Interlayer Hopping Research Articles

Interlayer hopping dynamics of bilayer water confined between graphene sheets

Abstract The ubiquitous existence of water confined in nano-capillaries is key to fundamental biological and technological applications. Using molecular dynamics simulations, we analyzed the hopping-like interlayer relocation dynamics of bilayer water confined between two parallel graphene sheets. In contrary to the common scheme that relocation is driven by density fluctuations, analysis of the transition path ensemble revealed that interlayer hopping is induced by local hydrogen bond configuration fluctuations coupled with activated consecutive transient angular reorientations. Our results consolidated the anisotropic nature of water relocation under strong ordering, which provided a mechanistic insight into the relaxation behavior at glass-forming water’s fragile-to-strong crossover.

The mirror asymmetry induced nontrivial properties of polar WSSe/MoSSe heterostructures

Janus MoSSe and WSSe as new members to the family of transitional metal dichalcogenides (TMDCs) present intriguing properties that absent in its parent MX2 (M = Mo, W; X = S, Se, Te) monolayers due to the out-of-plane mirror asymmetry. For WSSe/MoSSe van der Waals (vdW) heterostructures, intralayer/interlayer potential drops lead to significantly larger band offset than MX2 heterobilayers, ensuring the long lifetimes for valley polarized interlayer excitons. Regard to the spin–valley–layer locking effects in WSSe/MoSSe vdW heterostructures, the band offset larger than the Zeeman-type spin splitting guarantees effective interlayer hopping and, therefore, large degree of valley polarization. Rashba-type spin splitting can coexist with the valley spin splitting and thus add the carrier transport paths, and intralayer/interlayer potential drops show obvious effects on the Rashba parameter. According to these results, WSSe/MoSSe vdW heterostructures manifest themselves the most promising candidates for spintronics and valleytronics with superiorities to the MX2 counterparts.

Higher-order topological superconductivity: Possible realization in Fermi gases and Sr2RuO4

We propose to realize second-order topological superconductivity in bilayer spin-polarized Fermi gas superfluids. We focus on systems with intralayer chiral $p$-wave pairing and with tunable interlayer hopping and interlayer interactions. Under appropriate circumstances, an interlayer even-parity $s$- or $d$-wave pairing may coexist with the intralayer $p$-wave. Our model supports localized Majorana zero modes not only at the corners of the system geometry, but also at the terminations of certain one-dimensional defects, such as lattice line defects and superfluid domain walls. We show how such topological phases and the Majorana zero modes therein can be manipulated in a multitude of ways by tuning the interlayer pairing and hopping. Generalized to spinful systems, we further propose that the putative $p$-wave superconductor Sr$_{2}$RuO$_{4}$, when subject to uniaxial strains, may also realize the desired topological phase.

Peculiar optical properties of bilayer silicene under the influence of external electric and magnetic fields

We conduct a comprehensive investigation of the effect of an applied electric field on the optical and magneto-optical absorption spectra for AB-bt (bottom-top) bilayer silicene. The generalized tight-binding model in conjunction with the Kubo formula is efficiently employed in the numerical calculations. The electronic and optical properties are greatly diversified by the buckled lattice structure, stacking configuration, intralayer and interlayer hopping interactions, spin-orbital couplings, as well as the electric and magnetic fields ({E}_{z}hat{z}& {B}_{z}hat{z}). An electric field induces spin-split electronic states, a semiconductor-metal phase transitions and the Dirac cone formations in different valleys, leading to the special absorption features. The Ez-dependent low-lying Landau levels possess lower degeneracy, valley-created localization centers, peculiar distributions of quantum numbers, well-behaved and abnormal energy spectra in Bz-dependencies, and the absence of anti-crossing behavior. Consequently, the specific magneto-optical selection rules exist for diverse excitation categories under certain critical electric fields. The optical gaps are reduced as Ez is increased, but enhanced by Bz, in which the threshold channel might dramatically change in the former case. These characteristics are in sharp contrast with those for layered graphene.

