Superlattice Miniband Research Articles

Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry

Two-dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers. Published by the American Physical Society 2025

Infrared Spectroscopy for Diagnosing Superlattice Minibands in Twisted Bilayer Graphene near the Magic Angle.

Twisted bilayer graphene (TBG) represents a highly tunable, strongly correlated electron system. However, understanding the single-particle band structure alone has been challenging due to a lack of spectroscopic measurements over a broad energy range. Here, we probe the band structure of TBG around the magic angle using infrared spectroscopy and reveal spectral features that originate from interband transitions. In combination with quantum transport, we connect spectral features over a broad energy range (10-700 meV) and track their evolution with the twist angle. We compare our data with calculations of the band structures obtained via the continuum model and find good agreement only when considering a variation of interlayer/intralayer tunneling parameters with the twist angle. Our analysis suggests that the magic angle also shifts due to lattice relaxation and is better defined for a wide angular range of 0.9-1.1°. Additionally, our measurements offer an optical fingerprint of the magic angle for screening heterostructures before nanofabrication.

Optical Characterization of the Interband Cascade LWIR Detectors with Type-II InAs/InAsSb Superlattice Absorber.

The long-wave infrared (LWIR) interband cascade detector with type-II superlattices (T2SLs) and a gallium-free ("Ga-free") InAs/InAsSb (x = 0.39) absorber was characterized by photoluminescence (PL) and spectral response (SR) methods. Heterostructures were grown by molecular beam epitaxy (MBE) on a GaAs substrate (001) orientation. The crystallographic quality was confirmed by high-resolution X-Ray diffraction (HRXRD). Two independent methods, combined with theoretical calculations, were able to determine the transitions between the superlattice minibands. Moreover, transitions from the trap states were determined. Studies of the PL intensity as a function of the excitation laser power allowed the identification of optical transitions. The determined effective energy gap (Eg) of the tested absorber layer was 116 meV at 300 K. The transition from the first light hole miniband to the first electron miniband was red-shifted by 76 meV. The detected defects' energy states were constant versus temperature. Their values were 85 meV and 112 meV, respectively. Moreover, two additional transitions from acceptor levels in cryogenic temperature were determined by being shifted from blue to Eg by 6 meV and 16 meV, respectively.

Gain in Thermoelectric Figure of Merit of Al<sub>x</sub>Ga<sub>1-x</sub>As/GaAs Type Superlattices Induced by Strong Impurity Screening

In multi-layer structures impurity scattering is effectively reduced by the modulation doping in order to achieve high charge carrier mobility and, as a consequence, better device performance. In this paper, the thermoelectric properties of superlattices when electrons are scattered by strongly screened ionized impurities are discussed. In low-temperature and strong screening circumstances, dependence of the thermopower, power factor, and figure of merit on the superlattice period, miniband width, and screening radius is found. For the specified superlattice parameters and ionized impurity concentration, the figure of merit reaches the value of 2.6. The thermopower of the superlattices five times exceeds that of bulk samples.

Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates

We investigate the quantum-classical correspondence for a particle tunnelling through a periodic superlattice structure with an applied bias voltage and an additional tilted harmonic oscillator potential. We show that the quantum mechanical tunnelling rate between neighbouring quantum wells of the superlattice is determined by the topology of the phase trajectories of the analogous classical system. This result also enables us to estimate, with high accuracy, the tunnelling rate between two spatially displaced simple harmonic oscillator states using a classical model, and thus gain new insight into this generic quantum phenomenon. This finding opens new directions for exploring and understanding the quantum-classical correspondence principle and quantum jumps between displaced harmonic oscillators, which are important in many branches of natural science.

Kagome Quantum Oscillations in Graphene Superlattices.

Electronic spectra of solids subjected to a magnetic field are often discussed in terms of Landau levels and Hofstadter-butterfly-style Brown-Zak minibands manifested by magneto-oscillations in two-dimensional electron systems. Here, we present the semiclassical precursors of these quantum magneto-oscillations which appear in graphene superlattices at low magnetic field near the Lifshitz transitions and persist at elevated temperatures. These oscillations originate from Aharonov-Bohm interference of electron waves following open trajectories that belong to a kagome-shaped network of paths characteristic for Lifshitz transitions in the moire superlattice minibands of twistronic graphenes.

