By means of both a theory for pressure-induced shifts(PS) energy spectra and a theory for shifts of energy spectra due to electron-phonon interaction(EPIP.the pure electronic PS and the PS due to EPI of R1 line,R2 lin...By means of both a theory for pressure-induced shifts(PS) energy spectra and a theory for shifts of energy spectra due to electron-phonon interaction(EPIP.the pure electronic PS and the PS due to EPI of R1 line,R2 line,and U band of GSGG:Cr^3+ at 300 K have been calculated,respectively.The calcualted results are in good agreement with all the experimental data.Their physical origins have also been explained.It is found that the mixingdegree of t2^2(^3T1)e^4T2) and |t2^3 3E>base-wavefunctions in the wavefunctions of R1 level of GSGG:Cr^3+ at 300K is remarkable under normal pressure,and the mixing-degree rapidly decreases with increasing pressure.The change of the mixing-degree with pressure plays a key role not only for the pure electronic'PS of R1 line and R2 line but also the PS of R1 line and R2 line due to EPI.The pressure-dependent behaviors of the pure electronic 'PS of R1 line(or R2 line) and the PS of R1 line(or R2 line) due to EPI are quite different.It is the combined effect of them that gives rise to the total PS of R1 line(or R2 line).In the range of about 15 kar-45kbar,the mergence and /or order-reversal between t2^2(3T1)e^4T2 levels and t2^32T1 levels take place,which cause the fluctuation of the rate of PS for t2^2(3T1)e^4T2(or t2^32T1) with pressure,At 300K,both the temperature-dependent contribution to R1 line(Or R2 line or U band) from EPI and the temperature-independent one are important.展开更多
A new variational-ansatz of states of electrons and phonons was proposed on the basis of the Holstein model in strongly coupled electron-phonon systems for studying the influence of nonadiabatic phonon fluctuation,ari...A new variational-ansatz of states of electrons and phonons was proposed on the basis of the Holstein model in strongly coupled electron-phonon systems for studying the influence of nonadiabatic phonon fluctuation,arising from the motion and density fluctuation of electrons,on the properties of ground state,uncertainty relation,stability of polarons,charge density wave (CDW) and phonon staggered ordering. The new ansatz represents the correlation among the displacement and squeezing states of phonons and polaron’s state of electrons as well as the squeezing-antisqueezing effect. The correlation and squeezing-antisqueezing ef-fect result in the decrease of ground state energy,enhancement of stability of the systems,increase of binding energy of the polarons,weakening of the growing speed of polaron narrowing of the electron band,increase of the charge density wave order and suppression of the increased tendency of anomalous quantum fluctuation of the phonons in such a case,when compared with the uncorrelated case in the systems. The results obtained show that the ground state determined by the new state ansatz is most stable,thus the new ansatz describing the properties of the coupled electron phonon systems is very relevant and available,especially in strongly coupled and largely squeezed cases.展开更多
A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both thetemperature-independent contributions and the temperature-dependent ones of acoustic branches and optical bran...A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both thetemperature-independent contributions and the temperature-dependent ones of acoustic branches and optical brancheshave been derived. It is found that the temperature-independent contributions are very important, especially at lowtemperature. The total pressure-induced shift (PS) of a level (or spectral line or band) is the algebraic sum of its PSwithout EPI and its PS due to EPI. By means of both the theory for shifts of energy spectra due to EPI and the theoryfor PS of energy spectra, the total PS of R1 line of tunable laser crystal GSGG:Cr3+ at 70 K as well as the ones of itsR1 line, R2 line and U band at 300 K will be successfully calculated and explained in this series of papers.展开更多
With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunct...With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr3+ at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperatureindependent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of g||(R1) and g⊥(R1). It is found that the contribution from EPI to R1 line of GSGG:Cr3+ with taking into account spin-orbit interaction (Hso) and trigonal field (Vtrig) is much larger than the one with neglecting Hso and Vtrig, and accordingly it is essential for the calculation of the EPI effect to take first into account Hso and Vtrig. The admixture of base-wavefunctions, |t32 2E) and |t22(3T1)e4T2 ), the average energy separation △= E[t22 (3T1)e4T2]-E[t32 2E] and their variations with temperature have been calculated and discussed.展开更多
By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts ofenergy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of...By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts ofenergy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of R1 line ofGSGG:Cr3+ at 70 K have been calculated, respectively. Their physical origins have been revealed. It is found that theremarkable under the normal pressure, and the degree of the admixture rapidly decreases with increasing pressure. Thechange of the degree of the admixture with the pressure plays a key role for not only the pure electronic PS of R1 line butalso the PS ofR1 line due to EPL The detailed calculations and analyses show that the pressure-dependent behaviors ofthe pure electronic PS of R1 line and the PS of R1 line due to EPI are quite different. It is the combined effect of themthat gives rise to the total PS of R1 line, which has satisfactorily explained the experimental data (including a reversal ofPS of R1 line). In contributions to PS of R1 line due to EPI at 70 K, the temperature-independent contribution is muchlarger than the temperature-dependent contribution. The former results from the interaction between the zero-pointvibration of the lattice and localized electronic state.展开更多
