Interlayer Tunneling Research Articles

Percolation-Induced PT Symmetry Breaking.

We propose a new avenue in which percolation, which has been much associated with critical phase transitions, can also dictate the asymptotic dynamics of non-Hermitian systems by breaking PT symmetry. Central to it is our newly designed mechanism of topologically guided gain, where chiral edge wave packets in a topological system experience non-Hermitian gain or loss based on how they are topologically steered. For sufficiently wide topological islands, this leads to irreversible growth due to positive feedback from interlayer tunneling. As such, a percolation transition that merges small topological islands into larger ones also drives the edge spectrum across a real to complex transition. Our discovery showcases intriguing dynamical consequences from the triple interplay of chiral topology, directed gain, and interlayer tunneling, and suggests new routes for the topology to be harnessed in the control of feedback systems.

Keldysh Field Theory of Dynamical Exciton Condensation Transitions in Nonequilibrium Electron-Hole Bilayers.

Recent experiments have realized steady-state electrical injection of interlayer excitons in electron-hole bilayers subject to a large bias voltage. In the ideal case in which interlayer tunneling is negligibly weak, the system is in quasiequilibrium with a reduced effective band gap. Interlayer tunneling introduces a current and drives the system out of equilibrium. In this work we derive a nonequilibrium field theory description of interlayer excitons in biased electron-hole bilayers. In the large bias limit, we find that p-wave interlayer tunneling reduces the effective band gap and increases the effective temperature for intervalley excitons. We discuss possible experimental implications for InAs/GaSb quantum wells and transition metal dichalcogenide bilayers.

Strongly coupled magneto-exciton condensates in large-angle twisted double bilayer graphene

Excitons, pairs of electrons and holes, undergo a Bose-Einstein condensation at low temperatures. An important platform to study excitons is double-layer two-dimensional electron gases, with two parallel planes of electrons and holes separated by a thin insulating layer. Lowering this separation (d) strengthens the exciton binding energy, however, leads to the undesired interlayer tunneling, resulting in annihilation of excitons. Here, we report the observation of a sequences of robust exciton condensates (ECs) in double bilayer graphene twisted to ~ 10° with no insulating mid-layer. The large momentum mismatch between two graphene layers suppresses interlayer tunneling, reaching a d ~ 0.334 nm. Measuring the bulk and edge transport, we find incompressible states corresponding to ECs when both layers are in half-filled N = 0, 1 Landau levels (LLs). Theoretical calculations suggest that the low-energy charged excitation of ECs can be meron-antimeron or particle-hole pair, which relies on both LL index and carrier type. Our results establish a novel platform with extreme coupling strength for studying quantum bosonic phase.

Magic Angles and Fractional Chern Insulators in Twisted Homobilayer Transition Metal Dichalcogenides.

We explain the appearance of magic angles and fractional Chern insulators in twisted K-valley homobilayer transition metal dichalcogenides by mapping their continuum model to a Landau level problem. Our approach relies on an adiabatic approximation for the quantum mechanics of valence band holes in a layer-pseudospin field that is valid for sufficiently small twist angles and on a lowest Landau level approximation that is valid for sufficiently large twist angles. It provides a simple qualitative explanation for the nearly ideal quantum geometry of the lowest moiré miniband at particular twist angles, predicts that topological flat bands occur only when the valley-dependent moiré potential is sufficiently strong compared to the interlayer tunneling amplitude, and provides a convenient starting point for the study of interactions.

Absence of the impurity-resonance spot at a Bi defect located near the Zn impurity in Bi2Sr2Ca(Cu1-xZnx)2O8+δ

Zn dopants to Cu sites in high-Tc cuprates strongly suppress superconductivity and act as impurities with a strong quasiparticle scattering resonance. Using the scanning tunneling microscope, we investigate the electronic structure in the atomic scale around Zn impurities in Bi2Sr2Ca(Cu1-xZnx)2O8+δ. The intense scattering resonance of the Zn impurity in the CuO2 layer strongly affects the measured local density of states of the BiO layer on the surface. The pattern of the bound state induced by a Zn impurity consists of a central spot at the Bi atom just above the Zn impurity and eight symmetric spots at the next nearest neighboring (NNN) and the third nearest neighboring (3NN) sites of Bi atoms. When the Bi atom above the NNN Cu atom is missing, the corresponding scattering spot is absent simultaneously. Our results indicate that the measured impurity-induced bound state pattern is strongly influenced by Bi atoms on the surface and therefore supports the “filter” theoretical model of the nonlocal interlayer tunneling effect from the CuO2 layer to the BiO layer on the surface. Our research provides extra information about the impurity-induced bound state by Zn impurities.

