Session P07: Electronic Structure of Semiconductors: Theory and Spectra

Use and Misuse of Optical Dispersion Formulas for the IR Index of Silicon

Interference measurements of the IR refractive index of silicon conflict with prism measurements by an order of magnitude more than their precision. This arises from erroneous use of classical dispersion formulas for polar optical glass to analyze measurement on homopolar silicon. We show that many of these dispersion formulas, often considered empirical, follow from the Kramers-Kronig (K-K) relations:1) Binomial expansion of the K-K integrand gives the index as a series of absorption-spectrum moments leading to the Cauchy, Briot and Conrady formulas; 2) Expansion of the absorption spectrum in delta-functions yields the Sellmeier, Drude-Ketteler and Hartmann expressions. In these formulas the contribution from electronic polarization is explicit, but phonon terms are often obscure. In two specific cases for silicon, confusion of electronic and phonon excitation energies in the Li-Sellmeier formula and misunderstanding of the Cauchy and Briot expansions in the Baumeister-Edwards analysis distorted the original data. The latter are now lost precluding reanalysis. Hence, we recommend use of prism data until new interference measurements are made.   

Luminescent Emission from 1s, 2s, 3s and 4s Excitons of Monolayer WSe2 in High Magnetic Fields

The strong Coulomb interaction in 2D-TMDCs provides an outstanding platform for investigating the Rydberg exciton physics. In this study, we observed for the first time excitonic luminescence of up to the 4s excited state in ultrahigh quality BN/1L-WSe₂/BN heterostructures in a strong out-of-plane magnetic field. By analyzing the diamagnetic shift of the ground and excited exciton states, the radii of the 2s and 3s excitons are found to be 3.4 and 6 times larger comparing with the 1s exciton. Moreover, the Zeeman splitting measurement shows the monotonic increase of g factor from -4.4 to -4.8 for 1s to 3s, indicating existence of nontrivial differences of magnetic moment and effective mass between different Rydberg exciton states. Complementary to PLE and absorption measurements in literature, our results provide an alternative method to optically investigate tightly-bound electron-hole pairs and strong Coulomb interaction in 2D excitonic systems.
  

Structural Phase Transformations in Photoexcited Transition Metal Chalcogenide Monolayers Studied Using Combined Pump-Probe Experiments and Non-Adiabatic Molecular Dynamics Simulations

Optical control of structural phases in two dimensional chalcogenides is a promising route for precise functionalization of these materials for electronic, optical and catalytic applications. In this study, we use ab initio time dependent density functional theory simulations supported by ultrafast electron diffraction measurements to understand the electronic structure of electronically-excited MoTe₂ crystals as well as the resulting atomic dynamics responsible for transformation between the H and T’ crystal structures. Specifically, we identify a nesting of the excited-state Fermi surface that leads to softening of phonon modes at the Brillouin zone boundary. This modulation of the ionic potential energy surface exposes a low activation-energy-barrier pathway for the H-T’ phase transformation in this family of materials. This example of excitation-driven phase transformation has important advantages over other reported phase transformation mechanisms that rely on thermal and chemical driving forces or electron-doping.   

First-Principles Investigation of Nonlinear Optical Properties of 2D Materials

Understanding the interaction between 2D materials and strong electromagnetic field is important for the development of novel devices for optical spectroscopy and imaging, sensors and information technology. Here we present our recent studies of nolinear optical responses in 2D materials using our in-house developed nonlinear optical response codes based on first-principles density-functional theory. We will show that nanomaterials especially 2D materials exhibit large second and third order nonlinear optical responses, including second harmonic generation, shift current, circular photogalvanic current, and third harmonic generation. Their physical origin is closely related to topological quantity of intraband and interband Berry connection as well as electron/hole group velocity. The present results demonstrate the great potential of low-dimensional materials for nonlinear optical device and sensing applications. References: 1. Giant Optical Second Harmonic Generation in Two-Dimensional Multiferroics. Nano Letters 17, 5027-5034 (2017). 2. Two-dimensional multiferroics in monolayer group IV monochalcogenides. 2D Materials 4, 015042 (2017). 3. Third Harmonic Generation in 2D Materials. in preparation (2017).   

