems. While these potentials have induced correlated phenomena in almost all commonly studied 2D materials, monolayer graphene has remained an exception. We demonstrate theoretically that a single layer of graphene, when placed between two bulk boron nitride crystal substrates with the appropriate twist angles can support a robust topological ultra-flat band emerging from the second hole band. This is one of the simplest platforms to design and exploit topological flat bands.

The co-existence of ferromagnetism and superconductivity becomes possible through unconventional pairing in the superconducting state. Such materials are exceedingly rare in solid-state systems but are promising platforms to explore topological phases, such as Majorana bound states. Theoretical investigations date back to the late 1950s, but only a few systems have so far been experimentally identified as potential hosts. Here, we show that atomically-thin niobium diselenide (NbSe$_2$) intercalated with dilute cobalt atoms spontaneously displays ferromagnetism below the superconducting transition temperature ($T_c$). We elucidate the origin of this phase by constructing a magnetic tunnel junction that consists of cobalt and cobalt-doped niobium diselenide (Co-NbSe$_2$) as the two ferromagnetic electrodes, with an ultra-thin boron nitride as the tunnelling barrier. At a temperature well below $T_c$, the tunnelling magnetoresistance shows a bistable state, suggesting a ferromagnetic order in Co-NbSe$_2$. We propose a RKKY exchange coupling mechanism based on the spin-triplet superconducting order parameter to mediate such ferromagnetism. We further perform non-local lateral spin valve measurements to confirm the origin of the ferromagnetism. The observation of Hanle precession signals show spin diffusion length up to micrometres below Tc, demonstrating an intrinsic spin-triplet nature in superconducting NbSe$_2$. Our discovery of superconductivity-mediated ferromagnetism opens the door to an alternative design of ferromagnetic superconductors, Comment: 26 pages, 13 figures

The supermoir\'e lattice, built by stacking two moir\'e patterns, provides a platform for creating flat mini-bands and studying electron correlations. An ultimate challenge in assembling a graphene supermoir\'e lattice is in the deterministic control of its rotational alignment, which is made highly aleatory due to the random nature of the edge chirality and crystal symmetry of each component layer. Employing the so-called golden rule of three, here we present an experimental strategy to overcome this challenge and realize the controlled alignment of double-aligned hBN/graphene/hBN supermoir\'e lattice, where graphene is precisely aligned with both top hBN and bottom hBN. Remarkably, we find that the crystallographic edge of neighboring graphite can be used to better guide the stacking alignment, as demonstrated by the controlled production of 20 moir\'e samples with an accuracy better than 0.2 degree. Finally, we extend our technique to other strongly correlated electron systems, such as low-angle twisted bilayer graphene and ABC-stacked trilayer graphene, providing a strategy for flat-band engineering in these moir\'e materials., Comment: 20 pages, 4 figures

Electrons in condensed matter may transition into a variety of broken-symmetry phase states due to electron-electron interactions. Applying diverse mean-field approximations to the interaction term is arguably the simplest way to identify the phase states theoretically possible in a given setting. Here, we explore electron-electron attraction in a two-band system comprising symmetric conduction and valence bands touching each other at a single point. We assume a mean-field pairing between the electrons having opposite spins, momenta, and, in contrast to the conventional superconducting pairing, residing in opposite bands, i.e., having opposite energies. We show that electrons transition into a novel correlated ground state if and only if the bands are flat enough, i.e. the transition is impossible in the case of conventional parabolic bands. Although this state is not superconducting in the usual sense and does not exhibit a gap in its excitation spectrum, it is nevertheless immune to elastic scattering caused by any kind of disorder, and is therefore expected to exhibit high electric conductivity at low temperature, mimicking the behavior of a real superconductor. Having in mind the recent experimental realizations of flat-band electronic systems in twisted multilayers, we foresee an exciting opportunity for observing a new class of highly conductive materials., Comment: 12 pages strongly revised

