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Pj Image processing Rm Data presentation and visualization: algorithms and implementation Tp Computer modeling and simulation Wr Computer interfaces Df Sensors chemical, optical, electrical, movement, gas, etc. Hj Display and recording equipment, oscilloscopes, TV cameras, etc. Mp Transducers Tw Servo and control equipment; robots Vx Hygrometers; hygrometry Cm Micromechanical devices and systems Fq Vibration isolation Lw Balance systems, tensile machines, etc. Pz Instruments for strain, force, and torque Dt Thermometers Fw Calorimeters Hy Furnaces; heaters Ka High-temperature instrumentation; pyrometers Mc Cryogenics; refrigerators, low-temperature detectors, and other low-temperature equipment Pe Heat engines; heat pumps; heat pipes Bx Degasification, residual gas Cy Vacuum pumps Dz Vacuum gauges Hd Vacuum testing methods; leak detectors Kf Vacuum chambers, auxiliary apparatus, and materials Ek Circuits and circuit components Hp Electrical noise and shielding equipment Ls Electrometers Qx Signal processing electronics Db Generation of magnetic fields; magnets Ge Magnetometers for magnetic field measurements Jg Magnetometers for susceptibility, magnetic moment, and magnetization measurements Nk Magnetic shielding in instruments Hm Infrared, submillimeter wave, microwave, and radiowave sources Kp Bolometers; infrared, submillimeter wave, microwave, and radiowave receivers and detectors Pt Submillimeter wave, microwave and radiowave spectrometers; magnetic resonance spectrometers, auxiliary equipment, and techniques Ty Infrared spectrometers, auxiliary equipment, and techniques Dq Photometers, radiometers, and colorimeters Fs Polarimeters and ellipsometers Hv Refractometers and reflectometers Ly Interferometers Pb Conventional optical microscopes Rd Visible and ultraviolet spectrometers Vg Fiber-optic instruments Gx Atomic and molecular beam sources and detectors Ka Charged-particle beam sources and detectors Cz Scanning tunneling microscopes Fc Near-field scanning optical microscopes Lh Atomic force microscopes Pk Magnetic force microscopes Sp Friction force microscopes Jy Diffractometers Qe Synchrotron radiation instrumentation Tt X-ray microscopes Cd Axiomatic approach Ef Lagrangian and Hamiltonian approach Gh Renormalization Hi Renormalization group evolution of parameters Jj Asymptotic problems and properties Kk Field theories in dimensions other than four Lm Nonlinear or nonlocal theories and models Nx Noncommutative field theory St Bound and unstable states; Bethe-Salpeter equations Wx Finite-temperature field theory Bt General properties of perturbation theory Ex Spontaneous breaking of gauge symmetries Ha Lattice gauge theory Kc Classical and semiclassical techniques Me Strong-coupling expansions Pg Expansions for large numbers of components e.

Tk Other nonperturbative techniques Wx Topologically massive gauge theories Yc Chern-Simons gauge theory Db Properties of perturbation theory Hf Conformal field theory, algebraic structures Mj Compactification and four-dimensional models Pm Noncritical string theory Sq Nonperturbative techniques; string field theory Uv D branes Wx String and brane phenomenology Yb M theory Er Charge conjugation, parity, time reversal, and other discrete symmetries Fs Global symmetries e.

Mod-01 Lec-01 Principles of Condensed Matter Physics

Hv Flavor symmetries Ly Other internal and higher symmetries Na Nonlinear and dynamical symmetries spectrum-generating symmetries Pb Supersymmetry Qc Spontaneous and radiative symmetry breaking Rd Chiral symmetries Dw General theory of currents Ex Formal properties of current algebras Ha Partially conserved axial-vector currents Bq Analytic properties of S matrix Ds Exact S matrices Fv Dispersion relations Hx Sum rules Jy Regge formalism Cr Kinematical properties helicity and invariant amplitudes, kinematic singularities, etc.

Et Partial-wave analysis Fv Approximations eikonal approximation, variational principles, etc. Gw Multichannel scattering Jy Many-body scattering and Faddeev equation La Multiple scattering Dm Unified theories and models of strong and electroweak interactions Kt Unification of couplings; mass relations Ff Quark and lepton masses and mixing Ji Applications of electroweak models to specific processes Lk Electroweak radiative corrections Mm Neutral currents Ds Specific calculations Fv Experimental tests Aw General properties of QCD dynamics, confinement, etc.