Inversion symmetry in methylammonium lead iodided single crystals probed by second harmonic optical anisotropy

Single crystals of the methylammonium lead iodide perovskite (CH₃NH₃PbI₃) are promising candidates for solar cells due to their long (tens of microns) photo-carrier diffusion lengths.^[1] It has been proposed that such long diffusion lengths are a consequence of bulk static Rashba fields resulting from an absence of bulk inversion symmetry at room temperature.^[2] Here we directly probe the point group symmetries of CH₃NH₃PbI₃ using high sensitivity optical second harmonic rotational anisotropy measurements. We show that contrary to previous proposals, the bulk crystallographic structure of tetragonal CH₃NH₃PbI₃ at room temperature is centrosymmetric with a space group of I4/mcm. These results are consistent with our density functional theory calculations, which establish the absence of a large bulk Rashba effect and show that incorrect structural relaxations are responsible for the previously predicted large Rashba effect.

[1] S. D. Stranks et al. Science 342, 341-344 (2013).
[2] Y. Rakita et al. Proc. Natl. Ac. Sci. USA 114, 5504-5512 (2017).   

Thermal plasmon Frequency for tunable extrinsic Dirac structures

Analytic expressions have been obtained for the chemical potential of a variety of extrinsic (doped) gapped Dirac materials. We also created a reliable piecewise-linear model for the density-of-states in molybdenum disulfide, which demonstrates good agreement with previously obtained numerical results. A decrease of chemical potential with increasing temperature due to enhanced thermal populations of an upper subband in silicene was also shown. In MoS$_2$, the chemical potential is found to cross a zero-energy point at sufficiently high temperatures because of the broken symmetry with respect to electron and hole states.
  

Optical properties of a highly-excited exciton-polariton condensate

We theoretically investigate nonequilibrium effects on optical properties of a highly-excited exciton-polariton condensate. In this system, it has been theoretically predicted that a negative energy branch of the Bogoliubov dispersion (the so-called “ghost branch”) appear in photoluminescence, as a direct consequence of the quantum depletion of the Bose-condensate. However, in most experiments, the ghost branch is absent. In this work, by extending the combined generalized random phase approximation with the Hartree-Fock-Bogoliubov theory to the nonequilibrium Keldysh formalism, we show that nonequilibrium effects strongly suppress the visibility of the ghost branch. Our results are in qualitative agreement with experiments, where we see a blue shift of the condensate emission, appearance of the diffusive Goldstone mode, as well as the suppression of dispersive profile of the branch in the photoluminescence. Our results indicate that quantum depletion is strongly suppressed by the driven-dissipative nature of a nonequilibrium exciton-polariton condensate.   

Exciton fission in monolayer transition metal dichalcogenide semiconductors

When electron-hole pairs are excited in a semiconductor, it is a priori not clear if subsequent relaxation leads to a gas of bound excitons or to an interacting plasma of unbound electrons and holes. Usually, the exciton phase is associated with low temperatures. In atomically thin transition metal dichalcogenide semiconductors, excitons are particularly important even at room temperature due to strong Coulomb interaction and a large exciton density of states.
Using state-of-the-art many-body theory, we show that the thermodynamic fission-fusion balance of excitons and electron-hole plasma can be efficiently tuned via the dielectric environment as well as charge carrier doping. We observe entropy ionization of excitons at low excitation densities and a Mott transition to a fully ionized plasma at high densities between 3x10¹² cm^-2 and 1x10¹³ cm^-2 depending on experimental parameters.
We propose the observation of these effects by studying exciton satellites in photoemission and tunneling spectroscopy, which are sensitive to the single-particle spectral functions, thus containing information about the degree of exciton fission and the extent of exciton wave functions in reciprocal space.   

Effective Bond-Orbital Model of III-Nitride Wurtzite Structures Based on Modified Interaction Parameters of Zinc Blende Structures

A simple theoretical method for deducing the effective bond-orbital model (EBOM) of III-nitride wurtzite semiconductors from the zinc blende structure is presented. In the EBOM for a zinc blende structure one s-like and three p-like bond orbitals are assumed. The set of EBOM parameters are obtained by fitting the band energies at high symmetry points in reciprocal space with the first-principle calculation. It is shown that the band structures of the wurtzite structure can be produced by using the EBOM parameters derived for the zinc blende structure defined in the rotated frame by adding correction to three-center overlap integrals resulting from the rotation of atomic positions, which transfers the lattice symmetry from Td to C3v. Details of the parametrization of the EBOM Hamiltonian suitable for bulk III-nitride wurtzite semiconductors are presented. The band structures of bulk GaN, AlN, and InN with a zinc blende and wurtzite structure calculated in the same set of EBOM parameters with correction of three-center overlap integrals are presented and compared with first-principle calculations.   