Trap levels analysis in MWIR InAs/InAsSb T2SL photodiode

Mid-wave infrared (MWIR) photodiode with an InAs/InAsSb superlattice active layer was characterized by the photoluminescence (PL), spectral response (SR) and deep level transient spectroscopy (DLTS) measurements. Three independent methods, in combination with the theoretical calculations, were used to determine the transitions between superlattice minibands, as well as to and from the trap states. The determined effective band gap of the investigated superlattice is 251 meV at 70 K. Most of the detected trap states lie within the energy gap, around 60 and 80 meV below the first electron miniband, and near the mid-gap. Moreover, trap states located above the first electron miniband and below the first light hole miniband were also observed. It is worth emphasizing that the PL and DLTS measurements give consistent results. Additionally, the activation energy of 16 meV for the Be acceptor dopant was determined using the PL measurement.

Kagome network of miniband-edge states in double-aligned graphene–hexagonal boron nitride structures

Twistronic heterostructures have recently emerged as a new class of quantum electronic materials with properties determined by the twist angle between the adjacent two-dimensional materials. Here, we study moir\'e superlattice minibands in graphene (G) encapsulated in hexagonal boron nitride (hBN) with an almost perfect alignment with both the top and bottom hBN crystals. We show that, for such an orientation of the unit cells of the hBN layers that locally breaks inversion symmetry of the graphene lattice, the hBN/G/hBN structure features a kagome network of topologically protected states with energies near the miniband edge, propagating along the lines separating the areas with different miniband Chern numbers.

Nonlinear electron transport in miniband superlattice driven by dual terahertz fields and a transverse magnetic field

Time-dependent electron current response of GaAs-based miniband superlattice under dual ac electric fields and a magnetic field is studied using balance equation approach. The space charge-induced self-consistent electric field is taken into account in the model. The miniband superlattice operates in the diffusive regime without electric field domain formation. Electron current displays very complicated oscillating behavior with the influence of external fields. The effect of dissipation on nonlinear electron transport is carefully studied based on Poincaré bifurcation diagram and power spectrum. The exhibition of complicate nonlinear oscillation in superlattice is attributed to the nonlinearity induced by self-consistent field and interaction between external radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

Boundary Modes from Periodic Magnetic and Pseudomagnetic Fields in Graphene.

Single-layer graphene subject to periodic lateral strains is an artificial crystal that can support boundary spectra with an intrinsic polarity. This is analyzed by comparing the effects of periodic magnetic fields and strain-induced pseudomagnetic fields that, respectively, break and preserve time-reversal symmetry. In the former case, a Chern classification of the superlattice minibands with zero total magnetic flux enforces single counterpropagating modes traversing each bulk gap on opposite boundaries of a nanoribbon. For the pseudomagnetic field, pairs of counterpropagating modes migrate to the same boundary where they provide well-developed valley-helical transport channels on a single zigzag edge. We discuss possible schemes for implementing this situation and their experimental signatures.

Theoretical Analysis of Terahertz Frequency Multiplier Based on Semiconductor Superlattices.

We propose a terahertz frequency multiplier based on high order harmonic generation in a GaAs-based miniband superlattice driven by an electric field. The performance of the frequency multiplier is analyzed using the balance equation approach, which incorporates momentum and energy relaxation processes at different lattice temperatures. It is found that the generated high-order harmonic power is sensitive to temperature changes. The peak power appears around resonance between driving terahertz frequency and intrinsic Bloch frequency. In the presence of the magnetic field, the peak power shifts towards a stronger static electric field region. The simulated results about the dependence of the second and third harmonic powers on a DC electric field are in qualitative consistence with the experiments. The proposed terahertz frequency multiplier based on semiconductor superlattice, being compact and efficient, is provided as a good candidate for terahertz wave generation.

Band-gap formation and morphing in α−T3 superlattices

Electrons in $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ lattices behave as condensed-matter analogies of integer-spin Dirac fermions. The three atoms making up the unit cell bestow the energy spectrum with an additional energy band that is completely flat, providing unique electronic properties. The interatomic hopping term, $\ensuremath{\alpha}$, is known to strongly affect the electronic spectrum of the two-dimensional (2D) lattice, allowing it to continuously morph from graphenelike responses to the behavior of fermions in a dice lattice. For pristine lattice structures the energy bands are gapless, but small deviations in the atomic equivalence of the three sublattices will introduce gaps in the spectrum. It is unknown how these affect transport and electronic properties such as the energy spectrum of superlattice minibands. Here we investigate the dependency of these properties on the parameter $\ensuremath{\alpha}$ accounting for different symmetry-breaking terms, and we show how it affects band-gap formation. Furthermore, we find that superlattices can force band gaps to close and shift in energy. Our results demonstrate that $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ superlattices provide a versatile material for 2D band-gap engineering purposes.