Bx Perturbative calculations Cy Summation of perturbation theory Gc Lattice QCD calculations Lg Other nonperturbative calculations Mh Quark-gluon plasma Qk Experimental tests Ba Bag model Dc Skyrmions Fe Chiral Lagrangians Hg Heavy quark effective theory Jh Nonrelativistic quark model Ki Relativistic quark model Pn Potential models St Factorization Ee Statistical models Vv Vector-meson dominance Yx Hadron mass models and calculations Cn Extensions of electroweak gauge sector Fr Extensions of electroweak Higgs sector Jv Supersymmetric models Nz Technicolor models Rc Composite models Eb Decays of K mesons Fc Decays of charmed mesons He Decays of bottom mesons Jf Decays of other mesons Es Decays of K mesons Ft Decays of charmed mesons Hw Decays of bottom mesons Jx Decays of other mesons Ce Leptonic, semileptonic, and radiative decays Eg Hadronic decays Bv Decays of muons Dx Decays of taus Hb Decays of heavy neutrinos Be Decays of W bosons Dg Decays of Z bosons Dk Electromagnetic mass differences Em Electric and magnetic moments Gp Electromagnetic form factors Hq Electromagnetic decays Ks Electromagnetic corrections to strong- and weak-interaction processes Fz Elastic and Compton scattering Hb Total and inclusive cross sections including deep-inelastic processes Le Meson production Rj Baryon production Lm Processes in other lepton-lepton interactions Cs Nucleon-nucleon interactions Ev Hyperon-nucleon interactions Gx Pion-baryon interactions Jz Kaon-baryon interactions Lb Meson-meson interactions Dz Elastic scattering Fb Inelastic scattering: two-particle final states Hd Inelastic scattering: many-particle final states Lg Total cross sections Ni Inclusive production with identified hadrons Qk Inclusive production with identified leptons, photons, or other nonhadronic particles Rm Limits on production of particles Tp Cosmic-ray interactions Ce Production Fh Fragmentation into hadrons Dh Protons and neutrons Jn Hyperons Pt Exotic baryons Aq pi, K , and eta mesons Ev Other strange mesons Pq Heavy quarkonia Rt Exotic mesons Cd Electrons including positrons Ef Muons Fg Taus Hi Other charged heavy leptons Lm Ordinary neutrinos Pq Neutrino mass and mixing St Non-standard-model neutrinos, right-handed neutrinos, etc.

Bt Light quarks Dw Charmed quarks Fy Bottom quarks Ha Top quarks Jk Other quarks e. Bh Photons Dj Gluons Fm W bosons Hp Z bosons Kv Gravitons Pw Other gauge bosons Bn Standard-model Higgs bosons Cp Non-standard-model Higgs bosons Da Supersymmetric Higgs bosons Ec Other neutral Higgs bosons Fd Other charged Higgs bosons Hv Magnetic monopoles Ly Supersymmetric partners of known particles Mz Axions and other Nambu-Goldstone bosons Majorons, familons, etc.

