Despite the difficulties of developing accurate and efficient TDDFT approaches
for excitons, much progress has been made over the past few years. The path
forward is most likely to bring TDDFT and traditional many-body theory even
closer together, the outcome being xc kernels that are functionals of occupied as
well as unoccupied bands, similar in spirit to the nanoquanta and bootstrap kernels.
Hybrid xc kernels are another promising way forward; however, this means
abandoning pure TDDFT and admitting nonlocal exchange. This has been an
extremely successful strategy for finite systems: indeed, standard hybrid functionals
are widely used for excitons in polymers and other nanoscale systems
[138–141]. For periodic solids, the standard hybrid functionals may have to be
suitably modified to describe excitonic properties; work along these lines is in
progress [107].
Acknowledgments This work was supported by NSF grant DMR-1408904. We thank Lucia
Reining and Francesco Sottile for many helpful discussions. C.U. thanks the ETSF-Palaiseau
group for its hospitality and the Ecole Polytechnique for its support during an extended visit
in 2014.
References
1. Ullrich CA (2012) Time-dependent density-functional theory: concepts and applications.
Oxford University Press, Oxford
2. Marques MAL, Maitra NT, Nogueira FMS, Gross EKU, Rubio A (2012) Fundamentals of
time-dependent density functional theory. Springer, Berlin
3. Ullrich CA, Yang ZH (2014) Brazil J Phys 44:154
4. Hedin L (1965) Phys Rev 139:A796
5. Aryasetiawan F, Gunnarsson O (1998) Rep Prog Phys 61:237
6. Sham LS, Rice TM (1966) Phys Rev 144:708
7. Hanke W, Sham L (1979) Phys Rev Lett 43:387
8. Hanke W, Sham LS (1980) Phys Rev B 21:4656
9. Strinati G (1982) Phys Rev Lett 49:1519
10. Strinati G (1984) Phys Rev B 29:5718
11. Strinati G (1988) Riv Nuovo Cimento 11:1
12. Rohlfing M, Louie SG (1998) Phys Rev Lett 81:2312
13. Rohlfing M, Louie S (2000) Phys Rev B 62:4927
14. Onida G, Reining L, Rubio A (2002) Rev Mod Phys 74:601
15. Botti S, Schindlmayr A, Del Sole R, Reining L (2007) Rep Prog Phys 70:357
16. Turkowski V, Ullrich CA (2008) Phys Rev B 77:075204
17. Turkowski V, Leonardo A, Ullrich CA (2009) Phys Rev B 79:233201
18. Yang ZH, Li Y, Ullrich CA (2012) J Chem Phys 137:014513
19. Yang ZH, Ullrich CA (2013) Phys Rev B 87:195204
20. Yu P, Cardona M (2010) Fundamentals of semiconductors. Springer, Berlin
21. Liang WY (1970) Phys Educ 5:226
22. Knox RS (1963) Theory of excitons. Academic, New York
23. Frenkel J (1931) Phys Rev 37:17; 1276
24. Peierls R (1932) Ann Phys (Leipzig) 13:905
25. Davydov AS (1948) Zh Eksperim i Teor Fiz 18:210
26. Wannier GH (1937) Phys Rev 52:191
214
C.A. Ullrich and Z.-h. Yang
for excitons, much progress has been made over the past few years. The path
forward is most likely to bring TDDFT and traditional many-body theory even
closer together, the outcome being xc kernels that are functionals of occupied as
well as unoccupied bands, similar in spirit to the nanoquanta and bootstrap kernels.
Hybrid xc kernels are another promising way forward; however, this means
abandoning pure TDDFT and admitting nonlocal exchange. This has been an
extremely successful strategy for finite systems: indeed, standard hybrid functionals
are widely used for excitons in polymers and other nanoscale systems
[138–141]. For periodic solids, the standard hybrid functionals may have to be
suitably modified to describe excitonic properties; work along these lines is in
progress [107].
Acknowledgments This work was supported by NSF grant DMR-1408904. We thank Lucia
Reining and Francesco Sottile for many helpful discussions. C.U. thanks the ETSF-Palaiseau
group for its hospitality and the Ecole Polytechnique for its support during an extended visit
in 2014.
References
1. Ullrich CA (2012) Time-dependent density-functional theory: concepts and applications.
Oxford University Press, Oxford
2. Marques MAL, Maitra NT, Nogueira FMS, Gross EKU, Rubio A (2012) Fundamentals of
time-dependent density functional theory. Springer, Berlin
3. Ullrich CA, Yang ZH (2014) Brazil J Phys 44:154
4. Hedin L (1965) Phys Rev 139:A796
5. Aryasetiawan F, Gunnarsson O (1998) Rep Prog Phys 61:237
6. Sham LS, Rice TM (1966) Phys Rev 144:708
7. Hanke W, Sham L (1979) Phys Rev Lett 43:387
8. Hanke W, Sham LS (1980) Phys Rev B 21:4656
9. Strinati G (1982) Phys Rev Lett 49:1519
10. Strinati G (1984) Phys Rev B 29:5718
11. Strinati G (1988) Riv Nuovo Cimento 11:1
12. Rohlfing M, Louie SG (1998) Phys Rev Lett 81:2312
13. Rohlfing M, Louie S (2000) Phys Rev B 62:4927
14. Onida G, Reining L, Rubio A (2002) Rev Mod Phys 74:601
15. Botti S, Schindlmayr A, Del Sole R, Reining L (2007) Rep Prog Phys 70:357
16. Turkowski V, Ullrich CA (2008) Phys Rev B 77:075204
17. Turkowski V, Leonardo A, Ullrich CA (2009) Phys Rev B 79:233201
18. Yang ZH, Li Y, Ullrich CA (2012) J Chem Phys 137:014513
19. Yang ZH, Ullrich CA (2013) Phys Rev B 87:195204
20. Yu P, Cardona M (2010) Fundamentals of semiconductors. Springer, Berlin
21. Liang WY (1970) Phys Educ 5:226
22. Knox RS (1963) Theory of excitons. Academic, New York
23. Frenkel J (1931) Phys Rev 37:17; 1276
24. Peierls R (1932) Ann Phys (Leipzig) 13:905
25. Davydov AS (1948) Zh Eksperim i Teor Fiz 18:210
26. Wannier GH (1937) Phys Rev 52:191
214
C.A. Ullrich and Z.-h. Yang