Magneto-spectroscopy investigation of InAs/InAsSb superlattices for midwave infrared detection

Raising the operating temperature of the midwave infrared (MWIR) cameras up to 150 K without penalizing the performances of the photodetectors is one of the main challenges of the domain. Moreover, extending the range of detection up to 5 μm brings many advantages. Ga-free InAs/InAsSb superlattice based devices have been recently fabricated and they showed the first realization of these objectives. However, the band parameters (band offsets, effect of strain, effective mass) of this system have not been determined accurately, thus limiting the understanding and the prediction of the electronic properties of the devices. In this work, we determined the relevant parameters via magnetoabsorption measurements performed on dedicated superlattices. Interband magneto-optical transitions lead to an accurate mapping of the Landau levels. The Landau level energies have been calculated using an 8-band k⋅ p model, and the comparison with the experimental data provided a clear description of the type 2 superlattice miniband structure at 4.2 and 150 K, as well as its MWIR absorbance.

Enhancement of the Seebeck coefficient and power factor in gated silicene superlattices induced by aperiodicity

This paper theoretically investigates the impact of aperiodic sequences in the ballistic transport and thermoelectric effect in silicene gated superlattices. In our analysis, we have implemented the well-known Fibonacci, Thue–Morse, and triadic Cantor type sequences. The transfer matrix technique and the Landauer–Bütikker formalism are used to calculate the transmission probability and the conductance, respectively. The Cutler–Mott formula is employed to estimate the Seebeck coefficient, and the thermoelectric power factor is then obtained. We found that the transmission minibands of aperiodic superlattices exhibit a much more fragmented structure in comparison to that reported in the periodic case. Consequently, the conductance curve presents a more pronounced oscillating shape, which improves the thermoelectric properties. In particular, the Seebeck coefficient has reached values up to 78.2 mV/K for Fibonacci, 233.0 mV/K for Thue–Morse, and 436.3 mV/K for Cantor. In addition, the power factor has been substantially increased, reaching peaks of approximately 8.2, 50.2, and 2.1 nW/K2 for the mentioned sequences, respectively. The best results were obtained for spindown (spinup) charge carriers in the K (K′) valley. Besides, an additional improvement is obtained by considering superior generations of the aperiodic sequences. Finally, our findings are supported through the redistribution of the density of the states, which is induced by the aperiodicity of the nanostructure as well as by the low-dimensionality of the thermoelectric device.

Anomalous Cyclotron Motion in Graphene Superlattice Cavities.

We consider graphene superlattice miniband fermions probed by electronic interferometry in magnetotransport experiments. By decoding the observed Fabry-Pérot interference patterns together with our corresponding quantum transport simulations, we find that the Dirac quasiparticles originating from the superlattice minibands do not undergo conventional cyclotron motion but follow more subtle trajectories. In particular, dynamics at low magnetic fields is characterized by peculiar, straight trajectory segments. Our results provide new insights into superlattice miniband fermions and open up novel possibilities to use periodic potentials in electron optics experiments.

Chiral channel network from magnetization textures in two-dimensional MnBi2Te4

When atomically thin van der Waals (vdW) magnet forms long-period moir\'e pattern with a magnetic substrate, the sensitive dependence of interlayer magnetic coupling on the atomic registries can lead to moir\'e defined magnetization textures in the two-dimensional (2D) magnets. The recent discovery of 2D magnetic topological insulators such as MnBi2Te4 leads to the interesting possibility to explore the interplay of such magnetization textures with the topological surface states, which we explore here with a minimal model established for 2D MnBi2Te4. The sign flip of the exchange gap across a magnetization domain wall gives rise to a single in-gap chiral channel on each surface. In the periodic magnetization textures, such chiral spin channels at the domain walls couple to form a network and superlattice minibands emerge. We find that in magnetization textures with closed domain wall geometries, the formed superlattice miniband is a gapped Dirac cone featuring orbital magnetization from the current circulation in the close loops of chiral channels, while in magnetization textures with open domain wall geometries, gapless mini-Dirac cone is found instead. The miniband Bloch states feature a spatial texture of spin and local current density, which are clear manifestation of the spin-momentum locked chiral channels at the domain walls. The results suggest a new platform to engineer spin and current flows through the manipulation of magnetization domains for spintronic devices.