Electrically tunable interlayer recombination and tunneling behavior in WSe2/MoS2 heterostructure for broadband photodetector.

Electrically tunable band structure and light-matter interaction are of great importance in designing novel devices and constructing high-integrated and high-performance photodetector systems in the future. However, tunable mechanisms on the layered semiconductor, especially the heterojunction, are still unclear. Herein, the WSe2/MoS2 phototransistor with dual-gated configuration is fabricated, and its electrical and photoelectrical conversion has been studied to show large tunability. It was found that conduction and rectification characteristics can be tuned by dual gates showing four states, p-i, p-n, i-n, and n-n, as a result of the charging and depletion of WSe2 and MoS2. The rectifying ratio can be modulated across a large range from 102.5 to 10-3.2. Its photoelectronic characteristics were observed to exhibit bipolar and wavelength-dependent behaviors. The interlayer recombination of charge carriers dominates the photoresponse of the device under the illumination of visible light, while it is dominated by interlayer tunneling under the illumination of near-infrared wavelengths. This bipolar photoresponse is associated with different states of band alignment, which can be switched by dual-gating modulation. Finally, by tuning the gate voltage, responsivities reach 27 445 A W-1 and 2827 A W-1 at wavelengths of 400 and 1010 nm at room temperature, respectively, which directly extends the response region from visible light to near-infrared.

Flat bands and high Chern numbers in twisted multilayer graphene

Motivated by recent Physical Review Letters of Wang and Liu [Phys. Rev. Lett. 128(17), 176403 (2022)] and Ledwith, Vishwanath, and Khalaf [Phys. Rev. Lett. 128(17), 176404 (2022)], we study [G. Tarnopolsky, A. Kruchkov, and A. Vishwanath, Phys. Rev. Lett. 122(10), 106405 (2019)] chiral model of two sheets of n-layer Bernal stacked graphene twisted by a small angle using the framework developed by Becker et al. [Probab. Math. Phys. 3(1), 69 (2022)]. We show that magic angles of this model are exactly the same as magic angles of chiral twisted bilayer graphene with multiplicity. For small inter-layer tunneling potentials, we compute the band separation at Dirac points as we turning on the tunneling parameter. Flat band eigenfunctions are also constructed using a new theta function argument and this yields a complex line bundle with the Chern number −n.

Twisted-bilayer FeSe and the Fe-based superlattices

We derive BM-like continuum models for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: (I) a single monolayer experiencing an external periodic potential, and (II) twisted bilayers with long-range moire tunneling. A symmetry derivation for the inter-layer moire tunnelling is provided for both the \GammaΓ and MM high-symmetry points. In this paper, we focus on moire bands formed from hole-band maxima centered on \GammaΓ, and show the possibility of moire bands with C=0C=0 or ±1±1 topological quantum numbers without breaking time-reversal symmetry. In the C=0C=0 region for \theta→0θ→0 (and similarly in the limit of large superlattice period for I), the system becomes a square lattice of 2D harmonic oscillators. We fit our model to FeSe and argue that it is a viable platform for the simulation of the square Hubbard model with tunable interaction strength.

Nematic Excitonic Insulator in Transition Metal Dichalcogenide Moiré Heterobilayers.

We study the effect of interelectron Coulomb interactions on the displacement field induced topological phase transition in transition metal dichalcogenide moiré heterobilayers. We find a nematic excitonic insulator phase that breaks the moiré superlattice's threefold rotational symmetry and preempts the topological phase transition in both AA and AB stacked heterobilayers when the interlayer tunneling is weak, or when the Coulomb interaction is not strongly screened. The nematicity originates from the frustration between the nontrivial spatial structure of the interlayer tunneling, which is crucial to the existence of the topological Chern band, and the interlayer coherence induced by the Coulomb interaction that favors uniformity in layer pseudospin orientations. We construct a unified effective two-band model that captures the physics near the band inversion and applies to both AA and AB stacked heterobilayers. Within the two-band model the competition between the nematic excitonic insulator phase and the Chern insulator phase can be understood as the switching of the energetic order between the s-wave and the p-wave excitons upon increasing the interlayer tunneling.