Electrical and thermal conductivities of few-layer armchair graphene nanoribbons

The tight-binding Hamiltonian model and the Green’s function formalism have been employed to calculate the temperature dependent electrical and electronic thermal conductivities of metal and few-layer armchair graphene nanoribbon semiconductors and the results were compared with the mono-layer system. It was observed that due to the overlapping of the nonhybridized p z orbital perpendicular to the sheets, increasing the layers of the systems causes the conductivities of the layers to decrease. Also, these quantities are calculated for three different values of interlayer hopping of the nonhybridized p z orbitals. The results show that in low temperatures, the electrical and thermal conductivities of the system increase when the interlayer hopping term is increased. However, by increasing the temperature, the curves representing electrical conductivities converge to the same value while thermal conductivity decreases.

Excitonic Tunneling in the AB-bilayer Graphene Josephson Junctions

We have considered the AB-stacked bilayer graphene tunnel junction construction. The bilayers are supposed to be in the charge equilibrium states and at the half-filling in each of the electronic layers of the construction and at each value of the external gate potential. By considering the interacting bilayers in both sides of the junction and by taking into account both intralayer and interlayer Coulomb interaction effects, we have calculated the normal and excitonic tunnel currents through the junction. The electronic band renormalizations have been taken into account, due to the excitonic pairing effects and condensation in the BLGs. The exact four-band energy dispersions, including the excitonic renormalizations, have been used for the bilayers without any low-energy approximation. The normal and excitonic tunneling currents have been calculated for different values of the gate potential and for different values of the interlayer interaction parameters in both sides of the tunnel junction. We demonstrate the existence of the excitonic Josephson current through the junction which persist even for the non-interacting bilayer graphene junction. For the non-interacting case, the mechanism of the excitonic condensates formation and tunneling between the condensates is attributed to the interlayer hopping between the layers. The role of the charge neutrality point has been discussed in details.

Dimensionality-induced BCS-BEC crossover in layered superconductors

Based on a simple model of a layered superconductor with strong attractive interaction, we find that the separation of the pair-condensation temperature from the pair-formation temperature becomes more remarkable as the interlayer hopping gets smaller. We propose from this result the BCS-BEC crossover induced by the change in dimensionality, for instance, due to insertion of additional insulating layers or application of uniaxial pressure. The emergence of a pseudogap in the electronic density of states, which supports the idea of the dimensionality-induced BCS-BEC crossover, is also verified.

Electronic transport and dynamical polarization in bilayer silicene-like systems

Abstract We investigate the semiclassical electronic transport properties of the bilayer silicene-like systems in the presence of charged impurity. The trigonal warping due to the interlayer hopping, and its effect to the band structure of bilayer silicene is discussed. Besides the trigonal warping, the external field also gives rise to the anisotropic effect of the mobility (at finite temperature) which can be explored by the Boltzmann theory. The dynamical polarization as well as the scattering wave vector-dependent screening within random phase approximation are very important in determining the scattering behavior as well as the self-consistent transport. We detailedly discuss the transport behavior under the short- or long-range potential. The phonon scattering with the acoustic phonon mode which dominants at high temperature is also studied within the density functional theory (DFT). Our results are also valid for the bilayer graphene or bilayer MoS2, and other bilayer systems which with strong interlayer coupling.

Multiworm algorithm quantum Monte Carlo

We review the path-integral quantum Monte Carlo method and discuss its implementation by multiworm algorithms. We analyze in details the features of the algorithms, and focus our attention on the computation of the N-body density matrix to study N-body correlations. Finally, we demonstrate the validity of the algorithms on a system of dipolar bosons trapped in a stack of N one-dimensional layers in the case of zero and finite inter-layer hopping.