Asymmetric spin relaxation induced by residual electron spin in semiconductor quantum-dot-superlattice hybrid nanosystem

Asymmetric spin relaxation induced by the residual electron spin in semiconductor quantum dots (QDs) adjacent to a superlattice (SL) was studied using spin- and time-resolved photoluminescence under the selective photoexcitation of the SL miniband states. Spin-polarized electrons were photoexcited in the SL barrier and then injected into the QDs through spin-conserving tunneling. The spin-polarized electron transport and the faster transport of the electrons as compared to the holes generate the residual majority electron spins in the QDs. A reversal of the optical spin polarity was observed at the ground state of the QDs, depending on the excitation powers. A rate equation analysis considering the individual spin-flip times between spin-split QD states indicates that the polarity reversal originates from the asymmetric spin-flip process at the excited state of the QDs. The asymmetric spin relaxation is associated with the selective relaxation of the spin-flipped electron and hole to the unoccupied ground state, which is induced by the existence of the residual majority electron spin at this state. In addition, we observed a clear recovery of the optical spin polarity by eliminating the existence of the residual electron spin through heavy p-doping. These findings are important to attain a fundamental understanding of the spin relaxation mechanism within the QDs and provide an insight into the manipulation of the optical spin polarity by controlling the residual electron spins in the QDs.

Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene.

Superconductivity can occur under conditions approaching broken-symmetry parent states1. In bilayer graphene, the twisting of one layer with respect to the other at 'magic' twist angles of around 1 degree leads to the emergence of ultra-flatmoiré superlattice minibands. Such bands are a rich and highly tunable source of strong-correlation physics2-5, notably superconductivity, which emerges close to interaction-induced insulating states6,7. Here we report the fabrication of magic-angle twisted bilayer graphene devices with highly uniform twist angles. The reduction in twist-angle disorder reveals the presence of insulating states at all integer occupancies of the fourfold spin-valley degenerate flat conduction and valence bands-that is, at moiré band filling factors ν=0,±1,±2,±3. At ν≈-2, superconductivity is observed below critical temperatures of up to 3 kelvin. We also observe three new superconducting domes at much lower temperatures, close to the ν=0 and ν=±1 insulating states. Notably, at ν=±1 we find states with non-zero Chern numbers. For ν=-1 the insulating state exhibits a sharp hysteretic resistance enhancement when a perpendicular magnetic field greater than 3.6 tesla is applied, which is consistent with a field-driven phase transition. Our study shows that broken-symmetry states, interaction-driven insulators, orbital magnets, states with non-zero Chern numbers and superconducting domes occur frequently across a wide range of moiré flat band fillings, including close to charge neutrality. This study provides a more detailed view of the phenomenology of magic-angle twisted bilayer graphene, adding to our evolving understanding of its emergent properties.

Transport Properties of Se/As2Se3 Nanolayer Superlattice Fabricated Using Rotational Evaporation

AbstractSince their proposal by Esaki, superlattices have been observed to have fascinating features such as quantum size effects, negative differential resistance, and sequential resonant tunneling. However, the technology threshold for fabricating superlattices is high, requiring methods like molecular beam epitaxy (MBE) and atomic layer deposition (ALD), among others, even for amorphous materials. Thus, the desirable features from superlattices have not been extensively utilized. It is shown that superlattices of Se and As2Se3 (superlattice‐Se), fabricated using rotational evaporation, exhibit sequential tunneling, a typical superlattice feature. From current–voltage measurements of the superlattice deposited on n‐type Si, oscillations in the characteristics are observed. Using models of reverse‐biased Schottky barriers, the observations are explained as tunneling in sequence from superlattice minibands. The superlattice‐Se also shows carrier blocking, with a resistivity of the order of 1012 Ω cm in dark conditions at room temperature, despite the low resistivity (≈10 Ω cm) of the n‐type Si substrate. When the Si is illuminated, the device shows higher detectivity for weaker signals compared to higher illumination. The ease of fabrication, and the blocking and amplifying capabilities make superlattice‐Se an interesting “add‐on” structure to improve conventional photodetector materials such as Si or Ge, which have issues with dark currents at room temperature.

The detailed analysis of wavefunction overlaps for InAs/AlSb/GaSb based N-structure type-II SL pin photodetectors

We report on a detailed analysis of electron and hole wave functions with their overlap integrals for InAs/AlSb/GaSb based N-structure type-II superlattice (T2SL) pin detectors under applied reverse bias. Bandgap energies and superlattice minibands are performed by envelope function approximation using pseudopotential method for input parameters such as effective masses and envelope functions at Γ point. The layer thickness of detector structure is designed to operate in the long wavelength infrared range given with the maximum overlap of around 8.6 μm. Electron wave functions show strong localizations in the neighboring wells under low electrical fields resulting with lower overlap integrals. An increase in the electrical field causes strong overlap by reduced localizations.