Generalization of interlayer tunneling models to cuprate superconductors with charge density waves

At the beginning of cuprate superconductors, the interlayer tunneling (ILT) and Lawrence-Doniach (L-D) models, which connect the CuO planes by Josephson coupling were considered the leading theoretical proposals for these materials. However, measurements of the interlayer magnetic penetration depth $\lambda_{c}$ yielded larger values than required by the ILT model. After the discovery of planar stripes and incommensurate charge ordering, it was also possible to consider Josephson coupling between these mesoscopic charge domains or blocks. We show that the average intralayer is larger than the interlayer coupling and comparable with the condensation energy, leading to a superconducting transition by long-range phase order. Another consequence is that the ratio $[\lambda_{c}/\lambda_{ab}]^2$ is directly proportional resistivity ratio $\rho_c/ \rho_{ab}$ near the superconducting transition temperature in agreement with several measurements.

Twisted bilayer BC3 : Valley interlocked anisotropic flat bands

Here we propose ${\mathrm{BC}}_{3}$, a graphene derivative that has been synthesized, as a platform to realize exotic quantum phases by introducing a moir\'e pattern with mismatched stacking. In twisted bilayer ${\mathrm{BC}}_{3}$, it is shown that a crossover from two-dimensional to quasi-one-dimensional (quasi-1D) band structure takes place with the twist angle as a control parameter. This is a typical manifestation of the guiding principle in van der Waals stacked systems: The quantum interference between Bloch wave functions in adjacent layers has a striking effect on the effective interlayer tunneling. Interestingly, quasi one dimensionalization happens in a valley-dependent manner. Namely, there is interlocking between the valley index and the quasi-1D directionality, which makes ${\mathrm{BC}}_{3}$ a plausible candidate for valleytronics devices. In addition, the strongly correlated regime of the valley interlocked quasi-1D state reduces to an interesting variant of the Kugel-Khomskii model where intertwined valley and spin degrees of freedom potentially induce exotic quantum phases. Notably, this variant of the Kugel-Khomskii model cannot be realized in conventional solids due to the threefold valley degeneracy.

Excitonic Chern insulator and kinetic ferromagnetism in a MoTe2/WSe2 moiré bilayer

We propose an alternative mechanism for the quantum anomalous Hall (QAH) effect in the $AB$ stacked $\mathrm{Mo}{\mathrm{Te}}_{2}/\mathrm{W}{\mathrm{Se}}_{2}$ system. Based on the observation that interlayer tunneling is suppressed in $AB$ stacking, we consider a model with two layers coupled through the Coulomb interaction. The moir\'e lattices of the two layers are shifted to form a honeycomb lattice. Initially, the system is in a layer-polarized Mott insulator at ${\ensuremath{\nu}}_{T}=1$. But with a displacement field, an equal number of holes and electrons are doped into the two layers, forming interlayer exciton condensation. Through mean field theory, we find $p\ifmmode\pm\else\textpm\fi{}ip$ exciton condensation in a certain parameter regime, which leads to a Chern insulator with Chern number $\text{C}=\ifmmode\pm\else\textpm\fi{}1$. The valleys are polarized due to the kinetic energy instead of interaction, but the polarization in the two layers can be either the same or opposite. In particular, an intervalley-coherent (IVC) Chern insulator phase is possible, in agreement with the recent magnetic circular dichroism (MCD) measurement. Our work opens another direction in the search for a topologically nontrivial excitonic insulator with high angular momentum exciton pairing symmetry.

Coherent Interlayer Coupling in Quasi-Two-Dimensional Dirac Fermions in α-(BEDT-TTF)2I3

Theoretical and experimental studies have supported that the electronic structure of $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure is described by two-dimensional Dirac fermions. When the interlayer tunneling is coherent, the electronic structure of the system becomes three-dimensional, and we expect the peak structure to appear in the interlayer resistivity under magnetic fields. We theoretically and experimentally show that the peak appears in the interlayer resistivity at low temperatures and high magnetic fields. From the experiment, we estimate that the magnitude of the interlayer tunneling is $t_1 \sim 1$ meV. Our result opens the door to investigating the three-dimensional electronic structure of $\alpha$-(BEDT-TTF)$_2$I$_3$.

