Interlayer Tunneling Research Articles

Characteristics of Interlayer Tunneling Field-Effect Transistors Computed by a “DFT-Bardeen” Method

Theoretical predictions are made for the current-voltage characteristics of two-dimensional heterojunction interlayer tunneling field-effect transistors (Thin-TFETs), focusing on the magnitude of the current that is achievable in such devices. A theory based on the Bardeen tunneling method is employed, using wavefunctions from first-principles density-functional theory. This method permits convenient incorporation of differing materials into the source and drain electrodes, i.e. with different crystal structures, lattice constants, and/or band structures. Large variations in the tunnel currents are found, depending on the particular two-dimensional materials used for the source and drain electrodes. Tunneling between states derived from the center (Gamma-point) of the Brillouin zone (BZ) is found, in general, to lead to larger current than for zone-edge (e.g. K-point) states. Differences, as large as an order of magnitude, between the present results and various prior predictions are discussed. Predicted values for the tunneling currents, including subthreshold swing, are compared with benchmark values for low-power digital applications. Contact resistance is considered and its effect on the tunneling currents is demonstrated.

DFT simulations of inter-graphene-layer coupling with rotationally misaligned hBN tunnel barriers in graphene/hBN/graphene tunnel FETs

Van der Waal's heterostructures allow for novel devices such as two-dimensional-to-two-dimensional tunnel devices, exemplified by interlayer tunnel FETs. These devices employ channel/tunnel-barrier/channel geometries. However, during layer-by-layer exfoliation of these multi-layer materials, rotational misalignment is the norm and may substantially affect device characteristics. In this work, by using density functional theory methods, we consider a reduction in tunneling due to weakened coupling across the rotationally misaligned interface between the channel layers and the tunnel barrier. As a prototypical system, we simulate the effects of rotational misalignment of the tunnel barrier layer between aligned channel layers in a graphene/hBN/graphene system. We find that the rotational misalignment between the channel layers and the tunnel barrier in this van der Waal's heterostructure can significantly reduce coupling between the channels by reducing, specifically, coupling across the interface between the channels and the tunnel barrier. This weakened coupling in graphene/hBN/graphene with hBN misalignment may be relevant to all such van der Waal's heterostructures.

Vertical MoS2/hBN/MoS2 interlayer tunneling field effect transistor

Gate induced interlayer tunneling field effect transistor (iTFET) is studied analytically considering vertical heterostructure of boron nitride (BN) layer sandwiched between two monolayers of molybdenum disulfide (MoS2). The device structure in comparison to recently reported work shows subthreshold slope close to 60mV/decade and operation at upper GHz.

Surface nematic order in iron pnictides

Electronic nematicity plays important role in iron-based superconductors. These materials have layered structure and theoretical description of their magnetic and nematic transitions has been well established in two-dimensional approximation, i.e., when the layers can be treated independently. However, the interaction between iron layers mediated by electron tunneling may cause non-trivial three-dimensional behavior. Starting from the simplest model for orbital nematic in a single layer, we investigate the influence of interlayer tunneling on bulk nematic order and possible preemptive state where this order is only formed near the surface. We found that the interlayer tunneling suppresses the bulk nematicity which makes favorable formation of a surface nematic above the bulk transition temperature. The purely electronic tunneling Hamiltonian, however, favors alternating from layer-to-layer nematic order parameter in the bulk. The uniform bulk state typically observed experimentally may be stabilized by the coupling with the elastic lattice deformation. Depending on strength of this coupling, we found three regimes: (i) surface nematic and alternating bulk order, (ii) surface nematic and uniform bulk order, and (iii) uniform bulk order without the intermediate surface phase. The intermediate surface-nematic state may resolve the current controversy about the existence of the weak "meta-nematic transition" in the compound BaFe$_2$As$_{2-x}$P$_{x}$.

Charge 2e/3 Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States.