Fluid dynamics is one of the cornerstones of modern physics and has recently found applications in the transport of electrons in solids. In most solids electron transport is dominated by extrinsic factors, such as sample geometry and scattering from impurities. However in the hydrodynamic regime Coulomb interactions transform the electron motion from independent particles to the collective motion of a viscous `electron fluid'. The fluid viscosity is an intrinsic property of the electron system, determined solely by the electron-electron interactions. Resolving the universal intrinsic viscosity is challenging, as it only affects the resistance through interactions with the sample boundaries, whose roughness is not only unknown but also varies from device to device. Here we eliminate all unknown parameters by fabricating samples with smooth sidewalls to achieve the perfect slip boundary condition, which has been elusive both in molecular fluids and electronic systems. We engineer the device geometry to create viscous dissipation and reveal the true intrinsic hydrodynamic properties of a 2D system. We observe a clear transition from ballistic to hydrodynamic electron motion, driven by both temperature and magnetic field. We directly measure the viscosity and electron-electron scattering lifetime (the Fermi quasiparticle lifetime) over a wide temperature range without fitting parameters, and show they have a strong dependence on electron density that cannot be explained by conventional theories based on the Random Phase Approximation.

Vertical stacking of atomically thin materials offers a large platform for realizing novel properties enabled by proximity effects and moir\'e patterns. Here we focus on mechanically assembled heterostructures of graphene and ReS$_2$, a van der Waals layered semiconductor. Using scanning tunneling microscopy and spectroscopy (STM/STS) we image the sharp edge between the two materials as well as areas of overlap. Locally resolved topographic images revealed the presence of a striped superpattern originating in the interlayer interactions between graphene's hexagonal structure and the triclinic, low in-plane symmetry of ReS$_2$. We compare the results with a theoretical model that estimates the shape and angle dependence of the moir\'e pattern between graphene and ReS$_2$. These results shed light on the complex interface phenomena between van der Waals materials with different lattice symmetries., Comment: 8 pages, 4 figures

Understanding and tuning correlated states is of great interest and significance to modern condensed matter physics. The recent discovery of unconventional superconductivity and Mott-like insulating states in magic-angle twisted bilayer graphene (tBLG) presents a unique platform to study correlation phenomena, in which the Coulomb energy dominates over the quenched kinetic energy as a result of hybridized flat bands. Extending this approach to the case of twisted multilayer graphene would allow even higher control over the band structure because of the reduced symmetry of the system. Here, we study electronic transport properties in twisted trilayer graphene (tTLG, bilayer on top of monolayer graphene heterostructure). We observed the formation of van Hove singularities which are highly tunable by twist angle and displacement field and can cause strong correlation effects under optimum conditions, including superconducting states. We provide basic theoretical interpretation of the observed electronic structure., Comment: 16 pages, 9 figures

Na3Bi has attracted significant interest in both bulk form as a three-dimensional topological Dirac semimetal and in ultra-thin form as a wide-bandgap two-dimensional topological insulator. Its extreme air sensitivity has limited experimental efforts on thin- and ultra-thin films grown via molecular beam epitaxy to ultra-high vacuum environments. Here we demonstrate air-stable Na3Bi thin films passivated with magnesium difluoride (MgF2) or silicon (Si) capping layers. Electrical measurements show that deposition of MgF2 or Si has minimal impact on the transport properties of Na3Bi whilst in ultra-high vacuum. Importantly, the MgF2-passivated Na3Bi films are air-stable and remain metallic for over 100 hours after exposure to air, as compared to near instantaneous degradation when they are unpassivated. Air stability enables transfer of films to a conventional high-magnetic field cryostat, enabling quantum transport measurements which verify that the Dirac semimetal character of Na3Bi films is retained after air exposure.

Recent experiments have reported evidence of dominant electron-hole scattering in the electric conductivity of suspended bilayer graphene near charge neutrality. According to these experiments, plots of the electric conductivity as a function of $\mu/k_BT$ (chemical potential scaled with temperature) obtained for different temperatures in the range of $12\rm{K}\lesssim T \lesssim 40\rm{K}$ collapse on a single curve independent of $T$. In a recent theory, this observation has been taken as an indication that the main sub-dominant scattering process is not electron-impurity but electron-phonon. Here we demonstrate that the collapse of the data on a single curve can be explained without invoking electron-phonon scattering, but assuming that the suspended bilayer graphene is not a truly gapless system. With a gap of $\sim 5$ meV, our theory produces excellent agreement with the observed conductivity over the full reported range of temperatures. These results are based on the hydrodynamic theory of conductivity, which thus emerges as a solid foundation for the analysis of experiments and the estimation of the band-gap in multiband systems., Comment: 5 pages, 2 figures

