Narrow Miniband Research Articles

Obstruction and Interference in Low-Energy Models for Twisted Bilayer Graphene.

The electronic bands of twisted bilayer graphene (TBLG) with a large-period moiré superlattice fracture to form narrow Bloch minibands that are spectrally isolated by forbidden energy gaps from remote dispersive bands. When these gaps are sufficiently large, one can study a band-projected Hamiltonian that correctly represents the dynamics within the minibands. This inevitably introduces nontrivial geometrical constraints that arise from the assumed form of the projection. Here we show that this choice has a profound consequence in a low-energy experimentally observable signature that therefore can be used to tightly constrain the analytic form of the appropriate low-energy theory. We find that this can be accomplished by a careful analysis of the electron density produced by backscattering of Bloch waves from an impurity potential localized on the moiré superlattice scale. We provide numerical estimates of the effect that can guide experimental work to clearly discriminate between competing models for the low-energy band structure.

Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene

At very small twist angles of ∼0.1°, bilayer graphene exhibits a strain-accompanied lattice reconstruction that results in submicron-size triangular domains with the standard, Bernal stacking. If the interlayer bias is applied to open an energy gap inside the domain regions making them insulating, such marginally twisted bilayer graphene is expected to remain conductive due to a triangular network of chiral one-dimensional states hosted by domain boundaries. Here we study electron transport through this helical network and report giant Aharonov-Bohm oscillations that reach in amplitude up to 50% of resistivity and persist to temperatures above 100 K. At liquid helium temperatures, the network exhibits another kind of oscillations that appear as a function of carrier density and are accompanied by a sign-changing Hall effect. The latter are attributed to consecutive population of the narrow minibands formed by the network of one-dimensional states inside the gap.

Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides

Geometrical moir\'e patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moir\'e superlattice (mSL) effects in $\mathrm{MoSe}_2/\mathrm{WS}_2$ and $\mathrm{MoTe}_2/\mathrm{MoSe}_2$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of TMDs, including examples of narrow minibands close to the actual band edges. Such hybridization determines the optical activity of interlayer excitons in transition-metal dichalcogenide (TMD) heterostructures, as well as energy shifts in the exciton spectrum. We show that the resonantly hybridized exciton (hX) energy should display a sharp modulation as a function of the interlayer twist angle, accompanied by additional spectral features caused by umklapp electron-photon interactions with the mSL. We analyze the appearance of resonantly enhanced mSL features in absorption and emission of light by the interlayer exciton hybridization with both intralayer A and B excitons in $\mathrm{MoSe}_2/\mathrm{WS}_2$, $\mathrm{MoTe}_2/\mathrm{MoSe}_2$, $\mathrm{MoSe}_2/\mathrm{MoS}_2$, $\mathrm{WS}_2/\mathrm{MoS}_2$, and $\mathrm{WSe}_2/\mathrm{MoSe}_2$.

Emergent D6 symmetry in fully relaxed magic-angle twisted bilayer graphene

We present a tight-binding calculation of a twisted bilayer graphene at magic angle $\theta\sim 1.08^\circ$, allowing for full, in- and out-of-plane, relaxation of the atomic positions. The resulting band structure displays as usual four narrow mini bands around the neutrality point, well separated from all other bands after the lattice relaxation. A thorough analysis of the mini-bands Bloch functions reveals an emergent $D_6$ symmetry, despite the lack of any manifest point group symmetry in the relaxed lattice. The Bloch functions at the $\Gamma$ point are degenerate in pairs, reflecting the so-called valley degeneracy. Moreover, each of them is invariant under C$_{3z}$, i.e., transforming like one-dimensional, in-plane symmetric irreducible representation of an "emergent" $D_6$ group. Out of plane, the lower doublet is even under C$_{2x}$, while the upper doublet is odd, which implies that at least eight Wannier orbitals, two $s$-like and two $p_z$-like for each of the two supercell sublattices AB and BA are necessary, probably not sufficient, to describe the four mini bands. This unexpected one-electron complexity is likely to play an important role in the still unexplained metal-insulator-superconductor phenomenology of this system.

Quantum Dot Channel (QDC) Field Effect Transistors (FETs) Configured as Floating Gate Nonvolatile Memories (NVMs)

This paper presents quantum dot channel (QDC) Field Effect Transistors (FETs) which are configured as nonvolatile memories (NVMs) by incorporating cladded GeOx-Ge quantum dots in the floating gates as well as the transport channels. The current flow and the threshold characteristics were significantly improved when the gate dielectric was changed from silicon dioxide (SiO2) to hafnium aluminum oxide (HfAlO2), and the control dielectric was changed from silicon nitride (Si3N4) to hafnium aluminum oxide (HfAlO2). The device operations are explained by carrier transport in narrow energy mini-bands which are manifested in a quantum dot transport channel.