It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states. Here we propose an alternate route to creating, manipulating, and measuring topologically protected degeneracies in bilayer FQH states coupled to superconductors, without the creation of localized parafermion zero modes. We focus mainly on electron-hole bilayers, with a ±1/3 Laughlin FQH state in each layer, with boundaries that are proximity coupled to a superconductor. We show that the superconductor induces charge 2e/3 quasiparticle-pair condensation at each boundary of the FQH state, and that this leads to (i)topologically protected degeneracies that can be measured through charge sensing experiments and (ii)a fractional charge 2e/3 ac Josephson effect. We demonstrate that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode. We discuss several practical advantages of this proposal over previous work, and also several generalizations.

Effects of Electrode Layer Band Structure on the Performance of Multilayer Graphene-hBN-Graphene Interlayer Tunnel Field Effect Transistors.

Interlayer tunnel field-effect transistors based on graphene and hexagonal boron nitride (hBN) have recently attracted much interest for their potential as beyond-CMOS devices. Using a recently developed method for fabricating rotationally aligned two-dimensional heterostructures, we show experimental results for devices with varying thicknesses and stacking order of the graphene electrode layers and also model the current-voltage behavior. We show that an increase in the graphene layer thickness results in narrower resonance. However, due to a simultaneous increase in the number of sub-bands and decrease of sub-band separation with an increase in thickness, the negative differential resistance peaks becomes less prominent and do not appear for certain conditions at room temperature. Also, we show that due to the unique band structure of odd number of layer Bernal-stacked graphene, the number of closely spaced resonance conditions increase, causing interference between neighboring resonance peaks. Although this can be avoided with even number of layer graphene, we find that in this case the bandgap opening present at high biases tend to broaden the resonance peaks.

Inter-ribbon tunneling in graphene: An atomistic Bardeen approach

A weakly coupled system of two crossed graphene nanoribbons exhibits direct tunneling due to the overlap of the wavefunctions of both ribbons. We apply the Bardeen transfer Hamiltonian formalism, using atomistic band structure calculations to account for the effect of the atomic structure on the tunneling process. The strong quantum-size confinement of the nanoribbons is mirrored by the one-dimensional character of the electronic structure, resulting in properties that differ significantly from the case of inter-layer tunneling, where tunneling occurs between bulk two-dimensional graphene sheets. The current-voltage characteristics of the inter-ribbon tunneling structures exhibit resonance, as well as stepwise increases in current. Both features are caused by the energetic alignment of one-dimensional peaks in the density-of-states of the ribbons. Resonant tunneling occurs if the sign of the curvature of the coupled energy bands is equal, whereas a step-like increase in the current occurs if the signs are opposite. Changing the doping modulates the onset-voltage of the effects as well as their magnitude. Doping through electrostatic gating makes these structures promising for application towards steep slope switching devices. Using the atomistic empirical pseudopotentials based Bardeen transfer Hamiltonian method, inter-ribbon tunneling can be studied for the whole range of two-dimensional materials, such as transition metal dichalcogenides. The effects of resonance and of step-like increases in the current we observe in graphene ribbons are also expected in ribbons made from these alternative two-dimensional materials, because these effects are manifestations of the one-dimensional character of the density-of-states.

Interlayer tunneling spectroscopy of mixed-phase BSCCO superconducting whiskers

In this work, we present a study on the interlayer tunneling spectroscopy (ITS) of mixed-phase BiSrCaCuO (BSCCO) superconducting whiskers. The tunneling experiments were carried out on the artificial cross-whisker (twist angle of 90°) junctions. A multiple superconducting energy gap in the cross-whisker junctions was observed, which is attributed to the presence of different doping levels of two Bi2Sr2CaCu2O8+δ phases (Bi-2212), rather than two different phases, in the BSCCO whiskers, namely Bi2Sr2CaCu2O8+δ and Bi2Sr2Ca2Cu3O8+δ (Bi-2212 and Bi-2223). The temperature dependence of the energy gaps was discussed in the framework of the BCS T-dependence. On the other hand, the carrier concentration of the cross-whisker junction was changed by the carrier injection process. The effects of the carrier injection on the critical current, Ic, and the ITS of intrinsic Josephson junctions were investigated in details.