Analytical model of the energy spectrum and Landau levels of a twisted double bilayer graphene

Motivated by recent experiments Adak et al. (2020) and Szentpéter et al. (2021), in this work we have considered a twisted double bilayer graphene system. Within the low energy effective theory, the bandwidth expression of the moire flatbands (with weak dispersion and diverging effective mass) and Landau level spectrum of the Bernal stacked twisted double bilayer graphene are obtained analytically. We analyze the dependence of the bandwidth, effective mass, and Landau level spectrum on twist angle, inter layer tunneling, and interlayer potential difference. Also, we have investigated the phase diagram of the effective mass as a function of the twist angle and interlayer tunneling strength to seek the parameter space with diverging effective mass. We find that the magic angle at which the flat bands exist is increasing with increasing inter layer tunneling strength. • In this work, in this work we have considered a twisted double bilayer graphene system. • Within the low energy effective theory, the bandwidth expression of the moiré flatbands (with weak dispersion and diverging effective mass) and Landau level spectrum of the Bernal stacked twisted double bilayer graphene are obtained analytically. • We analyze the dependence of the bandwidth, effective mass, and Landau level spectrum on twist angle, inter layer tunneling, and interlayer potential difference. • Also, we have investigated the phase diagram of the effective mass as a function of the twist angle and interlayer tunneling strength to seek the parameter space with diverging effective mass. • We find that the magic angle at which the flat bands exist is increasing with increasing inter layer tunneling strength. • The results presented in this work will be useful for the experimental investigation of the tDBG system.

Enhanced superconductivity through virtual tunneling in Bernal bilayer graphene coupled to WSe2

Motivated by a recent experiment [arXiv:2205.05087], we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate WSe$_2$ monolayer. We show that the virtual tunneling between WSe$_2$ and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as functions of the twist angle between Bernal bilayer graphene and the WSe$_2$ monolayer. Our theory provides an intuitive and physical explanation for the intertwined relation between Ising spin-orbit coupling and superconductivity enhancement, which should motivate future studies.

Twisted bilayer U(1) Dirac spin liquids

When two layers of two-dimensional materials are assembled with a relative twist, moir\'e patterns arise, inducing a tremendous wealth of exotic phenomena. In this work, we consider twisting two triangular lattices hosting Dirac quantum spin liquids. A single decoupled layer is described by compact quantum electrodynamics in 2+1 dimensions (QED$_3$) with an emergent $\mathrm{U}(1)$ gauge field, which is assumed to flow to a strongly interacting fixed point in the IR with conformal symmetry. We use recent results for the quantum numbers of monopole operators, which tunnel $2 \pi$ fluxes of the compact gauge field. It is found that, in the bilayer system, interlayer monopole tunneling is a symmetry-allowed relevant perturbation which induces an (ordering) instability. We show using perturbation theory that upon twisting the two layers the system remains unstable under the interlayer interaction, but any finite twist angle softens this instability compared to the untwisted case. To analyse the resulting phase induced by the (twisted) interlayer tunneling, we use "conformal mean field theory", which reduces the interacting bilayer system to two copies of QED$_3$ coupled to background fields which are to be determined self-consistently. In the weak-coupling regime, where the interlayer coupling is weak compared to the energy scale set by the moir\'e lattice constant, we solve the self-consistency equations perturbatively. In the limit of strongly coupled layers, a local scaling approximation is used, and we find that the magnetically ordered state exhibits a lattice of magnetic vortices, with the lattice constant tunable through the twisting angle.

Twisted bilayers of thin film magnetic topological insulators

Twisted bilayer graphene (TBG) near ``magic angles'' has emerged as a rich platform for strongly correlated states of two-dimensional (2D) Dirac semimetals. Here we show that twisted bilayers of thin film magnetic topological insulators (MTIs) with large in-plane magnetization can realize flat bands near 2D Dirac nodes. Using a simple model for thin films of MTIs, we derive a continuum model for two such MTIs, twisted by a small angle with respect to each other. When the magnetization is in plane, we show that interlayer tunneling terms act as effective SU(2) vector potentials, which are known to lead to flat bands in TBG. We show that by changing the in-plane magnetization, it is possible to tune the twisted bilayer MTI band dispersion to quadratic band touching or to flat bands, similar to the TBG. If realized, this system can be a highly tunable platform for strongly correlated phases of two-dimensional Dirac semimetals.