A first-principles view of pyroelectricity

The pyroelectric effect is the response of the spontaneous polarization with respect to the temperature fluctuation. It impacts a wide range of applications. Pyroelectricity arises from the primary effect (at constant external strain) and the secondary effect (thermal expansion alters piezoelectric polarization). Here a computational route from first principles is developed. Calculations are made for the pyroelectric coefficients of wurtzite GaN and ZnO. An excellent agreement with experimental data is found. In these bulk materials, we reveal the crucial role of the primary pyroelectricity arising from the electronic redistribution induced by atomic thermal vibrations. For 2D materials, we demonstrate out-of-plane pyroelectricity in the recently synthesized Janus MoSSe monolayer and in-plane pyroelectricity in the theoretically stable group-IV monochalcogenide GeS monolayer. For GeS monolayer, it is notable that the secondary pyroelectricity is significant, and hence applying strains can dramatically tune its intrinsic pyroelectricity.   

Developing Structure-Property Relations in Metal-Insulator Transition Materials

Materials which undergo a metal-insulator transition- a rapid change in resistivity upon temperature, pressure, or composition- have potential for the next generation of electronic switching devices. The underlying mechanisms which drive metal-insulator transitions are of interest both fundamentally in the field of condensed-matter physics and practically for the design of high-performance electronic materials. We develop a link between crystal structure and macroscopic electronic properties to realize new metal-insulator transition materials. We start by examining the AB₄Q₈ defect spinel system, where A is Al, Ga, Ge, B is Ti, V, Nb, Mo, Ta, and Q is S/Se. These materials, with molecular-orbital-like clusters, start at a cubic F-43m structure at room temperature and then distort to R3m or Imm2 at low temperatures.¹ Detailed analysis of the local structure, through pair-distribution function analysis, and the average structure, through high-resolution diffraction, can provide insights into subtle links between structure and electronic behavior.
Reference:
1) D. Johrendt, Z. Anorg. Allg. Chem. 624 (1998) 952   

Electronic Raman scattering due to spin-orbit split-off band in tensilely-strained Ge

Electronic Raman scattering is an inelastic two-photon process involving electronic transitions rather than elementary excitations like phonons. Ge exhibits ERS spectra dominated by the light-hole valence subband when excited by the 1064-nm light. Here we attempt to observe the strain-induced development of the ERS due to the spin-orbit split-off (SO) valence subband, which is invisible otherwise. To this end, a sub-ns pulse laser was used, which helped discriminate the relevant transition as a pronounced spectral peak with negative circular polarization, as opposed to the cw or fs excitations. A similar negative-helicity peak was confirmed for the ERS due to the light-hole subband as expected. We therefore infer that the otherwise inexplicable negative helicity near the direct band-edge in unstrained Ge is most likely due to the ERS involving SO. Based on these, an argument is invoked which takes account of the electron-electron scattering as the microscopic mechanism of an enhanced ERS in the strained multivalleyed Ge where the intervalley scattering of electrons in the conduction band plays a pivotal role. The possibility of a near-edge Raman gain will be discussed in light of the absorption characteristics.   

Cross-over from Trion-hole Complex to Exciton Polaron for n-doped Two-dimensional Semiconductors

We study the excitation spectra of n-doped two-dimensional semiconductors due to the absorption of a photon. Because of the interaction between the photocreated exciton and the Fermi sea electrons, exotic new states can emerge. We show that an exciton-single-pair complex can exist by only keeping single electron-hole pair excitations in the Fermi sea. This 4-body complex behaves like a Fermi-sea hole weakly bound to a trion for k_F a_x << 1, where k_F is the Fermi wave-vector and a_x the exciton Bohr radius. The oscillator strength of photo-absorption associated with this trion-hole bound state increases as k_F increases. As k_F continues to increase, the feature of trion-hole bound state becomes unrecognizable, while the exciton state dressed by scattered electron-hole pairs (which can be interpreted as an exciton-polaron) becomes more pronounced. The evolution of the excitation spectra of these 4-particle coupled states (one exciton and one Fermi-sea electron-hole pair) as k_F increases reveals the cross-over from trion-hole resonance to exciton-polaron resonance, which is associated with the internal reconfiguration of the 4-body complex in the presence of the Fermi sea.