The diverse magneto-optical selection rules in bilayer black phosphorus

The magneto-optical properties of bilayer phosphorene is investigated by the generalized tight-binding model and the gradient approximation. The vertical inter-Landau-level transitions, being sensitive to the polarization directions, are mainly determined by the spatial symmetries of sub-envelope functions on the distinct sublattices. The anisotropic excitations strongly depend on the electric and magnetic fields. A uniform perpendicular electric field could greatly diversify the selection rule, frequency, intensity, number and form of symmetric absorption peaks. Specifically, the unusual magneto-optical properties appear beyond the critical field as a result of two subgroups of Landau levels with the main and side modes. The rich and unique magnetoabsorption spectra arise from the very close relations among the geometric structures, multiple intralayer and interlayer hopping integrals and composite external fields.

New Pathway for Hot Electron Relaxation in Two-Dimensional Heterostructures.

Two-dimensional (2D) heterostructures composed of transition-metal dichalcogenide atomic layers are the new frontier for novel optoelectronic and photovoltaic device applications. Some key properties that make these materials appealing, yet are not well understood, are ultrafast hole/electron dynamics, interlayer energy transfer and the formation of interlayer hot excitons. Here, we study photoexcited electron/hole dynamics in a representative heterostructure, the MoS2/WSe2 interface, which exhibits type II band alignment. Employing time-dependent density functional theory in the time domain, we observe ultrafast charge dynamics with lifetimes of tens to hundreds of femtoseconds. Most importantly, we report the discovery of an interfacial pathway in 2D heterostructures for the relaxation of photoexcited hot electrons through interlayer hopping, which is significantly faster than intralayer relaxation. This finding is of particular importance for understanding many experimentally observed photoinduced processes, including charge and energy transfer at an ultrafast time scale (<1 ps).

Spin Accumulation and Dynamics in Inversion-Symmetric van der Waals Crystals.

Inversion-symmetric materials are forbidden to show an overall spin texture in their band structure in the presence of time-reversal symmetry. However, in van der Waals materials which lack inversion symmetry within a single layer, it has been proposed that a layer-dependent spin texture can arise leading to a coupled spin-layer degree of freedom. Here we use time-resolved Kerr rotation in inversion-symmetric WSe_{2} and MoSe_{2} bulk crystals to study this spin-layer polarization and unveil its dynamics. Our measurements show that the spin-layer relaxation time in WSe_{2} is limited by phonon scattering at high temperatures and that the interlayer hopping can be tuned by a small in-plane magnetic field at low temperatures, enhancing the relaxation rates. We find a significantly lower lifetime for MoSe_{2} which agrees with theoretical expectations of a spin-layer polarization stabilized by the larger spin-orbit coupling in WSe_{2}.

Asymmetric response of magnetic impurity in Bernal-stacked bilayer honeycomb lattice**Project supported by the National Natural Science Foundation of China (Grant No. 11604166), the Zhejiang Open Foundation of the Most Important Subjects, China (Grant No. xkzw11609), and the K. C. Wong Magna Fund in Ningbo University, China.

We utilize the Hirsch–Fye quantum Monte Carlo method to investigate the local moment formation of a magnetic impurity in a Bernal-stacked bilayer honeycomb lattice. A tight-binding model with the two most significant inter-layer hoppings, t1 between pairs of dimer sites and t3 between pairs of non-dimer sites, is used to describe the kinetic energy of the system. The local moment formed shows an asymmetric response to the inter-layer hoppings depending on which sublattice the impurity is coupled to. In the dimer and non-dimer couplings, the effects of t1 and t3 onto the local moment are quite opposite. When tuning the local moment, this asymmetric response is observed in a wide parameter range. This asymmetric response is also discussed by the computations of spectral densities, as well as correlation functions between the magnetic impurity and the conduction electrons.

