**Speakers:** Dr Valerio Olevano (Institut Néel, Grenoble, France) & Dr Paolo. E. Trevisanutto (NUS)

**Host:** Prof Vitor M. Pereira

**Programme:** Session 1 30 Mar (10:00 – 11:30)

Session 2 31 Mar (10:00 – 11:30)

Session 3 03 Apr (14:00 – 15:30)

Session 4 04 Apr (10:00 – 11:30)

Synopsis

The workshop consists of a cycle of 4 seminars on methods beyond density-functional theory (DFT) ab initio theories to calculate excitations and spectroscopy. DFT [1] is to be considered today as the standard model of condensed matter theory, and in the last 50 years revealed a very successful approach [2] to calculate ab initio ground-state properties (atomic structures, elastic constants, etc.).

In the first seminar, a critical review of DFT will be presented, showing the successes but insisting in particular to its limits, namely the possibility for DFT to access excitations, excited state properties and spectroscopy.

In the second seminar, we will introduce time-dependent density-functional theory (TDDFT) [3], an extension of DFT able to address excited-state properties and spectroscopy like optical absorption, energy-loss spectra (EELS), etc. TDDFT is an in principle exact theory to calculate neutral excitations. However, like in DFT, the exchange-correlation functional, a fundamental ingredient of the theory, is unknown. One must resort to approximations and, unlike DFT, the local-density approximation (LDA) has limited validity, in particular on optical absorption spectra. We will introduce the fundamentals of TDDFT and discuss the limits of standard approximations with the help of examples on prototypical systems (bulk silicon, graphite, graphene, etc.), also presenting recent developments [4].

In the third seminar, we will introduce the ab initio many-body perturbation theory (MBPT) relying on the Green function (instead than the density like in DFT) as fundamental degree of freedom. MBPT is an in principle exact framework to calculate both ground and excited states, both neutral (like TDDFT) but also charged excitations. We will focus in particular on the GW approximation of the self-energy, showing its performances in the calculation of band gaps, band plots, ARPES spectral functions, also in prototypical systems.

Also within the framework of MBPT, in the 4th seminar we will talk on the Bethe-Salpeter equation (BSE) approach to calculate optical spectra and neutral excitations, in particular excitons. The BSE is an equation that allows to directly calculate the two-particle Green function, whose poles are the neutral excitations of a system. With respect to TDDFT, BSE provides access also to, e.g., exciton wavefunctions. We will show examples of calculations of excitations and spectra on bulk solids (silicon, etc.) and isoltated systems (helium atom, etc.) and discuss the limits of the approximations usually done on the kernel of the BSE.

References

[1] P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn, L. J. Sham, ibid 140, A1133 (1965).

[2] S. Redner, Physics Today 58, 49 (June 2005).

[3] W. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984); E. K. U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985).

[4] V. Olevano, M. Palummo, G. Onida and R. Del Sole, Phys. Rev. B 60, 14224 (1999); L. Reining, V. Olevano, A. Rubio, and G. Onida, Phys. Rev. Lett. 88, 066404 (2002); F. Sottile, M. Marsili, V. Olevano, and L. Reining, Phys. Rev. B 76, 161103(R) (2007); P. E. Trevisanutto, L. A. Constantin, A. Terentjevs, V. Olevano and F. Della Sala, Phys. Rev. B 87, 205143 (2013).

**About the Speakers: **Valerio Olevano is research director since 2012 at the CNRS (French national research council) where he also obtained a permanent position in 2000. He earned in 1993 his Laurea in physics at the University of Rome "La Sapienza" (computational subnuclear physics, lattice QCD) and his PhD in 1999 at the University of Rome "Tor Vergata" (computational ab initio condensed matter theory, DFT and beyond). He also got an European grant for acquiring expertise in XPS/UPS photoemission and research staff working in developments of the ab initio Bethe-Salpeter equation to calculate optical spectra in solids. His present research lines insist on developments and applications of ab initio many-body theory within the GW approximation and beyond, as well as methods based on the Bethe-Salpeter equation.

Valerio Olevano is a developer of the ABINIT first-principles code framework, and the main developer of DP (a linear response time-dependent DFT code, www.dp-code.org) and EXC (an exciton code for the dielectric and optical properties based on the solution of the Bethe-Salpeter equation, www.bethe-salpeter.org).

Paolo E. Trevisanutto is a senior research fellow in the Centre for Advanced 2D materials & Graphene research at NUS, which he joined in 2014. His current research interests are concerned with the development and applications of ab initio Many Body Perturbation Theory (MBPT) and Time Dependent Density Functional Theory (TD-DFT) methods in two dimension materials.

He obtained his Ph.D. in Physics at University College London in 2008 under the supervision of Prof. A.L. Shluger. From 2007 to 2014, he was a postdoctoral researcher in several European Institutes connected to the European Theoretical Spectroscopy Facility network (ETSF) such as CNRS (France), Max Planck Institut (Germany) and, CNR (Italy).