Nb Neutralinos and charginos Pq R-hadrons Rt Kaluza-Klein excitations Sv Leptoquarks Tt Technicolor Va Axions and other Nambu-Goldstone bosons Majorons, familons, etc. Dr Binding energies and masses Ft Charge distribution Gv Nucleon distributions and halo features Hw Spin, parity, and isobaric spin Jx Spectroscopic factors and asymptotic normalization coefficients Ky Electromagnetic moments Ma Level density Pc Single-particle levels and strength functions Re Collective levels Sf Coulomb energies, analogue states Tg Lifetimes, widths Cb Nuclear forces in vacuum Fe Forces in hadronic systems and effective interactions Bc Two-nucleon system Ff Three-nucleon forces Cs Shell model De Ab initio methods Ev Collective models Fw Models based on group theory Gx Cluster models Ka Monte Carlo models Cd Asymmetric matter, neutron matter Ef Symmetry energy Jk Mesons in nuclear matter Mn Equations of state of nuclear matter Qr Quark matter En Angular distribution and correlation measurements Gq Multipole mixing ratios Js Multipole matrix elements Nx Internal conversion and extranuclear effects including Auger electrons and internal bremsstrahlung Ra Internal pair production Bw Weak-interaction and lepton Hc Relation with nuclear matrix elements and nuclear structure Cn Many-body theory Eq Coupled-channel and distorted-wave models Ht Optical and diffraction models Jv Relativistic models Lx Monte Carlo simulations including hadron and parton cascades and string breaking models Nz Hydrodynamic models Pa Thermal and statistical models Cz Giant resonances Gd Other resonances Dr Statistical compound-nucleus reactions Gv Statistical multistep direct reactions Ky Fluctuation phenomena Lz Chaos in nuclear systems Dc Photon absorption and scattering Lj Photoproduction reactions Bf Elastic electron scattering Dh Inelastic electron scattering to specific states Fj Inelastic electron scattering to continuum Hm Positron-induced reactions Mr Muon-induced reactions including the EMC effect Pt Neutrino-induced reactions Rw Electroproduction reactions Cm Elastic proton scattering Dn Elastic neutron scattering Ep Inelastic proton scattering Fq Inelastic neutron scattering Hs Transfer reactions Kv Charge-exchange reactions Lw Radiative capture Ny Resonance reactions Sc Spallation reactions De Elastic and inelastic scattering Hi Transfer reactions Kk Charge-exchange reactions Ci Elastic and inelastic scattering Hp Transfer reactions Kr Charge-exchange reactions Bx Elastic scattering Dz Interaction and reaction cross sections Gc Breakup and momentum distributions Je Transfer reactions Lg Charge-exchange reactions Pj Fusion reactions Tv Radiative capture Bc Elastic and quasielastic scattering De Coulomb excitation Ef Resonances Gh Compound nucleus Jj Fusion and fusion-fission reactions Lm Strongly damped collisions Mn Projectile and target fragmentation Pq Multifragment emission and correlations Ag Global features in relativistic heavy ion collisions Bh Hard scattering in relativistic heavy ion collisions Cj Photon, lepton, and heavy quark production in relativistic heavy ion collisions Dw Particle and resonance production Gz Particle correlations and fluctuations Ld Collective flow Nq Quark deconfinement, quark-gluon plasma production, and phase transitions Dj Pion elastic scattering Ek Pion inelastic scattering Gn Pion charge-exchange reactions Hp Pion-induced reactions Ls Pion inclusive scattering and absorption Nv Kaon-induced reactions Pw Hyperon-induced reactions Ca Spontaneous fission Ec Neutron-induced fission Ge Charged-particle-induced fission Jg Photofission Cd Stellar hydrogen burning Fj Stellar helium burning Kn s-process Np Nucleosynthesis in late stellar evolution Qr Quasistatistical processes Ca Explosive burning in accreting binary systems novae, x-ray bursts Ef Explosive burning in supernovae shock fronts Hj r-process Jk Weak interaction and neutrino induced processes, galactic radioactivity Dd Neutron star core Gj Neutron star crust Kp Equations of state of neutron-star matter Cz Neutron scattering Fc Neutron absorption Gd Neutron transport: diffusion and moderation Ka Thermal neutron cross sections Pr Neutron imaging; neutron tomography Ak Theory, design, and computerized simulation Bm Fuel elements, preparation, reloading, and reprocessing Fr Reactor coolants, reactor cooling, and heat recovery Kw Radioactive wastes, waste disposal My Reactor control systems Pa Moderators Qb Structural and shielding materials Rc Instrumentation Te Protection systems, safety, radiation monitoring, accidents, and dismantling Vx Fuel cycles Dr Research reactors Ft Fast and breeder reactors Hw Power and production reactors Ky Propulsion reactors Ma Auxiliary generators Av Theory, design, and computerized simulation Cx Fueling, heating and ignition Fa Materials Lf Components and instrumentation Nh Safety Ba Electrostatic accelerators