Strong and weak second-order topological insulators with hexagonal symmetry and ℤ 3 index

We propose second-order topological insulators (SOTIs) whose lattice structure has the hexagonal symmetry $C_{6}$ in three and two dimensions. We start with a three-dimensional weak topological insulator constructed on the stacked triangular lattice, which has only side topological surface states. We then introduce an additional mass term which gaps out the side surface states but preserves the hinge states. The resultant system is a three-dimensional SOTI. The bulk topological quantum number is shown to be the $\mathbb{Z}_{3}$ index protected by the inversion time-reversal symmetry $IT$ and the rotoinversion symmetry $C_{6}I$. We obtain three phases; trivial, strong and weak SOTI phases. We argue the origin of these two types of SOTIs. A hexagonal prism is a typical structure respecting these symmetries, where six topological hinge states emerge at the side. The building block is a hexagon in two dimensions, where topological corner states emerge at the six corners in the SOTI phase. Strong and weak SOTIs are obtained when the interlayer hopping interaction is strong and weak, respectively. They are characterized by the emergence of hinge states attached to or detached from the bulk bands.

Temperature-driven evolution of critical points, interlayer coupling, and layer polarization in bilayer MoS2

The recently emerging two-dimensional (2D) transition-metal dichalcogenides (TMDCs) have been a fertile ground for exploring abundant exotic physical properties. Critical points, the extrema or saddle points of electronic bands, are the cornerstone of condensed-matter physics and fundamentally determine the optical and transport phenomena of the TMDCs. However, for bilayer $\mathrm{Mo}{\mathrm{S}}_{2}$, a typical TMDC and the unprecedented electrically tunable venue for valleytronics, there has been a considerable controversy on its intrinsic electronic structure, especially for the conduction band-edge locations. Moreover, interlayer hopping and layer polarization in bilayer $\mathrm{Mo}{\mathrm{S}}_{2}$ which play vital roles in valley-spintronic applications have remained experimentally elusive. Here, we report the experimental observation of intrinsic critical points locations, interlayer hopping, layer-spin polarization, and their evolution with temperature in bilayer $\mathrm{Mo}{\mathrm{S}}_{2}$ by performing temperature-dependent photoluminescence. Our measurements confirm that the conduction-band minimum locates at the ${K}_{\mathrm{c}}$ instead of ${Q}_{\mathrm{c}}$, and the energy splitting between ${Q}_{\mathrm{c}}$ and ${K}_{\mathrm{c}}$ redshifts with a descent of temperature. Furthermore, the interlayer hopping energy for holes and temperature-dependent layer polarization are quantitatively determined. Our observations are in good harmony with density-functional theory calculations.

Fermiology and Superconductivity of Topological Surface States in PdTe_{2}.

We study the low-energy surface electronic structure of the transition-metal dichalcogenide superconductor PdTe_{2} by spin- and angle-resolved photoemission, scanning tunneling microscopy, and density-functional theory-based supercell calculations. Comparing PdTe_{2} with its sister compound PtSe_{2}, we demonstrate how enhanced interlayer hopping in the Te-based material drives a band inversion within the antibonding p-orbital manifold well above the Fermi level. We show how this mediates spin-polarized topological surface states which form rich multivalley Fermi surfaces with complex spin textures. Scanning tunneling spectroscopy reveals type-II superconductivity at the surface, and moreover shows no evidence for an unconventional component of its superconducting order parameter, despite the presence of topological surface states.

Transport anisotropy and electron correlations in the layered molecular compoundsZ[Pd(dmit)2]2(Z=Me4N,Et2Me2As,EtMe3P) with different interlayer coupling