Controlled formation of isolated miniband in bilayer graphene on almost commensurate 3×3 substrate

We investigate theoretically the interplay between the effects of a perpendicular electric field and incommensurability at the interface on the electronic properties of a heterostructure of bilayer graphene and a semiconducting substrate with a unit cell almost three times larger then that of graphene. It is known that the former introduces an asymmetry in the distribution of the electronic wave function between the layers and opens a band gap in the electronic spectrum. The latter generates a long wavelength periodic moir\'{e} perturbation of graphene electrons which couples states in inequivalent graphene Brillouin zone corners and leads to the formation of minibands. We show that, depending on the details of the moir\'{e} perturbation, the miniband structure can be tuned from that with a single band gap at the neutrality point and over-lapping minibands on the conduction/valence band side to a situation where a single narrow miniband is separated by gaps from the rest of the spectrum.

Quantum Dot Channel (QDC) FETs with Wraparound II–VI Gate Insulators: Numerical Simulations

This paper presents simulations predicting the feasibility of 9-nm wraparound quantum dot channel (QDC) field-effect transistors (FETs). In particular, II–VI lattice-matched layers which reduce the density of interface states, serving as top (tunnel gate), side, and bottom gate insulators, have been simulated. Quantum simulations show FET operation with voltage swing of ~0.2 V. Incorporation of cladded quantum dots, such as SiOx–Si and GeOx–Ge, under the gate tunnel oxide results in electrical transport in one or more quantum dot layers which form a quantum dot superlattice (QDSL). Long-channel QDC FETs have experimental multistate drain current (ID)–gate voltage (VG) and drain current (ID)–drain voltage (VD) characteristics, which can be attributed to the manifestation of extremely narrow energy minibands formed in the QDSL. An approach for modeling the multistate ID–VG characteristics is reported. The multistate characteristics of QDC FETs permit design of compact two-bit multivalued logic circuits.

MOCVD-grown heterostructures with GaAs/AlGaAs Superlattices: Growth features and optical and transport characteristics

The results of studies of MOCVD growth regularities of GaAs/AlGaAs superlattices with narrow forbidden minibands are presented. The spectra of photoluminescence and X-ray diffraction are measured, the concentration distribution profiles of components are determined by secondary-ion mass spectrometry, and the concentration distribution of charge carriers are determined by the method of capacitance profiling. The relation of the growth modes of heterostructures to their crystalline characteristics and luminescent and electrical properties are studied. The photoluminescence measurements indicate the high quality of the superlattices. X-ray diffraction and the data on secondary ions confirm the high periodicity of the superlattices grown in the optimized modes. The nonlinear current-voltage characteristics with a region of negative differential conductivity at moderate voltages and subsequent current increase at higher voltages because of tunneling between the minibands is found for the superlattices grown in the optimal growth modes. Current oscillations at frequencies of ∼60 MHz were observed in the region of negative differential conductivity. The negative differential conductivity and oscillations confirm the presence of the electron localization effect in moderate electric fields in the first conductivity miniband, which emerges due to the Bragg reflection of carriers in the superlattice.

Modeling and Fabrication of Quantum Dot Channel Field Effect Transistors Incorporating Quantum Dot Gate

ABSTRACTQuantum dot gate (QDG) field-effect transistors (FET) have shown three-state transfer characteristics. Quantum dot channel (QDC) field-effect transistors (FET) have exhibited fourstate ID-VG characteristics. This project aims at studying the effect of incorporating cladded quantum dot layers in the gate region of QDC-FET. Four-state characteristics are explained by carrier transport in narrow energy mini-bands which are manifested in a quantum dot superlattice (QDSL) channel. QDSL is formed by an array of cladded quantum dots (such as SiOx-Si and GeOx-Ge). Multi-state FETs are needed in multi-valued logic (MVL) that can reduce the number of gates and transistors in digital circuits. The fabricated device showed the four-state characteristic (OFF, ‘I1’, ‘I2’, ON).

Field localization on the defect of inversion type in a one-dimensional fotonic crystal structure

Modification of the transmission spectrum and wave field distribution in a one-dimensional photonic crystal with single or double defect of inversion type is investigated. It is demonstrated that in the presence of the defect, a narrow transmission miniband is formed in the non-transmission band gap of the defectless crystal. In this case, the field is strongly localized in the defect region depending on the defect type, its position, and the number of complete periods in the structure. The formation of the double defect of inversion type leads to the formation of two defect minibands in the spectrum and the redistribution of the wave field in the structure.