Understanding the normal-metal state transport in twisted bilayer graphene near magic angle is of fundamental importance as it provides insights into the mechanisms responsible for the observed strongly correlated insulating and superconducting phases. Here we provide a rigorous theory for phonon-dominated transport in twisted bilayer graphene describing its unusual signatures in the resistivity (including the variation with electron density, temperature, and twist angle) showing good quantitative agreement with recent experiments. We contrast this with the alternative Planckian dissipation mechanism that we show is incompatible with available experimental data. An accurate treatment of the electron-phonon scattering requires us to go well beyond the usual treatment, including both interband and intraband processes, considering the finite-temperature dynamical screening of the electron-phonon matrix element, and going beyond the linear Dirac dispersion. In addition to explaining the observations in currently available experimental data, we make concrete predictions that can be tested in ongoing experiments., Comment: 25 pages, 15 figures

Electrons commonly couple through Fr\"ohlich interactions with longitudinal optical phonons to form polarons. However, trions possess a finite angular momentum and should therefore couple instead to rotational optical phonons. This creates a polaronic trion whose binding energy is determined by the crystallographic orientation of the lattice. Here, we demonstrate theoretically within the Fr\"ohlich approach and experimentally by photoluminescence emission that the bare trion binding energy (20 meV) is significantly enhanced by the phonons at the interface between the two-dimensional semiconductor MoS$_2$ and the bulk transition metal oxide SrTiO$_3$. The low-temperature {binding energy} changes from 60 meV in [001]-oriented substrates to 90 meV for [111] orientation, as a result of the counter-intuitive interplay between the rotational axis of the MoS$_2$ trion and that of the SrTiO$_3$ phonon mode., Comment: 5+ pages (4 figures) + Suppl. Materials (7 figures), to appear in Phys. Rev. Lett. (August 2020)

Using the semiclassical quantum Boltzmann theory and employing the Dirac model with twist angle-dependent Fermi velocity we obtain results for the electrical resistivity, the electronic thermal resistivity, the Seebeck coefficient, and the Wiedemann-Franz ratio in near magic angle twisted bilayer graphene, as functions of doping density (around the charge-neutrality-point) and modified Fermi velocity $\tilde v$. The $\tilde v$-dependence of the relevant scattering mechanisms, i.e. electron-hole Coulomb, long-ranged impurities, and acoustic gauge phonons, is considered in detail. We find a range of twist angles and temperatures, where the combined effect of momentum-non-conserving collisions (long-ranged impurities and phonons) is minimal, opening a window for the observation of strong hydrodynamic transport. Several experimental signatures are identified, such as a sharp dependence of the electric resistivity on doping density and a large enhancement of the Wiedemann-Franz ratio and the Seebeck coefficient., Comment: 7 pages, 5 figures

A purely electronic mechanism is proposed for the unconventional superconductivity recently observed in twisted bilayer graphene (tBG) close to the magic angle. Using the Migdal-Eliashberg framework on a one parameter effective lattice model for tBG we show that a superconducting state can be achieved by means of collective electronic modes in tBG. We posit robust features of the theory, including an asymmetrical superconducting dome and the magnitude of the critical temperature that are in agreement with experiments., Comment: 5 pages, 3 figures

Electronic transport in the regime where carrier-carrier collisions are the dominant scattering mechanism has taken on new relevance with the advent of ultraclean two-dimensional materials. Here we present a combined theoretical and experimental study of ambipolar hydrodynamic transport in bilayer graphene demonstrating that the conductivity is given by the sum of two Drude-like terms that describe relative motion between electrons and holes, and the collective motion of the electron-hole plasma. As predicted, the measured conductivity of gapless, charge-neutral bilayer graphene is sample- and temperature-independent over a wide range. Away from neutrality, the electron-hole conductivity collapses to a single curve, and a set of just four fitting parameters provides quantitative agreement between theory and experiment at all densities, temperatures, and gaps measured. This work validates recent theories for dissipation-enabled hydrodynamic conductivity and creates a link between semiconductor physics and the emerging field of viscous electronics., Comment: Completely rewritten. Accepted for publication in Science Advances. 63 pages, 20 figures

