Query: Complex band structure and superlattice electronic states

Candidate papers:

abstract: The complex band structures of the bulk materials which constitute the alternating layer (001) semiconductor semiconductor superlattice are investigated. The complex bands near the center of the Brillouin zone in the [001] direction are studied in detail. The decay lengths of superlattice states whose energies lie in the bulk band gaps of one of the semiconductors are determined from the dispersion curves of these bands for imaginary \stackrel{\ensuremath{\rightarrow}\mathrm{k} This method is applied using a tight binding band structure calculation to two superlattices: the AlAs GaAs superlattice and the CdTe HgTe superlattice. The decay lengths of AlAs GaAs superlattice conduction band minimum states are found to be substantially shorter than those for the CdTe HgTe superlattice. These differences in the decay of the states in the two superlattices result in differences in the variation of the conduction band effective masses with the thickness of the AlAs and CdTe layers. The conduction band effective masses increase more rapidly with AlAs thickness in the AlAs GaAs superlattice than with CdTe thickness in the CdTe HgTe superlattice.
author_names: J Schulman

T C Mcgill
title: Complex band structure and superlattice electronic states
year: 1981

abstract: Twisted bilayer graphene (TBLG) is one of the simplest van der Waals heterostructures, yet it yields a complex electronic system with intricate interplay between moire physics and interlayer hybridization effects. We report on electronic transport measurements of high mobility small angle TBLG devices showing clear evidence for insulating states at the superlattice band edges, with thermal activation gaps several times larger than theoretically predicted. Moreover, Shubnikov de Haas oscillations and tight binding calculations reveal that the band structure consists of two intersecting Fermi contours whose crossing points are effectively unhybridized. We attribute this to exponentially suppressed interlayer hopping amplitudes for momentum transfers larger than the moire wave vector.
author_names: Y Cao

J Y Luo

Valla Fatemi

Shiang Fang

Javier D Sanchez-Yamagishi

K Watanabe

Takashi Taniguchi

Efthimios Kaxiras

Pablo Jarillo-Herrero
title: Superlattice Induced Insulating States and Valley Protected Orbits in Twisted Bilayer Graphene.
venue: Physical review letters
year: 2016

abstract: A pseudopotential complex band structure approach is used to investigate the valence band electronic structure of GaAs/AlGaAs superlattice. The form of the subband energy spectrum and wavefunctions is studied within subbands that exhibit a changeover between heavy and light hole character as a function of the superlattice wave vector and period; the results are compared with a simple position dependent effective mass theory.
author_names: Stuart Brand

Scott Monaghan

Paul P Szydlik
title: Calculations of electronic states in the valence band of (100) GaAs/AlGaAs superlattices
year: 1987

abstract: In the present study we investigate the effect of component interdiffusion across the interfaces on the electronic structure of a quantum well embedded in a short period superlattice. We calculate the energies of the bound states for an 18 monolayer (5 nm) thick GaAs quantum well embedded in an (AlAs)4/(GaAs)8 superlattice in comparison with two AlxGa1 xAs/GaAs (x 1 and 0.33) single quantum wells with the same thickness. The calculations are made within the framework of the envelope function approximation. The behaviour of the lowest electron and hole bound states is studied for values of the diffusion length from 0 to 4 monolayers. The contribution of the X point conduction band minima to the electronic structure is discussed. The calculated transition energies are shown to be in agreement with photoluminescence spectra of such structures. The presented approach can be used to assess the effect of the component intermixing on the electronic structure of various complex multilayered systems.
author_names: N Shtinkov

Vesselin Donchev

K G Germanova

Hristo Kolev
title: Electronic structure of quantum wells embedded in short period superlattices with graded interfaces
year: 2000

abstract: Much understanding of the electronic and optical properties of a semiconductor superlattice can be obtained by relating the superlattice electronic wave functions and band structure to those of the two bulk semiconductors from which it is constructed. In this paper, the relationship is studied within the framework of the empirical tight binding model, which is solved using the reduced Hamiltonian technique. The superlattice wave functions are described as linear combinations of bulk Bloch functions with complex wave vectors, twenty (including spin) for each of the two constituent materials. The bulk Bloch function composition of the superlattice wave function is studied as a function of layer thickness, alloy composition, and energy. The GaAs \mathrm{Ga}}_{1\mathrm{\ensuremath{ \mathrm{x}\mathrm{Al}}_{\mathrm{x}$As and InAs GaSb superlattices are examined in detail. Comparisons with simpler Kronig Penney and envelope function models are made. It is found that the lowest superlattice conduction band states are primarily derived from the expected bulk states with wave vectors near the center of the Brillouin zone, with a small admixture of zone edge components. The energies and general form of the wave functions are modified only slightly, except close to the interfaces. There, the admixture can significantly affect the interfacial boundary conditions beyond those employed by commonly used envelope function approximations. Valence band states are more complicated in that the superlattice periodic potential mixes the bulk heavy hole, light hole, and spin orbit split off bands, even at the superlattice Brillouin zone center. Crossover effects occur in which a given superlattice subband can have a varying proportion of light hole like or heavy hole like character depending on superlattice layer thickness. The dispersion of the subbands away from the zone center also causes the mixing of bands and results in modifications of the superlattice band structure as compared with band structures produced by simpler models.
title: Band mixing in semiconductor superlattices.
venue: Physical review. B, Condensed matter
year: 1985

abstract: Along with the growing interest in semiconductor superlattices, various theoretical schemes have been proposed to study the nature of the electronic states within these structures. The work presented here highlights a new method to investigate the electronic and optical properties of semiconductor superlattices. The backbone of the theory rests on a realistic description of the complex k band structure of the constituent semiconductors coupled with a suitable set of boundary conditions for the superlattice wave function. The bulk Bloch solutions, propagating and evanescent, in each semiconductor are described within a full zone k p Hamiltonian that provides an accurate description of the solutions up to the first Brillouin zone edge. An attractive feature of the present treatment is that the complex k bulk Bloch solutions of each constituent semiconductor are expanded on the same set of zone center basis functions. A new technique for constructing the k p Hamiltonian of each constituent semiconductor
author_names: Christian Mailhiot