In-plane resistivity ${\ensuremath{\rho}}_{\ensuremath{\parallel}}$ and out-of-plane resistivity ${\ensuremath{\rho}}_{\ensuremath{\perp}}$ were investigated across the pressure-induced Mott transition in molecular Mott insulators $Z{[\mathrm{Pd}{(\mathrm{dmit})}_{2}]}_{2}$ ($Z={\mathrm{Et}}_{2}{\mathrm{Me}}_{2}\mathrm{As}$, ${\mathrm{Me}}_{4}\mathrm{N}$, and ${\mathrm{EtMe}}_{3}\mathrm{P}$) having a triangular lattice. All three compounds exhibit superconducting transition with ${T}_{c}=5.5--7.0$ K in the metallic phase near the Mott insulating phase. For the ${\ensuremath{\beta}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{Et}}_{2}{\mathrm{Me}}_{2}\mathrm{As}$ salt, the anisotropy ${\ensuremath{\rho}}_{\ensuremath{\perp}}/{\ensuremath{\rho}}_{\ensuremath{\parallel}}$ exceeds ${10}^{3}$ at low temperatures, indicating a highly two-dimensional electronic state with incoherent interlayer hopping. The $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Me}}_{4}\mathrm{N}$ salt has a smaller ${\ensuremath{\rho}}_{\ensuremath{\perp}}/{\ensuremath{\rho}}_{\ensuremath{\parallel}}$ exhibiting a weak interlayer coupling. The resistivity is dominated by electron-electron scattering in the metallic state for these two compounds, as expected in a correlated Fermi liquid. On the other hand, the ${\mathrm{EtMe}}_{3}\mathrm{P}$ salt with a valence bond order state becomes a nearly three-dimensional metal across the Mott transition, in which the electron correlation is strongly suppressed. Instead, the electron-phonon scattering plays a significant role in the resistivity. The different interlayer coherence is quantitatively explained by the calculated interlayer transfer integrals between $\mathrm{Pd}{(\mathrm{dmit})}_{2}$ molecules. These results suggest that the dimensionality governs the nature of electron correlations in the Fermi liquid state.

Predicting Two-Dimensional C3B/C3N van der Waals p-n Heterojunction with Strong Interlayer Electron Coupling and Enhanced Photocurrent.

The interlayer coupling in 2D van der Waals (vdW) heterostructures (HTS) plays the main role in generating new physics. However, the interlayer coupling is often weak, and little information on the strength of interlayer interaction in HTS is available. On the basis of density functional theory, we demonstrate that an effective electron coupling can be created in 2D C3B/C3N vdW HTS. The experimentally synthesized monolayers C3B and C3N are p- and n-type doped large gap semiconductors, respectively. However, the formed vdW HTS exhibits novel Dirac fermion. The strong interlayer electron coupling results in a large interlayer built-in electric field and improved optical properties of the 2D C3B/C3N vdW HTS. Moreover, a simple tight-binding model of C3B/C3N HTS with the nonzero interlayer hopping parameters captures the physical picture of interlayer coupling. Our results demonstrate the importance of interlayer electron coupling in the modulation of materials properties of 2D vdW HTS.

Magnetotransport in Layered Dirac Fermion System Coupled with Magnetic Moments

We theoretically investigate the magnetotransport of Dirac fermions coupled with localized moments to understand the physical properties of the Dirac material EuMnBi$_2$. Using an interlayer hopping form, which simplifies the complicated interaction between the layers of Dirac fermions and the layers of magnetic moments in EuMnBi$_2$, the theory reproduces most of the features observed in this system. The hysteresis observed in EuMnBi$_2$ can be caused by the valley splitting that is induced by the spin-orbit coupling and the external magnetic field with the molecular field created by localized moments. Our theory suggests that the magnetotransport in EuMnBi$_2$ is due to the interplay among Dirac fermions, localized moments, and spin-orbit coupling.

Controlling the layer localization of gapless states in bilayer graphene with a gate voltage

Experiments in gated bilayer graphene with stacking domain walls present topological gapless states protected by no-valley mixing. Here we research these states under gate voltages using atomistic models, which allow us to elucidate their origin. We find that the gate potential controls the layer localization of the two states, which switches non-trivially between layers depending on the applied gate voltage magnitude. We also show how these bilayer gapless states arise from bands of single-layer graphene by analyzing the formation of carbon bonds between layers. Based on this analysis we provide a model Hamiltonian with analytical solutions, which explains the layer localization as a function of the ratio between the applied potential and interlayer hopping. Our results open a route for the manipulation of gapless states in electronic devices, analogous to the proposed writing and reading memories in topological insulators.