Bilayer MoS2 is a centrosymmetric semiconductor with degenerate spin states in the six valleys at the corners of the Brillouin zone. It has been proposed that breaking of this inversion symmetry by an out-of-plane electric field breaks this degeneracy, allowing for spin and valley lifetimes to be manipulated electrically in bilayer MoS2 with an electric field. In this work, we report phase-coherent transport properties of double-gated mono-, bi-, and tri-layer MoS2. We observe a similar crossover from weak localization to weak anti-localization, from which we extract the spin relaxation time as a function of both electric field and temperature. We find that the spin relaxation time is inversely proportional to momentum relaxation time, indicating that D'yakonov-Perel mechanism is dominant in all devices despite its centrosymmetry. Further, we found no evidence of electric-field induced changes in spin-orbit coupling strength. This suggests that the interlayer coupling is sufficiently weak and that electron-doped dichalcogenide multilayers behave electrically as decoupled monolayers., Comment: 21 pages, 7 figures

We present low-temperature transport measurements of a gate-tunable thin film topological insulator system that features high mobility and low carrier density. Upon gate tuning to a regime around the charge neutrality point, we infer an absence of strong localization even at conductivities well below $e^2/h$, where two dimensional electron systems should conventionally scale to an insulating state. Oddly, in this regime the localization coherence peak lacks conventional temperature broadening, though its tails do change dramatically with temperature. Using a model with electron-impurity scattering, we extract values for the disorder potential and the hybridization of the top and bottom surface states., Comment: 6 pages, 4 figures, with 11 pages of supplementary information

Both insulating and conducting electronic behaviors have been experimentally seen in clean bilayer graphene samples at low temperature, and there is still no consensus on the nature of the interacting ground state at half-filling and in the absence of a magnetic field. Theoretically, several possibilities for the insulating ground states have been predicted for weak interaction strength. However, a recent renormalization-group calculation on a Hubbard model for charge-neutral bilayer graphene with short-range interactions suggests the emergence of low-energy Dirac fermions that would stabilize the metallic phase for weak interactions. Using a non-perturbative projective quantum Monte Carlo, we calculate the ground state for bilayer graphene using a realistic model for the Coulomb interaction that includes both short-range and long-range contributions. We find that a finite critical onsite interaction is needed to gap bilayer graphene, thereby confirming the Hubbard model expectations even in the presence of a long-range Coulomb potential, in agreement with our theoretical renormalization group analysis. In addition, we also find that the critical onsite interactions necessary to destabilize the metallic ground state decreases with increasing interlayer coupling., Comment: 7 pages, 4 figures

We present systematic ab initio calculations of the charge carrier correlations between adjacent layers of two-dimensional materials in the presence of both charged impurity and strain disorder potentials using the examples of monolayer and bilayer graphene. For the first time, our analysis yields unambiguous first-principles quantum corrections to the Thomas--Fermi densities for interacting two-dimensional systems described by orbital-free density functional theory. Specifically, using density-potential functional theory, we find that quantum corrections to the quasi-classical Thomas-Fermi approximation have to be taken into account even for heterostructures of mesoscopic size. In order for the disorder-induced puddles of electrons and holes to be anti-correlated at zero average carrier density for both layers, the strength of the strain potential has to exceed that of the impurity potential by at least a factor of ten, with this number increasing for smaller impurity densities. Furthermore, our results show that quantum corrections have a larger impact on puddle correlations than exchange does, and they are necessary for properly predicting the experimentally observed Gaussian energy distribution at charge neutrality., Comment: 13 pages, 11 figures, 2 tables

Starting from the strong-coupling limit of an extended Hubbard model, we develop a spin-fermion theory to study the insulating phase and pairing symmetry of the superconducting phase in twisted bilayer graphene. Assuming that the insulating phase is an anti-ferromagnetic insulator, we show that fluctuations of the anti-ferromagnetic order in the conducting phase can mediate superconducting pairing. Using a self-consistent mean-field analysis, we find that the pairing wave function has a chiral d-wave symmetry. Consistent with this observation, we show explicitly the existence of chiral Majorana edge modes by diagonalizing our proposed Hamiltonian on a finite-sized system. These results establish twisted bilayer graphene as a promising platform to realize topological superconductivity.