Thermoelectric transport in periodic one-dimensional stacks of InAs/GaAs quantum dots

We investigate the effect of the narrow electronic minibands of periodic one-dimensional stacks of disk-shaped InAs quantum dots (QDs) in GaAs on their electronic transport characteristics by employing an empirical tight-binding calculation and a continuum model of the electronic structure. Our model includes both the minibands and the continuum of the host conduction band. The rate of the electron-acoustic-phonon scattering is found using Boltzmann's semiclassical transport theory. The electric conductivity, the Seebeck coefficient and the thermoelectric figure-of-merit for $n$-doped QD arrays are then analyzed as a function of the donor concentration and temperature. For QDs several nanometers in height, the figure-of-merit at temperatures below 100 K as a function of doping is richly structured, reflecting the miniband electron energy spectrum of a QD stack. Certain windows of concentration are revealed, where QD arrays display a geometry-controlled enhanced efficiency as thermoelectric converters. For optimizing the peak values of the figure-of-merit attainable for donor concentrations within the experimentally accessible range, a very thin spacer layer between the QDs $(\ensuremath{\lesssim}5\text{ }\text{nm})$ is found to be most suitable. Assuming that the lattice thermal conductivity can be reduced below $0.5\text{ }\text{W}/(\text{m}\phantom{\rule{0.2em}{0ex}}\text{K})$, a figure-of-merit larger than 2 appears within reach.

Transport in GaAs/Al x Ga1−x As superlattices with narrow forbidden minibands: Low-frequency negative differential conductivity and current oscillations

Current-voltage characteristics have been measured and low-frequency current instabilities have been studied for GaAs/Al x Ga1−x As superlattices with narrow forbidden minibands. At relatively low electric fields, a saw-like structure for current-voltage characteristics with alternating portions of positive and negative differential conductivity and spontaneous generation of low-frequency current oscillations with a complex frequency spectrum (varying from discrete to continuous) are observed. It is shown that the observed specific features of electron transport are caused by the spatial-temporal dynamics of electric-field domains (dipoles and monopoles). The effects of the bifurcation, hysteresis, and multistability of current-voltage characteristics are also observed. At high fields, regular features are observed and identified in the current-voltage characteristics; these features are caused by resonance tunneling of electrons between the levels of the Wannier-Stark ladders belonging to quantum wells separated by several periods.

Transport in GaAs/Al x Ga1−x As superlattices with narrow minibands: Effects of interminiband tunneling

The results of experimental investigations for the I–V characteristics are presented for superlattices based on GaAs/AlxGa1−xAs with thin barriers in the electric-field region with an intense interminiband tunneling. The regular features for the I–V characteristics are found in the voltage range adequate to the static positive differential conductivity in the superlattice. On the basis of calculations for the Wannier-Stark levels, it is established that the observed features are associated with the resonant tunneling between these levels belonging to quantum wells located at a distance from 6–13 superlattice periods from each other. It is noted that the similar resonant delocalization of Wannier-Stark wave functions can lead to the existence of dynamic negative differential conductivity for the laser type of an appreciable value in such superlattices.

Two-color pump-probe studies of intraminiband relaxation in doped GaAs∕AlGaAs superlattices

The miniband relaxation dynamics of electrons in doped GaAs∕AlGaAs superlattices are investigated by two-color infrared pump-probe experiments. By this technique, we are able to separate the different contributions from inter- and intraminiband relaxations to the transient behavior after an ultrafast excitation. In particular, the intraminiband relaxation is studied for different miniband widths below and above the optical phonon energy of GaAs. For minibands wider than this critical value, we find fast relaxation, nearly constant for different excitation intensities, whereas for narrow minibands, a strong temperature and intensity dependence of the relaxation is found. The results are in good agreement with previously published Monte Carlo simulations.

Compressibility of electron liquid in the quantized Hall phase of GaAs/AlGaAs multi-layers

Magneto-capacitance was studied in narrow miniband GaAs/AlGaAs superlattices where quasi-two dimensional electrons revealed the integer quantum Hall effect. The interwell tunneling was shown to reduce the effect of the quantization of the density of states on the capacitance of the superlattices. In such case the minimum of the capacitance observed at the filling factor ν = 2 was attributed to the decrease of the electron compressibility due to the formation of the incompressible quantized Hall phase. In accord with the theory this phase was found strongly inhomogeneous. The incompressible fraction of the quantized Hall phase was demonstrated to rapidly disappear with the increasing temperature.