Dh Storage rings Ej Linear accelerators Fj Betatrons Hm Cyclotrons Lq Synchrotrons Bx Electron sources Dz Neutron sources Lg Ion sources: polarized Ni Ion sources: positive and negative Pj Polarized and other targets Rm Sources of radioactive nuclei Ac Beam injection and extraction Bd Beam dynamics; collective effects and instabilities Eg Beam handling; beam transport Fh Beam characteristics Hj Polarized beams Aj Charged-particle spectrometers: electric and magnetic Dn Electron spectroscopy Ep Charged-particle spectroscopy Hs Neutron spectroscopy Lw Nuclear orientation devices Db Fast radioactive beam techniques Gj Reaccelerated radioactive beams Cs Gas-filled counters: ionization chambers, proportional, and avalanche counters Gx Tracking and position-sensitive detectors Ka Cherenkov detectors Mc Scintillation detectors Rg Nuclear emulsions Vj Calorimeters Wk Solid-state detectors Ca Data acquisition and sorting Fj Data analysis Ar Ab initio calculations Dv Coupled-cluster theory Ew Density-functional theory Fx Finite-difference schemes Gy Semiclassical methods Hz Group theory Ja Hyperspherical methods Kb Path-integral methods Lc Quasiparticle methods Md Perturbation theory Ne Self-consistent-field methods Pf Variational techniques Qg Molecular dynamics and other numerical methods Rh Valence bond calculations Eb Electron correlation calculations for atoms and ions: ground state Jf Electron correlation calculations for atoms and ions: excited states Nj Electron correlation calculations for diatomic molecules Qm Electron correlation calculations for polyatomic molecules Gs Hyperfine interactions and isotope effects Jv Relativistic and quantum electrodynamic effects in atoms and molecules Bc Potential energy surfaces for ground electronic states Df Potential energy surfaces for excited electronic states Gh Surface crossings, non-adiabatic couplings Dk Environmental and solvent effects Hq Time-dependent phenomena: excitation and relaxation processes, and reaction rates Ks Molecular solids Bi Atomic masses, mass spectra, abundances, and isotopes Dk Electric and magnetic moments, polarizabilities Ee Magnetic bound states, magnetic trapping of Rydberg states Fn Fine and hyperfine structure Hq Ionization potentials, electron affinities Bv Radio-frequency, microwave, and infrared spectra Dx Magnetic resonance spectra Jc Visible and ultraviolet spectra Rj X-ray spectra Cs Oscillator strengths, lifetimes, transition moments Fw Absolute and relative intensities Jz Line shapes, widths, and shifts Aa Inner-shell excitation and ionization Bx Level crossing and optical pumping Cy Atomic scattering, cross sections, and form factors; Compton scattering Dz Autoionization Ee Rydberg states Fb Photoionization of atoms and ions Gc Photodetachment of atomic negative ions Hd Auger effect Lg Mechanical effects of light on atoms, molecules, and ions Pj Optical cooling of atoms; trapping Qk Coherent control of atomic interactions with photons Rm Multiphoton ionization and excitation to highly excited states Wr Other multiphoton processes Xx Level crossing and optical pumping Ys Weak-interaction effects in atoms Zb Autoionization Bh General molecular conformation and symmetry; stereochemistry Dj Interatomic distances and angles Fm Bond strengths, dissociation energies Hp Barrier heights internal rotation, inversion, rotational isomerism, conformational dynamics Kr Electric and magnetic moments and derivatives , polarizability, and magnetic susceptibility Mt Rotation, vibration, and vibration-rotation constants Pw Fine and hyperfine structure Ry Ionization potentials, electron affinities, molecular core binding energy Ta Mass spectra Vb Correlation times in molecular dynamics J- Ultrafast spectroscopy Bx Radio-frequency and microwave spectra Ea Infrared spectra Fb Raman and Rayleigh spectra including optical scattering Kf Visible spectra Lg Ultraviolet spectra Ni Vacuum ultraviolet spectra Rm X-ray spectra Sn Rotational analysis Tp Vibrational analysis Vq Vibration-rotation analysis Wr Vibronic, rovibronic, and rotation-electron-spin interactions Xx Spectra induced by strong-field or attosecond laser irradiation Dq Fluorescence and phosphorescence spectra Hv Radiationless transitions, quenching Ad Optical activity, optical rotation; circular dichroism Be Zeeman and Stark effects Fi Other magnetooptical and electrooptical effects Cv Ultraviolet and vacuum ultraviolet photoelectron spectra Fy X-ray photoelectron spectra Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors Fd Absolute and relative line and band intensities Jg Line and band widths, shapes, and shifts Be Level crossing and optical pumping Eh Autoionization, photoionization, and photodetachment Gj Diffuse spectra; predissociation, photodissociation Ps Optical cooling of molecules; trapping Rv Multiphoton ionization and excitation to highly excited states e.