Recent experimental and numerical evidence suggest an intriguing universal relationship between the Fermi surface anisotropy of the non-interacting parent two-dimensional electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filing. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed non-perturbative and numerically-exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For the half-filled composite Fermi liquid, this result is surprising since a Dirac fermion ground state was only recently proposed as an alternative to the usual HLR state. The importance of the long-range interaction, expected for Dirac systems, is also consistent with recent transport measurements. Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators organic conductors, and magic-angle twisted bilayer graphene., Comment: 4 pages, 3 figures

Using the continuum model for low energy non-interacting electronic structure of moir\'e van der Waals heterostructures developed by Bistritzer and MacDonald [1], we study the competition between spin, charge, and superconducting order in twisted bilayer graphene. Surprisingly, we find that for a range of small angles inclusive of the so-called magic angle, this model features robust Fermi pockets that preclude any Mott insulating phase at weak coupling. However, a Fermi surface reconstruction at $\theta \gtrsim 1.2^{\circ}$ gives emergent van Hove singularities without any Fermi pockets. Using a hot-spot model for Fermi surface patches around these emergent saddle points, we develop a random-phase approximation from which we obtain a phase diagram very similar to that obtained recently by Isobe, Yuan, and Fu using the parquet renormalization group [2] but with additional insights. For example, our model shows strong nesting around time-reversal symmetric points at a moderate doping of $\sim 2 \times 10^{11} \text{cm}^{-2}$ away from the van Hove singularity. When this nesting dominates, we predict that charge-order enhances singlet superconductivity, while spin-order suppresses superconductivity. Our theory also provides additional possibilities for the case of unnested Fermi surfaces., Comment: 7 pages, 5 figures

The electric field induced quantum phase transition from topological to conventional insulator has been proposed as the basis of a topological field effect transistor [1-4]. In this scheme an electric field can switch 'on' the ballistic flow of charge and spin along dissipationless edges of the two-dimensional (2D) quantum spin Hall insulator [5-9], and when 'off' is a conventional insulator with no conductive channels. Such as topological transistor is promising for low-energy logic circuits [4], which would necessitate electric field-switched materials with conventional and topological bandgaps much greater than room temperature, significantly greater than proposed to date [6-8]. Topological Dirac semimetals(TDS) are promising systems in which to look for topological field-effect switching, as they lie at the boundary between conventional and topological phases [3,10-16]. Here we use scanning probe microscopy/spectroscopy (STM/STS) and angle-resolved photoelectron spectroscopy (ARPES) to show that mono- and bilayer films of TDS Na3Bi [3,17] are 2D topological insulators with bulk bandgaps >400 meV in the absence of electric field. Upon application of electric field by doping with potassium or by close approach of the STM tip, the bandgap can be completely closed then re-opened with conventional gap greater than 100 meV. The large bandgaps in both the conventional and quantum spin Hall phases, much greater than the thermal energy kT = 25 meV at room temperature, suggest that ultrathin Na3Bi is suitable for room temperature topological transistor operation.

Electrons behave like a classical fluid with a momentum distribution function that varies slowly in space and time when the quantum mechanical carrier-carrier scattering dominates over all other scattering processes. Recent experiments in monolayer and bilayer graphene have reported signatures of such hydrodynamic electron behavior in ultra-clean devices. In this theoretical work, starting from a microscopic treatment of electron-electron, electron-phonon and electron-impurity interactions within the Random Phase Approximation, we demonstrate that monolayer and bilayer graphene both host two different hydrodynamic regimes. We predict that the hydrodynamic window in bilayer graphene is stronger than in monolayer graphene, and has a characteristic `v-shape' as opposed to a `lung-shape'. Finally, we collapse experimental data onto a universal disorder-limited theory, thereby proving that the observed violation of Wiedemann-Franz law in monolayers occurs in a regime dominated by impurity-induced electron-hole puddles., Comment: 6 pages, 4 figures