Anomalous Interlayer Transport of Quantum Hall Bilayers in the Strongly Josephson-Coupled Regime.

We investigate Josephson coupling in a closely spaced quantum Hall bilayer. Reduction of the interlayer barrier from the widely used values of 10-12nm to the present one of 8nm leads to qualitatively different interlayer transport properties. The breakdown of interlayer coherence can be spatially confined in regions that are smaller than the device size. Such a spatial inhomogeneity depends crucially on the Josephson-coupling strength and can be removed by adding an in-plane magnetic field of about 0.5T. At higher in-plane fields, the interlayer tunneling I-V curve develops unexpected overshoot features. These results challenge current theoretical understanding and suggest that our bilayer system has entered a previously unexplored regime.

Quantum oscillation as diagnostics of pseudogap state in underdoped cuprates

The Fermi surface in underdoped cuprates is reconstructed by the charge density wave (CDW) order in the pseudogap phase. Theoretical proposals can be divided into two classes: one assumes the underlying Fermi surface without CDW as a conventional large surface; the other assumes small hole-like Fermi pockets. In both scenarios, we theoretically study the quantum oscillation and find three evenly spaced peaks in the oscillation spectra. The central dominant peak is induced by the CDW order. Its effective mass is strongly enhanced as the CDW vanishes in agreement with experiments. But the two scenarios have different understandings of the subdominant satellite peaks. In the large-surface scenario they are induced by the interlayer tunneling between the bilayer CuO2 planes. Their effective masses are also enhanced with descreasing CDW. In the small-pocket scenario one of the subdominant peaks comes from the original small Fermi pockets of the pseudogap state. Its effective mass is nearly independent of the CDW strength and increases monotonically with the doping. We propose future quantum oscillation experiments to test these different predictions and thus to clarify the underlying Fermi surface structure of the pseudogap state.

Piezoresistive and posistor effects in polymer-semiconductor and polymer-ferropiezoceramic composites

In this study, piezoresistive and posistor effects in polymer-semiconductor and polymer-ferropiezoceramic composites have been investigated. The results show that composites based on crystallizable polymers, such as PVDF, HDPE, and PP dispersed by semiconductors and ferropiezoelectric fillers have piezoresistive and posistor properties, respectively. At low pressure, charge carriers tunneling through the located thin polymer among filler particles into the barrier define the conductivity of the composite. When pressure value is increased from 0 to 1 MPa, the thickness of the interlayer decreases and tunnel conductivity descends exponentially depending on barrier height. The piezoresistor sensitivity of a composite based on PVDF-70 vol % + Si-30 vol % is higher than a composite based on HDPE-70 vol % + Ge-30 vol %. Furthermore, the posistor properties of polymer composites dispersed by ferropiezoceramic are determined as the maximum resistance that varies significantly with temperature. Posistor effect in composites based on polymer + ferropiezoceramic is associated with the height of the barrier layer, which changes according to properties of filler, polymer, and dielectric permittivity of two-phase composites. The highest specific resistance related to HDPE-70 vol % + BaTiO3-30 vol % composite was observed at ~403 K.

Observation of a subharmonic gap singularity in interlayer tunneling characteristics ofBi2Sr2CaCu2O8+δ

A subharmonic structure in Josephson junctions appears due to Andreev reflections within the junction. Here we report on experimental observation of a subharmonic half-gap singularity in interlayer tunneling characteristics of a layered high temperature superconductor Bi2Sr2CaCu2O8+d. The singularity is most pronounced in optimally doped crystals and vanishes with decreasing doping. It indicates existence of non-vanishing electronic density of states and certain metallic properties in the intermediate BiO layers, which grows stronger with increasing doping. This provides an additional coherent interlayer transport channel and can explain a gradual transition from an incoherent quasi-two-dimensional $c$-axis transport in underdoped to a coherent metallic transport in overdoped cuprates. Furthermore, due to a very small sub-gap current, the singularity allows unambiguous extraction of the superconducting gap, without distortion by self-heating.