Conductivity of charge-ordered layered crystals in quantizing magnetic fields in the inversion region of the nonoscillating magnetoresistance component

The conductivity of charge-ordered layered crystals in electric and quantizing magnetic fields orthogonal to the layers is calculated. Charge ordering is considered as an alternation of layers with different charge-carrier densities. When scattering by acoustic phonons, conductivity is calculated in the approximation of profound quantization, so that the intersubband transitions can be assumed to be suppressed. It is shown that, in the transition of the layered crystal from the disordered to almost completely ordered state, the conductivity oscillations exhibit double periodicity. In this case, the high “carrier” frequency is controlled by the effective attractive electron-electron interaction responsible for charge ordering, whereas the low “modulation” frequency is defined by the width of the narrow miniband orthogonal to the layers. It is also shown that, in the transition from a disordered to an almost completely ordered state, the longitudinal conductivity of layered crystals decreases by two or three orders of magnitude. At the same time, the relative contribution of oscillations sharply increases, with satisfactory agreement to the experimental data.

A quasi-classical description of the conductivity oscillations in layered crystals under the condition of charge-carrier scattering by acoustic phonons

The oscillating part of the longitudinal conductivity of layered crystals is considered within the quasi-classical approximation, where both the electric field and quantizing magnetic field are perpendicular to the layers. Our approach differs from the conventional one by taking into account both the nonparabolicity of a narrow conduction miniband and the dependence of the Fermi surface size in the direction of the magnetic field on charge-carrier concentration. This approach makes it possible to consider not only the standard case, with open Fermi surfaces, but also the case of closed Fermi surfaces. It is shown that, for closed Fermi surfaces, the existence of frequencies that do not correspond to extreme cross sections of the Fermi surfaces cut by planes normal to the magnetic field can serve as a criterion for the narrowness of the conduction miniband, which determines the translational motion of charge carriers across the layers.

Chains of Artificial Atoms in a Magnetic Field

The energy structure of one-dimensional chains of spherical nanocrystals is investigated. Both, uniform and multilayer nanocrystals are studied. Calculations are performed with the k·p method and the envelope function approximation (EFA). The valence subband mixing is accounted for by considering a four-band Hamiltonian. The high (spherical) symmetry of the building blocks leads to a unique energy structure with miniband widths depending on the z-component of the angular momentum. These minibands are (2L + 1) quasi-degenerated in the low-coupling regime, L being the quantum number of the angular momentum. The magnetic field splits quasidegeneracy leading to a mixture of successive narrow and wide minibands. The ground miniband of chains built of antidots becomes very narrow in the strong coupling regime and separates from the rest of the spectrum, so that a strong luminescence red-shift is predicted.

Nanocrystal molecules and chains

The electron energy structure of linear artificial molecules and one-dimensional chains formed of spherical semiconductor nanocrystals is investigated with and without an applied magnetic field. Both uniform and multilayer nanocrystals are studied. The calculations are performed within the effective mass model by numerically integrating the effective mass equation on a two-dimensional cylindrical grid. Some calculations are, for comparison, performed also in the tight-binding approach. Density contours are presented to illustrate the transformation of states in systems of strongly interacting coupled quantum dots. Strong interaction between the quantum-dot–quantum-well structures in a chain of nanocrystals can lead to the formation of a very narrow ground-state miniband, well separated from the excited levels with the energies almost independent of the magnetic field.

QUANTUM TRANSPORT IN SEMICONDUCTOR SUPERLATTICES BEYOND THE KADANOFF–BAYM ANSATZ

Quantum transport in semiconductor superlattices subject to quantizing parallel electric and magnetic fields is studied based on the Kadanoff–Baym–Keldysh double-time Green function approach. Exploiting the symmetry properties of the underlying Hamiltonian, coupled kinetic equations are derived and analytically solved for the density-of-states and the carrier distribution function. Scattering giving rise to collisional broadening plays an important role in our transport model, whose unperturbed eigenstates are completely discrete due to Wannier–Stark and Landau quantization. It is shown that a correct description of the stationary quantum transport in superlattices with field-induced localized eigenstates requires the determination of a time-dependent distribution function from a kinetic equation, which emerges beyond the Kadanoff–Baym Ansatz. Depending on the scattering strength, gaps are predicted to occur in the electric and magnetic field dependence of the current density. The rigorous quantum-mechanical approach reveals the hopping nature of the nonlinear transport in narrow miniband superlattices. This is compared with results obtained recently within the density-matrix approach.