Large-area thin films of topological Dirac semimetal Na$_3$Bi are grown on amorphous SiO$_2$:Si substrates to realise a field-effect transistor with the doped Si acting as back gate. As-grown films show charge carrier mobilities exceeding 7,000 cm$^2$/Vs and carrier densities below 3 $\times $10$^{18}$ cm$^{-3}$, comparable to the best thin-film Na$_3$Bi. An ambipolar field effect and minimum conductivity are observed, characteristic of Dirac electronic systems. The results are quantitatively understood within a model of disorder-induced charge inhomogeneity in topological Dirac semimetals. Due to the inverted band structure, the hole mobility is significantly larger than the electron mobility in Na$_3$Bi, and when present, these holes dominate the transport properties., Comment: 5 pages, 4 figures; minor corrections and revisions for readability

Heterostructures of atomically-thin materials have attracted significant interest owing to their ability to host novel electronic properties fundamentally distinct from their constituent layers. In the case of graphene on boron nitride, the closely-matched lattices yield a moir\'e superlattice that modifies the graphene electron dispersion and opens gaps both at the primary Dirac point (DP) and the moir\'e-induced secondary Dirac point (SDP) in the valence band. While significant effort has focused on controlling the superlattice period via the rotational stacking order, the role played by the magnitude of the interlayer coupling has received comparatively little attention. Here, we modify the interaction between graphene and boron nitride by tuning their separation with hydrostatic pressure. We observe a dramatic enhancement of the DP gap with increasing pressure, but little change in the SDP gap. Our surprising results identify the critical role played by atomic-scale structural deformations of the graphene lattice and reveal new opportunities for band structure engineering in van der Waals heterostructures., Comment: 26 Pages, 16 Figures. (v2) Main text and figures are updated

Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Hamiltonian perturbed by smoothly varying moir\'e pattern pseudospin fields. Here, we present the moir\'e-band model of G/BN for arbitrary small twist angles under a framework that combines symmetry considerations with input from ab-initio calculations. Our analysis of the band gaps at the primary and secondary Dirac points highlights the role of inversion symmetry breaking contributions of the moir\'e patterns, leading to primary Dirac point gaps when the moir\'e strains give rise to a finite average mass, and to secondary gaps when the moir\'e pseudospin components are mixed appropriately. The pseudomagnetic strain fields which can reach values of up to $\sim$40 Tesla near symmetry points in the moir\'e cell stem almost entirely from virtual hopping and dominate over the contributions arising from bond length distortions due to the moir\'e strains., Comment: 14 pages, 8 figures, 3 tables

A linear unsaturating magnetoresistance at high perpendicular magnetic fields, together with a quadratic positive magnetoresistance at low fields, has been seen in many different experimental materials, ranging from silver chalcogenides and thin films of InSb to topological materials like graphene and Dirac semimetals. In the literature, two very different theoretical approaches have been used to explain this classical magnetoresistance as a consequence of sample disorder. The phenomenological Random Resistor Network model constructs a grid of four-terminal resistors, each with a varying random resistance. The Effective Medium Theory model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. Here, we demonstrate numerically that both models belong to the same universality class and that a restricted class of the Random Resistor Network is actually equivalent to the Effective Medium Theory. Both models are also in good agreement with experiments on a diverse range of materials. Moreover, we show that in both cases, a single parameter, i.e. the ratio of the fluctuations in the carrier density to the average carrier density, completely determines the magnetoresistance profile., Comment: 6 pages, 5 figures

The electronic structure of a crystalline solid is largely determined by its lattice structure. Recent advances in van der Waals solids, artificial crystals with controlled stacking of two-dimensional (2D) atomic films, have enabled the creation of materials with novel electronic structures. In particular, stacking graphene on hexagonal boron nitride (hBN) introduces moir\'e superlattice that fundamentally modifies graphene's band structure and gives rise to secondary Dirac points (SDPs). Here we find that the formation of a moir\'e superlattice in graphene on hBN yields new, unexpected consequences: a set of tertiary Dirac points (TDPs) emerge, which give rise to additional sets of Landau levels when the sample is subjected to an external magnetic field. Our observations hint at the formation of a hidden Kekul\'e superstructure on top of the moir\'e superlattice under appropriate carrier doping and magnetic fields.