Phase diagram ofν=12+12bilayer bosons with interlayer couplings

We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor $\ensuremath{\nu}=1$ in the lowest Landau level. We consider short-range interactions within and between the two layers, as well as the interlayer tunneling. In the fully polarized regime, we provide an updated detailed numerical analysis to establish the presence of the Moore-Read phase of both even and odd numbers of particles. In the actual bilayer situation, we find that both interlayer interactions and tunneling can provide the physical mechanism necessary for the low-energy physics to be driven by the fully polarized regime, thus leading to the emergence of the Moore-Read phase. Interlayer interactions favor a ferromagnetic phase when the system is $\mathrm{SU}(2)$ symmetric, while the interlayer tunneling acts as a Zeeman field polarizing the system. Besides the Moore-Read phase, the $(220)$ Halperin state and the coupled Moore-Read state are also realized in this model. We study their stability against each other.

A Graphene Switching Transistor for Vertical Circuit Design

A graphene switching transistor (GST) is proposed based on graphene-hexagonal boron nitride (hBN)-graphene vertical heterostructure. The carrier transport between source and drain is controlled by the shift in Fermi level in the channel from vertical interlayer tunneling between top and bottom graphene layers through three layers of hBN. Analytical current transport equation is derived and its characteristics are studied. GST operating at 0.1 V supply voltage gives a steep subthreshold slope of 2.97 mV/decade with an on/off current ratio of 2.45 × 104. Drive current of 88 μA/μm2 is estimated for an effective channel area of 0.05 μm2. The voltage transfer characteristic of GST-based vertical inverter is also studied and it is noted that for sharp transition from off to on state. The GST dissipates 15 times less dynamic power and 194 times less off state leakage power in comparison to a projected 2020 nMOSFET.

Interaction-driven capacitance in graphene electron-hole double layer in strong magnetic fields

Fabrication of devices made by isolated Graphene or Graphene-like single layers (such as h-BN) has opened up possibility of examining highly correlated states of electron systems in parts of their phase diagram that is impossible to access in their counterpart devices such as semiconductor heterostructures. An example of such states are Graphene (or Graphene like) double layer electron-hole systems under strong magnetic fields where the separation between layers can be of the order of one magnetic length with interlayer tunneling still suppressed. In those separations correlations between electrons and holes are of crucial importance and must be included in determination of observable quantities. Here we report a thorough mean-field study of the coherent and crystalline ground states of the interacting balanced electron-hole Graphene systems in small and intermediate separations with each layer occupying up to four lowest lying Landau levels. We calculate the capacitance of such states as a function of layer separation and filling factor. Our calculations show significant enhancement of the capacitance compared to geometrical value due to quantum mechanical corrections.

Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: Application to the square lattice bilayer and honeycomb lattice

We consider an efficient scheme to simulate fermionic Hubbard models with nonlocal density-density interactions in two dimensions, based on bond-centered auxiliary-field quantum Monte Carlo. The simulations are shown to be sign-problem free within a finite, restricted parameter range. Using this approach, we first study the Hubbard model on the half-filled square lattice bilayer, including an interlayer repulsion term in addition to the local repulsion, and present the ground state phase diagram within the accessible parameter region. Starting from the antiferromagnetically ordered state in the absence of interlayer repulsion, the interlayer interactions are found to destabilize the antiferromagnetic order, leading to a band insulator state. Moreover, for sufficiently strong interlayer tunneling, we also observe the emergence of a direct dimer product state of mixed D-Mott and S-Mott character along the equal coupling line. We discuss the stability range of this state within strong-coupling perturbation theory. Furthermore, we consider the Hubbard model on the honeycomb lattice with next-nearest-neighbor interactions. Such an interaction is found to enhance both charge density and spin-current correlations within the semimetallic region. However, inside the accessible parameter region, they do not stabilize long-ranged charge density wave order nor a quantum spin Hall state, and the only insulating state that we observe exhibits long-range antiferromagnetism.