T C Mcgill

Darryl L Smith
title: New approach to the k p theory of semiconductor superlattices
year: 1984

author_names: Lama Khalil

Evangelos Papalazarou

Marco Caputo

Niloufar Nilforoushan

Luca Perfetti

Amina Taleb-Ibrahimi

V Kandyba

Alexei Barinov

Quinn D Gibson

Robert J Cava

Marino Marsi
title: Electronic band structure for occupied and unoccupied states of the natural topological superlattice phase Sb2Te
year: 2017

abstract: A mismatch of atomic registries between single layer transition metal dichalcogenides (TMDs) in a two dimensional van der Waals heterostructure produces a moire superlattice with a periodic potential, which can be fine tuned by introducing a twist angle between the materials. This approach is promising both for controlling the interactions between the TMDs and for engineering their electronic band structures, yet direct observation of the changes to the electronic structure introduced with varying twist angle has so far been missing. Here, we probe heterobilayers comprised of singlelayer MoS2 and WS2 with twist angles of (2.0+ 0.5) (13.0+ 0.5) and (20.0+ 0.5) and investigate the differences in their electronic band structure using micro focused angle resolved photoemission spectroscopy. We find strong interlayer hybridization between MoS2 and WS2 electronic states at the G point of the Brillouin zone, leading to a transition from a direct bandgap in the single layer to an indirect gap in the heterostructure. Replicas of the hybridized states are observed at the centre of twist angle dependent moire mini Brillouin zones. We confirm that these replica features arise from the inherent moire potential by comparing our experimental observations with density functional theory calculations of the superlattice dispersion. Our direct visualization of these features underscores the potential of using twisted heterobilayer semiconductors to engineer hybrid electronic states and superlattices that alter the electronic and optical properties of 2D heterostructures.
author_names: Alfred J H Jones

Ryan Muzzio

Sahar Pakdel

Deepnarayan Biswas

Davide Curcio

Nicola Lanata

Philip Hofmann

Kathleen M McCreary

Berend T Jonker

Kenji Watanabe

Takashi Taniguchi

Simranjeet Singh

Roland J Koch

Chris Jozwiak

Eli Rotenberg

Aaron Bostwick

Jill A Miwa

Jyoti Katoch

Soren Ulstrup
title: Visualizing band structure hybridization and superlattice effects in twisted MoS$_2$/WS$_2$ heterobilayers
year: 2021

abstract: It is natural to characterize materials in transport junctions by their conductance length dependence, b. Theoretical estimations of b are made employing two primary theories: complex band structure and density functional theory (DFT) Landauer transport. It has previously been shown that the b value derived from total Landauer transmission can be related to the b value from the smallest |ki| complex band; however, it is an open question whether there is a deeper relationship between the two. Here we probe the details of the relationship between transmission and complex band structure, in this case individual eigenchannel transmissions and different complex bands. We present calculations of decay constants for the two most conductive states as determined by complex band structure and standard DFT Landauer transport calculations for one semi conductor and two molecular junctions. The molecular junctions show that both the length dependence of the total transmission and the individual transmission eigenvalues can be, almost always, found through the complex band structure. The complex band structure of the semi conducting material, however, does not predict the length dependence of the total transmission but only of the individual channels, at some k points, due to multiple channels contributing to transmission. We also observe instances of vertical bands, some of which are the smallest |ki| complex bands, that do not contribute to transport. By understanding the deeper relationship between complex bands and individual transmission eigenchannels, we can make a general statement about when the previously accepted wisdom linking transmission and complex band structure will fail, namely, when multiple channels contribute significantly to the transmission.
author_names: Anders Jensen

Mikkel Strange

S Smidstrup

Kurt Stokbro

Gemma C Solomon

Matthew G Reuter
title: Complex band structure and electronic transmission eigenchannels.
venue: The Journal of chemical physics
year: 2017

abstract: Nanostructured TiN(001) dot/MgO(001) 4 x 4 and 5 x 5 superlattices based on a repeated slab model have been investigated. The electronic states of TiN(001) dot/MgO(001) 4 x 4 and 5 x 5 superlattices were obtained by using the total energy pseudopotential method. The internal atomic coordinates in a unit cell were fully relaxed. We consider two types of TiN dot structures as rectangular and rectangular parallelepiped. They all correspond to semiconductor, although relaxed rectangular parallelepiped TiN(001) dot/MgO(001) 2 x 2 and 3 x 3 superlattices correspond to metallicity. A bandgap value of the rectangular TiN(001) dot/MgO(001) superlattice increases with increasing the size of the MgO substrate, although the difference in the band gap between 4 x 4 and 5 x 5 is small at approximately 0.01 eV. Their electronic properties depend on the shape of the TiN dot and the size of the MgO substrate. The bandgap value is corrected by using a generalized density functional theory.
author_names: Kazuaki Kobayashi

Hirokazu Takaki

Masato Shimono

Nobuhiko P Kobayashi

Kenji Hirose
title: Electronic band structure of TiN/MgO 4 x 4 and 5 x 5 nanostructures
venue: Japanese Journal of Applied Physics
year: 2019