The close approach of the Fermi energy EF of a Dirac semimetal to the Dirac point ED uncovers new physics such as velocity renormalization,1,2,3 and the Dirac plasma 4,5 at |EF -ED| < kBT, where kBT is the thermal energy. In graphene, substrate disorder drives fluctuations in EF. Three-dimensional topological Dirac semimetals (TDS)6,7 obviate the substrate, and should show reduced EF fluctuations due to better metallic screening and higher dielectric constants. Here we map the potential fluctuations in TDS Na3Bi using a scanning tunneling microscope. The rms potential fluctuations are significantly smaller than room temperature ({\Delta}EF,rms = 4-6 meV = 40-70 K) and comparable to the highest quality graphene on h-BN;8 far smaller than graphene on SiO2,9,10 or the Dirac surface state of a topological insulator.11 Surface Na vacancies produce a novel resonance close to the Dirac point with surprisingly large spatial extent and provides a unique way to tune the surface density of states in a TDS thin-film material., Comment: 25 pages (7 main manuscript), 9 figues (4 main manuscript)

Coulomb drag between parallel two-dimensional electronic layers is an excellent tool for the study of electron-electron interactions. In actual experiments, the layers display spatial charge density fluctuations due to imperfections such as external charged impurities. However, at present a systematic way of taking these inhomogeneities into account in drag calculations has been lacking, making the interpretation of experimental data problematic. On the other hand, there exists a highly successful and widely accepted formalism describing transport within single inhomogeneous layers known as effective medium theory. In this work, we generalize the standard effective medium theory to the case of Coulomb drag between two inhomogeneous sheets and demonstrate that inhomogeneity in the layers has a strong impact on drag transport. In the case of exciton condensation between the layers, we show that drag resistivity takes on a value determined by the amplitude of density fluctuation. Next we consider drag between graphene sheets, in which the existence of spatial charge density fluctuations is well-known. We show that these inhomogeneities play a crucial role in explaining existing experimental data. In particular, the temperature dependence of the experimentally observed peaks in drag resistivity can only be explained by taking the layer density fluctuations into account. We also propose a method of extracting information on the correlations between the inhomogeneities of the layers. The effective medium theory of Coulomb drag derived here is general and applies to all two-dimensional materials., Comment: 15 pages, 8 figures. Substantially rewritten to better reflect generality of the results. Numerical errors fixed

We report on spin transport features which are unique to high quality bilayer graphene, in absence of magnetic contaminants and strong intervalley mixing. The time-dependent spin polarization of propagating wavepacket is computed using an efficient quantum transport method. In the limit of vanishing effects of substrate and disorder, the energy-dependence of spin lifetime is similar to monolayer graphene with a M-shape profile and minimum value at the charge neutrality point, but with an electron-hole asymmetry fingerprint. In sharp contrast, the incorporation of substrate-induced electron-hole puddles (characteristics of supported graphene either on SiO2 orhBN) surprisingly results in a large enhancement of the low-energy spin lifetime and a lowering of its high-energy values. Such feature, unique to bilayer, is explained in terms of a reinforced Dyakonov-Perel mechanism at the Dirac point, whereas spin relaxation at higher energies is driven by pure dephasing effects. This suggests further electrostatic control of the spin transport length scales in graphene devices., Comment: To appear in Physics Review B as Rapid Communication