The optical conductivity in double and three layer graphene systems

Abstract We investigate the longitudinal optical conductivity in few-layer monolayer graphene systems, which is different from the bilayer or trilayer graphene structures analytically and numerically. Here, few isolated parallel two-dimensional (2D) monolayer graphene are separated by a distance d with no interlayer tunneling, where the finite width thickness has to be taken into account. The carrier׳s energy structure and states for each layer are unaffected by the others. The carrier density in each layer is assumed to be tuned by the corresponding gate voltage. The optical conductivity depends on the electron density, the number of layer, and the broadening width at low temperature. However, analytical and numerical results show that the optical conductivity has little dependence on the distance between the adjacent layers. It is found that two intra- and inter-band transition channels for optical transition via absorption scattering in each layer can be observed. When the optical energy is larger than two times the kinetic energy at the Fermi energy, the optical conductivity is proportional to the layer numbers of monolayer graphene that can determine the number of the monolayer graphene layer. In sharp contrast to the bilayer or trilayer graphene systems, several turning points can be observed. Increasing the broadening width, the turning area becomes gradual. The main difference on the optical conductivity for double layer graphene and bilayer graphene is in the intermediate energy region where the threshold structure is observed.

Fractional Solitons in Excitonic Josephson Junctions.

The Josephson effect is especially appealing to physicists because it reveals macroscopically the quantum order and phase. In excitonic bilayers the effect is even subtler due to the counterflow of supercurrent as well as the tunneling between layers (interlayer tunneling). Here we study, in a quantum Hall bilayer, the excitonic Josephson junction: a conjunct of two exciton condensates with a relative phase ϕ0 applied. The system is mapped into a pseudospin ferromagnet then described numerically by the Landau-Lifshitz-Gilbert equation. In the presence of interlayer tunneling, we identify a family of fractional sine-Gordon solitons which resemble the static fractional Josephson vortices in the extended superconducting Josephson junctions. Each fractional soliton carries a topological charge Q that is not necessarily a half/full integer but can vary continuously. The calculated current-phase relation (CPR) shows that solitons with Q = ϕ0/2π is the lowest energy state starting from zero ϕ0 – until ϕ0 > π – then the alternative group of solitons with Q = ϕ0/2π − 1 takes place and switches the polarity of CPR.

Non-Abelian phases in two-componentν=2/3fractional quantum Hall states: Emergence of Fibonacci anyons

Recent theoretical insights into the possibility of non-Abelian phases in $\nu=2/3$ fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body interlayer couplings on the $(330)$ bilayer state and exactly solve the Hamiltonian for up to $14$ electrons on sphere and torus geometries. We consider interlayer tunneling, short-ranged repulsive/attractive pseudopotential interactions and Coulomb repulsion. We find a 6-fold ground-state degeneracy on the torus when the interlayer hollow-core interaction is dominant. To identify the topological nature of this phase we measure the orbital-cut entanglement spectrum, quasihole counting, topological entanglement entropy, and wave-function overlap. Comparing the numerical results to the theoretical predictions, we interpret this 6-fold ground-state degeneracy phase to be the non-Abelian bilayer Fibonacci state.

Tunneling Plasmonics in Bilayer Graphene.

We report experimental signatures of plasmonic effects due to electron tunneling between adjacent graphene layers. At subnanometer separation, such layers can form either a strongly coupled bilayer graphene with a Bernal stacking or a weakly coupled double-layer graphene with a random stacking order. Effects due to interlayer tunneling dominate in the former case but are negligible in the latter. We found through infrared nanoimaging that bilayer graphene supports plasmons with a higher degree of confinement compared to single- and double-layer graphene, a direct consequence of interlayer tunneling. Moreover, we were able to shut off plasmons in bilayer graphene through gating within a wide voltage range. Theoretical modeling indicates that such a plasmon-off region is directly linked to a gapped insulating state of bilayer graphene, yet another implication of interlayer tunneling. Our work uncovers essential plasmonic properties in bilayer graphene and suggests a possibility to achieve novel plasmonic functionalities in graphene few-layers.