Wz Other multiphoton processes Cf Interatomic potentials and forces Gj Intermolecular and atom-molecule potentials and forces Mq Potential energy surfaces for collisions Bw Energy loss and stopping power Cx Elastic; ultracold collisions Dy Interactions of atoms and molecules with surfaces; photon and electron emission; neutralization of ions Ez Rotational and vibrational energy transfer Fa Electronic excitation and ionization of atoms including beam-foil excitation and ionization Gb Electronic excitation and ionization of molecules Lf Chemical reactions Pi State-to-state scattering analyses Rk Laser-modified scattering and reactions Bm Elastic scattering Dp Atomic excitation and ionization Gs Molecular excitation and ionization Ht Dissociation and dissociative attachment Kw Electron-ion scattering; excitation and ionization Lx Recombination, attachment, and positronium formation My Fundamental electron inelastic processes in weakly ionized gases Nz Spin dependence of cross sections; polarized beam experiments Pa Coherence and correlation Qb Laser-modified scattering This expression covers actually all the energy levels n where the particles might be and spin value of interacting particles.

Our calculations are very close to results found in literature Since our model exclude any other environmental effects such as substrate or crystal structure, we found a little bit lower value for an exciton binding energy. The experimental measurements of an exciton binding energy are based on the photo-excitation of an electron from a valance to a conduction band leaving a hole behind.

While the interaction between an electron and a hole is totally attractive, the screening effect allows an exciton to be created. Since we only use the masses of the electron and the hole in our calculations, the calculated value for exciton energy 0. Moreover, we presume that the differences between exciton binding energies in the literature even for the same samples- WS 2 14 , 15 stem from surrounding environment such as substrate or crystal structure.

Moreover, we think that the origin of the differences in experimental results of exciton binding energy is due to screening effect depending on the substrate or the crystal structure.

Excitation Energy Transfer Processes in Condensed Matter: Theory and Applications / Edition 1

Therefore, experimental measurements include this screening energy. Another interesting result of our calculations is that the interaction energy of 2-fermions possesses imaginary part. In this work, we found a general definition of interaction energy for 2-interacting fermions. For solution of this equation, we separated center of mass and relative coordinates by using explicit form of the equation.

Then, we obtained 1 st order coupled radial differential equation set.

Supplementary files

Since the masses of an electron and a hole are very small m 1 and m 2 , we neglected M 1 2 and M 2 2 values in our equations. The solution of 2-interacting fermions in our model indicates that one can obtain general definition for an interaction energy including quantum numbers. We apply our model to an exciton and found its binding energy which is very close to results found in literature.

All authors equally contributed to preparation of the manuscript. National Center for Biotechnology Information , U. Sci Rep. Published online Jun Author information Article notes Copyright and License information Disclaimer. Yusuf Sucu, Email: rt. Corresponding author.

Exact solution of an exciton energy for a monolayer medium

Received Oct 19; Accepted Jun 5. Subject terms: Quantum optics, Theoretical physics. Introduction Since its invention of monolayer form 1 , graphene has attracted noticeable interest due to its extraordinary optical 2 , electrical 3 and structural 4 properties apart from its bulk form of graphite especially. Solution for a Coulomb Interaction Since the exciton is composed of an electron and hole, the interaction between them can be written in terms of Coulomb potential.

Table 1 Interaction energies for an exciton. Open in a separate window. Discussion Our calculations are very close to results found in literature Conclusion In this work, we found a general definition of interaction energy for 2-interacting fermions. Author Contributions A.

Competing Interests The authors declare no competing interests. References 1. The rise of graphene. Graphene photonics and optoelectronics. The electronic properties of graphene. Singh V, et al. Graphene based materials: Past, present and future. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Atomically thin MoS 2 : A new direct-gap semiconductor. Mak KF, Shan J.


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Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Novoselov K, et al. Two-dimensional atomic crystals. The Natl. The United States Am. Measurement of high exciton binding energy in the monolayer transition-metal dichalcogenides WS 2 and WSe 2. Solid State Commun. Singh, J. Theory of Excitons , 1— Nozik AJ, et al.

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Semiconductor quantum dots and quantum dot arrays and applications of multiple exciton generation to third-generation photovoltaic solar cells. Zhao W-W, et al. Exciton-plasmon interactions between cds quantum dots and ag nanoparticles in photoelectrochemical system and its biosensing application. Using dark states for exciton storage in transition-metal dichalcogenides. Physics-Condensed Matter.

Ye Z, et al. Probing excitonic dark states in single-layer tungsten disulphide. Chernikov A, et al. Exciton binding energy and nonhydrogenic rydberg series in monolayer WS 2. Ramasubramaniam A.

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Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Quasiparticle band structures and optical properties of strained monolayer MoS 2 and WS 2. Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Excitons and trions in monolayer transition metal dichalcogenides: A comparative study between the multiband model and the quadratic single-band model.

Excitons, trions, and biexcitons in transition-metal dichalcogenides: Magnetic-field dependence.