The elimination of extrinsic sources of spin relaxation is key in realizing the exceptional intrinsic spin transport performance of graphene. Towards this, we study charge and spin transport in bilayer graphene-based spin valve devices fabricated in a new device architecture which allows us to make a comparative study by separately investigating the roles of substrate and polymer residues on spin relaxation. First, the comparison between spin valves fabricated on SiO2 and BN substrates suggests that substrate-related charged impurities, phonons and roughness do not limit the spin transport in current devices. Next, the observation of a 5-fold enhancement in spin relaxation time in the encapsulated device highlights the significance of polymer residues on spin relaxation. We observe a spin relaxation length of ~ 10 um in the encapsulated bilayer with a charge mobility of 24000 cm2/Vs. The carrier density dependence of spin relaxation time has two distinct regimes; n<4 x 1012 cm-2, where spin relaxation time decreases monotonically as carrier concentration increases, and n>4 x 1012 cm-2, where spin relaxation time exhibits a sudden increase. The sudden increase in the spin relaxation time with no corresponding signature in the charge transport suggests the presence of a magnetic resonance close to the charge neutrality point. We also demonstrate, for the first time, spin transport across bipolar p-n junctions in our dual-gated device architecture that fully integrates a sequence of encapsulated regions in its design. At low temperatures, strong suppression of the spin signal was observed while a transport gap was induced, which is interpreted as a novel manifestation of impedance mismatch within the spin channel.

Twisted bilayer graphene (tBLG) forms a quasicrystal whose structural and electronic properties depend on the angle of rotation between its layers. Here we present a scanning tunneling microscopy study of gate-tunable tBLG devices supported by atomically-smooth and chemically inert hexagonal boron nitride (BN). The high quality of these tBLG devices allows identification of coexisting moir\'e patterns and moir\'e super-superlattices produced by graphene-graphene and graphene-BN interlayer interactions. Furthermore, we examine additional tBLG spectroscopic features in the local density of states beyond the first van Hove singularity. Our experimental data is explained by a theory of moir\'e bands that incorporates ab initio calculations and confirms the strongly non-perturbative character of tBLG interlayer coupling in the small twist-angle regime., Comment: 4 figures

The conductivity of graphene on a boron nitride substrate exhibits features in the terahertz (THz) and infrared (IR) frequency regimes that are associated with the periodic moir\'e pattern formed by the weakly coupled two-dimensional materials. The THz and IR features are strongest when the two honeycomb lattices are orientationally aligned, and in this case are Pauli blocked unless the Fermi level is close to $\pm 150$ meV relative to the graphene sheet Dirac point. Because the transition energies between moir\'e bands formed above the Dirac point are small, ac conductivity features in n-doped graphene tend to be overwhelmed by the Drude peak. The substrate-induced band splitting is larger at energies below the Dirac point, however, and can however lead to sharp features at THz and IR frequencies in p-doped graphene. In this Letter we focus on the strongest few THz and IR features, explaining how they arise from critical points in the moir\'e-band joint density-of-states, and commenting on the interval of Fermi energy over which they are active.

We present a comparative measurement of the G-peak oscillations of phonon frequency, Raman intensity and linewidth in the Magneto-Raman scattering of optical E2g phonons in mechanically exfoliated ABA- and ABC-stacked trilayer graphene (TLG). Whereas in ABA-stacked TLG, we observe magnetophonon oscillations consistent with single-bilayer chiral band doublets, the features are flat for ABC-stacked TLG up to magnetic fields of 9 T. This suppression can be attributed to the enhancement of band chirality that compactifies the spectrum of Landau levels and modifies the magnetophonon resonance properties. The drastically different coupling behaviour between the electronic excitations and the E2g phonons in ABA- and ABC-stacked TLG reflects their different electronic band structures and the electronic Landau level transitions and thus can be another way to determine the stacking orders and to probe the stacking-order-dependent electronic structures. In addition, the sensitivity of the magneto-Raman scattering to the particular stacking order in few layers graphene highlights the important role of interlayer coupling in modifying the optical response properties in van der Waals layered materials., Comment: 25 pages, 6 figures

All local electronic properties of graphene on a hexagonal boron nitride (hBN) substrate exhibit spatial moir\'e patterns related to lattice constant and orientation differences between shared triangular Bravais lattices. We apply a previously derived effective Hamiltonian for the $\pi$-bands of graphene on h-BN to address the carrier-dependence of transport properties, concentrating on the conductivity features at four electrons and four holes per unit cell. These transport features measure the strength of Bragg scattering of $\pi$-electrons off the moir\'e pattern, and exhibit a striking particle-hole asymmetry that we trace to specific features of the effective Hamiltonian that we interpret physically.