Theory of the temperature dependence of electronic band structures

Allen, Philip B.; Heine, Volker

doi:10.1088/0022-3719/9/12/013

Cited by 364 publications

(365 citation statements)

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“…The temperature dependence of E g in a semiconductor or insulator can be explained by the sum of two distinct mechanisms: thermal expansion of the lattice and the electron-phonon interaction. 23,24 In the case of CdTe, it is known that the lattice dilatation effect contributes more to the bandgap shift than the electron-phonon interaction above 100 K, while below 100 K the electron-phonon interaction is responsible for the energy shift. 23,25 The PL peak centered near 530 nm, which is thought to be caused by an interband transition, varied within a range of energies between the indirect and direct E g values (Fig.…”

Section: Resultsmentioning

confidence: 99%

Temperature dependence of the interband transition in a V2O5 film

et al. 2013

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The temperature dependence of the interband transition in an α-V2O5 film was investigated using absorption and photoluminescence spectral measurements at a temperature range of 10–300 K. Transmission measurements in the experimental temperature range indicate that the α-V2O5 film has two distinct interband transitions, implying indirect and direct transitions. This result was confirmed by spectroscopic ellipsometry. The blue shift of both the transitions in the α-V2O5 film with decreasing temperature was explained by a reduction in the lattice-dilatation effect and the electron-phonon interaction. The PL measurements in the experimental temperature range showed that the emission near 530 nm is due to the indirect transition in the α-V2O5 film

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Section: Resultsmentioning

confidence: 99%

Temperature dependence of the interband transition in a V2O5 film

et al. 2013

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“…These effects vary markedly depending on whether the temperature T is larger or smaller than the Fermi temperature T F (typically a few eV). At "cool" temperatures, where T is much smaller than T F , electrons are nearly degenerate, and Fermi factors and excitations such as phonons dominate the thermal behavior [1][2][3]. In contrast thermal occupations become nearly semi-classical and electronic excitations such as plasmons become important in the warm-dense-matter (WDM) regime, where T is of order T F or larger, and condensed matter is partially ionized.…”

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Finite Temperature Green’s Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter

Kas

Rehr

2017

Phys. Rev. Lett.

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We present a finite-temperature extension of the retarded cumulant Green's function for calculations of exited-state and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction W and improves excited state properties compared to the GW approximation of many-body perturbation theory. Results for the homogeneous electron gas are presented for a wide range of densities and temperatures, from cool to warm dense matter regime, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high T while the exchange-correlation energy becomes small. In addition, the spectral function broadens and damping increases with temperature, blurring the usual quasi-particle picture. Similarly Compton scattering exhibits substantial many-body corrections that persist at normal densities and intermediate T . Results for exchange-correlation energies and potentials are in good agreement with existing theories and finite-temperature DFT functionals. Finite temperature (FT) effects in electronic systems are both of fundamental interest and practical importance. These effects vary markedly depending on whether the temperature T is larger or smaller than the Fermi temperature T F (typically a few eV). At "cool" temperatures, where T is much smaller than T F , electrons are nearly degenerate, and Fermi factors and excitations such as phonons dominate the thermal behavior [1][2][3]. In contrast thermal occupations become nearly semi-classical and electronic excitations such as plasmons become important in the warm-dense-matter (WDM) regime, where T is of order T F or larger, and condensed matter is partially ionized. Recently there has been considerable interest in both experimental and theoretical investigations of WDM for applications ranging from laser-shocked systems and inertial confinement fusion to astrophysics [4,5]. Many of these studies focus on equilibrium thermodynamic properties, e.g., using the FT generalization of density functional theory (DFT) [6][7][8]. Although in principle, FT DFT is exact [9][10][11], practical applications require exchange-correlation functionals which must be approximated, e.g., by constrained fits [12] to theoretical electron gas calculations [8,[13][14][15][16][17]. However, these approaches have various limitations. First, many materials properties such as optical and x-ray spectra depend on quasi-particle or excited-state effects. For example, band-gaps depend on quasi-particle energies, and calculations of x-ray spectra [18] and Compton scattering require correlation corrections [19]. Although methods like quantum Monte-Carlo and the random phase approximation (RPA) can provide accurate correlation energies, they are not directly applicable to such excited state properties. Secondly, currently available exchangecorrelation functionals can exhibit unphysical behavior outside the range of validity of theoretical data [20]. On the other hand Green's function (GF) methods within...

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“…4(b)]. This redshift, which is analogous to the temperature-induced renormalization of the electronic band gap [13], can be expressed in the harmonic approximation as…”

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Phonon-Induced Optical Superlattice

et al. 2005

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We demonstrate the formation of a dynamic optical superlattice through the modulation of a semiconductor microcavity by stimulated acoustic phonons. The high coherent phonon population produces a folded optical dispersion relation with well-defined energy gaps and renormalized energy levels, which are accessed using reflection and diffraction experiments. DOI: 10.1103/PhysRevLett.94.126805 PACS numbers: 73.21.Cd, 42.65.Es, 42.70.Qs, 77.65.Dq The notion of a superlattice, a periodic stack of layers of different materials, was originally introduced as a way of tailoring the electronic band structure of semiconductors via quantum size effects [1]. The dispersion relation of elementary excitations in superlattices is characterized by minibands within a folded mini-Brillouin zone (MBZ) defined by the artificial periodicity and separated by minigaps corresponding to regions without propagating modes. The superlattice concept was later extended to phonons [2]. Although optical superlattices in the form of Bragg mirrors have been known for a long time, their two-and threedimensional counterparts, typically referred to as photonic crystals, are presently receiving considerable attention due to the ability to induce light localization and control spontaneous emission [3,4].Elementary excitations such as phonons, plasmons, and spin waves also create, when stimulated with a welldefined wave vector, a periodic modulation of the material's optical properties. In fact, this modulation provides a primary source of information about their energy dispersion when accessed using techniques such as Raman and Brillouin spectroscopy. An interesting question is whether an elementary excitation can create a dynamic optical superlattice with a folded dispersion and energy gaps. The interaction with photons, however, is usually very weak with induced energy shifts smaller than the characteristic width of the spectral lines. This interaction becomes enhanced for photon energies in resonance with the elementary excitation (resonant scattering) or by artificially increasing their population above the equilibrium (stimulated scattering). We point out that excitations of a bosonic nature are more appropriate for optical modulation with a high excitation density in order to avoid the broadening of the spectral features due to many-body effects [5]. The previous conditions may lead to the formation of new quasiparticles, as exemplified by the different forms of polaritons.The interaction with photons can be further enhanced in low-dimensional structures. Strong optical fields in semiconductor microcavities have been shown to increase the cross section for Raman scattering by thermal vibrations by several orders of magnitude [6]. In addition, Brillouin scattering efficiencies exceeding 40% have been reported in microcavities exposed to a high, nonthermal population of coherent acoustic modes [7]. A zone folded energy dispersion with minigaps has also been predicted for cavity polaritons modulated by coherent acoustic phonons [5]. To our knowl...

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Theory of the temperature dependence of electronic band structures

Cited by 364 publications

References 11 publications

Temperature dependence of the interband transition in a V2O5 film

Temperature dependence of the interband transition in a V2O5 film

Finite Temperature Green’s Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter

Phonon-Induced Optical Superlattice

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