文摘By means of both a theory for pressure-induced shifts(PS) energy spectra and a theory for shifts of energy spectra due to electron-phonon interaction(EPIP.the pure electronic PS and the PS due to EPI of R1 line,R2 line,and U band of GSGG:Cr^3+ at 300 K have been calculated,respectively.The calcualted results are in good agreement with all the experimental data.Their physical origins have also been explained.It is found that the mixingdegree of t2^2(^3T1)e^4T2) and |t2^3 3E>base-wavefunctions in the wavefunctions of R1 level of GSGG:Cr^3+ at 300K is remarkable under normal pressure,and the mixing-degree rapidly decreases with increasing pressure.The change of the mixing-degree with pressure plays a key role not only for the pure electronic'PS of R1 line and R2 line but also the PS of R1 line and R2 line due to EPI.The pressure-dependent behaviors of the pure electronic 'PS of R1 line(or R2 line) and the PS of R1 line(or R2 line) due to EPI are quite different.It is the combined effect of them that gives rise to the total PS of R1 line(or R2 line).In the range of about 15 kar-45kbar,the mergence and /or order-reversal between t2^2(3T1)e^4T2 levels and t2^32T1 levels take place,which cause the fluctuation of the rate of PS for t2^2(3T1)e^4T2(or t2^32T1) with pressure,At 300K,both the temperature-dependent contribution to R1 line(Or R2 line or U band) from EPI and the temperature-independent one are important.
基金the National "973" Project of China (Grant No. 2007CB6103)
文摘A new variational-ansatz of states of electrons and phonons was proposed on the basis of the Holstein model in strongly coupled electron-phonon systems for studying the influence of nonadiabatic phonon fluctuation,arising from the motion and density fluctuation of electrons,on the properties of ground state,uncertainty relation,stability of polarons,charge density wave (CDW) and phonon staggered ordering. The new ansatz represents the correlation among the displacement and squeezing states of phonons and polaron’s state of electrons as well as the squeezing-antisqueezing effect. The correlation and squeezing-antisqueezing ef-fect result in the decrease of ground state energy,enhancement of stability of the systems,increase of binding energy of the polarons,weakening of the growing speed of polaron narrowing of the electron band,increase of the charge density wave order and suppression of the increased tendency of anomalous quantum fluctuation of the phonons in such a case,when compared with the uncorrelated case in the systems. The results obtained show that the ground state determined by the new state ansatz is most stable,thus the new ansatz describing the properties of the coupled electron phonon systems is very relevant and available,especially in strongly coupled and largely squeezed cases.
文摘A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both thetemperature-independent contributions and the temperature-dependent ones of acoustic branches and optical brancheshave been derived. It is found that the temperature-independent contributions are very important, especially at lowtemperature. The total pressure-induced shift (PS) of a level (or spectral line or band) is the algebraic sum of its PSwithout EPI and its PS due to EPI. By means of both the theory for shifts of energy spectra due to EPI and the theoryfor PS of energy spectra, the total PS of R1 line of tunable laser crystal GSGG:Cr3+ at 70 K as well as the ones of itsR1 line, R2 line and U band at 300 K will be successfully calculated and explained in this series of papers.
文摘With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr3+ at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperatureindependent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of g||(R1) and g⊥(R1). It is found that the contribution from EPI to R1 line of GSGG:Cr3+ with taking into account spin-orbit interaction (Hso) and trigonal field (Vtrig) is much larger than the one with neglecting Hso and Vtrig, and accordingly it is essential for the calculation of the EPI effect to take first into account Hso and Vtrig. The admixture of base-wavefunctions, |t32 2E) and |t22(3T1)e4T2 ), the average energy separation △= E[t22 (3T1)e4T2]-E[t32 2E] and their variations with temperature have been calculated and discussed.
文摘By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts ofenergy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of R1 line ofGSGG:Cr3+ at 70 K have been calculated, respectively. Their physical origins have been revealed. It is found that theremarkable under the normal pressure, and the degree of the admixture rapidly decreases with increasing pressure. Thechange of the degree of the admixture with the pressure plays a key role for not only the pure electronic PS of R1 line butalso the PS ofR1 line due to EPL The detailed calculations and analyses show that the pressure-dependent behaviors ofthe pure electronic PS of R1 line and the PS of R1 line due to EPI are quite different. It is the combined effect of themthat gives rise to the total PS of R1 line, which has satisfactorily explained the experimental data (including a reversal ofPS of R1 line). In contributions to PS of R1 line due to EPI at 70 K, the temperature-independent contribution is muchlarger than the temperature-dependent contribution. The former results from the interaction between the zero-pointvibration of the lattice and localized electronic state.