Highly Zn2+-conductive and robust modified montmorillonite protective layer of electrodes toward high-performance rechargeable zinc-ion batteries

• A protective layer of electrodes with expanded and robust interlayer. • Protective layer is prepared from organic montmorillonite and ZnSO 4 /MnSO 4 solution. • Protective layer with low-cost, high ionic conductivity and Zn 2+ transfer number. • Alleviate Zn corrosion, MnO 2 dissolution, side-reaction and Zn dendrite generation. • Improved rate capability and cyclability of the battery with the protective layer. The corrosion, parasitic side-reaction and dendrite of Zn anode as well as the dissolution of MnO 2 cathode limit the commercial application of zinc-ion batteries (ZIBs). Herein, a novel coating layer on Zn anode and MnO 2 cathode of rechargeable ZIBs is rationally designed by mixing hexadecyl trimethyl ammonium bromide(CTAB)-pillared organic montmorillonite with ZnSO 4 /MnSO 4 solution (ZnOMMT). ZnOMMT can serve as the protective layer to alleviate Zn corrosion and MnO 2 dissolution while the unique interlayer structure of ZnOMMT can also offer a selective pathway for fast Zn 2+ transfer and uniform Zn 2+ diffusion to inhibit the side-reaction and Zn dendrite generation. Notably, by the powerful pillaring of CTAB cations, the expanded and robust nanoscale interlayer tunnels of ZnOMMT for Zn 2+ diffusion are constructed to guarantee outstanding ionic conductivity (6.52 mS cm −1 ), high Zn 2+ transference number ( t + =0.66) and outstanding cyclic stability during deep cycles. Therefore, ZIBs with ZnOMMT coating layer deliver a steady long-term reversible capacity (267 mAh g −1 until 300 cycles at 0.5 A g −1 , 205 mAh g −1 until 700 cycles at 1.0 A g −1 ). The rational design of CTAB-pillared montmorillonite protective layer brings a brand-new opportunity to the realization of high-performance rechargeable ZIBs. A novel protective layer of electrodes with outstanding ionic conductivity, high Zn 2+ transference number, low-cost, expanded and robust nanoscale interlayer is fabricated from CTAB-pillared organic montmorillonite and ZnSO 4 /MnSO 4 solution, and utilized to alleviate Zn corrosion, MnO 2 dissolution, side-reaction and Zn dendrite generation and thus improve cyclability and rate capability.

Relaxation effects in twisted bilayer graphene: A multiscale approach

We present a multiscale density functional theory (DFT) informed molecular dynamics and tight-binding approach to capture the interdependent atomic and electronic structures of twisted bilayer graphene. We calibrate the flat band magic angle to be at ${\ensuremath{\theta}}_{\mathrm{M}}=1.{08}^{\ensuremath{\circ}}$ by rescaling the interlayer tunneling for different atomic structure relaxation models as a way to resolve the indeterminacy of existing atomic and electronic structure models whose predicted magic angles vary widely between $0.{9}^{\ensuremath{\circ}}$ and $1.{3}^{\ensuremath{\circ}}$. The interatomic force fields are built using input from various stacking and interlayer distance-dependent DFT total energies including the exact exchange and random phase approximation ($\mathrm{EXX}+\mathrm{RPA}$). We use a Fermi velocity of ${\ensuremath{\upsilon}}_{\mathrm{F}}\ensuremath{\simeq}{10}^{6}$ m/s for graphene that is enhanced by $\ensuremath{\sim}15%$ over the local density approximation (LDA) values. Based on this atomic and electronic structure model we obtain high-resolution spectral functions comparable with experimental angle-resolved photoemission spectroscopy. Our analysis of the interdependence between the atomic and electronic structures indicates that the intralayer elastic parameters compatible with the DFT-LDA, which are stiffer by $\ensuremath{\sim}30%$ than widely used reactive empirical bond order force fields, can combine with $\mathrm{EXX}+\mathrm{RPA}$ interlayer potentials to yield the magic angle at $\ensuremath{\sim}1.{08}^{\ensuremath{\circ}}$ without further rescaling of the interlayer tunneling.

Tunable Feshbach Resonances and Their Spectral Signatures in Bilayer Semiconductors.

Feshbach resonances provide an invaluable tool in atomic physics, enabling precise control of interactions and the preparation of complex quantum phases of matter. Here, we theoretically analyze a solid-state analog of a Feshbach resonance in two dimensional semiconductor heterostructures. In the presence of interlayer electron tunneling, the scattering of excitons and electrons occupying different layers can be resonantly enhanced by tuning an applied electric field. The emergence of an interlayer Feshbach molecule modifies the optical excitation spectrum, and can be understood in terms of Fermi polaron formation. We discuss potential implications for the realization of correlated Bose-Fermi mixtures in bilayer semiconductors.