1
Dipartimento di Fisica e Astronomia, Universit´a di Padova, via Marzolo 8, I-35131 Padova, Italy
2
ETSF and Dipartimento di Fisica, Universit´a di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Rome, Italy
3
Roma Tre University, Department of Engineering, Via della Vasca Navale 79, 00146 Rome, Italy
❆❜str❛❝t✳ In this report we account for the studies we carried out in the last year using the ENEA-CRESCO facilities. Our studies were mainly devoted on the first-principle determination of ground and excited state properties of 2D systems (surfaces and monolayers). In particular here we report our results concerning the simulation of the transient absorption of monolayer MoS2, of the low-coverage
structure of tartaric acid on Cu(110), and of the electronic and optical properties of 2D nitrides.
1
Transient absorption in monolayer MoS
2Transition metal dichalcogenides monolayers recently raised great interest for potential optoelectronics and spintronics applications [11] and for the fundamental study of the behaviour of matter at low dimensionalities. Transient absorption (TA) spectroscopy monitors the change over time of the optical properties of a material after it has been driven out of equilibrium by a laser pump. It thus provides a wealth of information on excitation and carrier relaxation processes. The equilibrium absorption spectrum of monolayer MoS2, one of the best characterized material of this class, is well known [4] and
studied. It is characterized by two, strongly bound, spin-orbit-split, excitonic transitions, namely the A and B excitons, at 2.1 eV and 2.2 eV, and a loosely bound exciton, namely the C exciton, at 2.6 eV, see Fig. 1. Interstingly, it was found that, regardless of the excitation energy, i.e. either pumping at the energy of the A, B or C exciton, the same features appear in the MoS2 experimental TA spectra.
In all cases simultaneous bleaching of the three excitonic structures and, correspondingly, the presence of photoinduced absorption at lower energies [6] are found.
1.1
Theoretical approach and codes
To simulate TA spectroscopy we employ a novel first-principle theoretical approach capable to describe both the excitonic character of MoS2 excited states and the coupling with the laser pump through
the combination of density-functional and non equilibrium Green’s function theories [13, 5, 3]. The calculation method involves basically two steps: (1) the determination of the non-equilibrium population of the electronic bands due to the laser pump; (2) the calculation of the perturbed response function. In the presence of an external time-dependent potential the evolution of the electronic system can be described by the Kadanoff-Baym equations (KBE) [15]. In particular, in our approach, we follow the evolution of the lesser Green’s function G<by propagating its equation of motion. From G<’s diagonal
elements we obtain the non-equilibrium population of the single-particle electronic states [2]. From the knowledge of the non-equilibrium population, in the adiabatic approximation and assuming we are in the weak pump field regime [5], we re-compute the optical absorption spectra, either keeping fixed or recomputing the poles of the response functions. For the determination of the ground state properties of our system, i.e its geometry, total energy, single-particle Kohn-Sham orbitals, etc..., we employed density-functional theory (DFT) [10, 12] by using the electronic structure code pw.x of the Quantum Espresso suite [8] which makes use of plane-wave basis set and pseudopotentials [16]. The codes that was used for the determination of equilibrium and non equilibrium excited state properties is the Yambo suite [1]. Both codes are open source, released under the GPL licence, make use of LAPACK and BLAS libraries, and present a hybrid MPI and OpenMP parallelism. The Yambo code makes also use of the NETCDF libraries which were installed locally by one of the users. All run were performed on the CRESCO 4 cluster, using between 64 and 1200 cores (mainly 128 and 256).
1.2
Results
The knowledge of the time-dependent off-diagonal elements of G<allows to compute the time-dependent
polarization function P (t). If the external electric field E(t) is delta-like, then, by Fourier transforming P (t), we obtain the optical susceptibility; this is the so called time-dependent Bethe-Salpeter (TDBSE) approach [2].
Figure 1: TDBSE absorption spectrum (dashed-red) compared to standard BSE.
In Fig. 1 we see that indeed by using the TDBSE approach the BSE spectrum is recovered. This is an important step in order to check if the scheme is working properly and in order to determine the excitation energies at which the simulated system responds.
We then simulate the ultrafast laser pump by using a sinusoidal time-dependent external potential convoluted with a Gaussian function, centered at the frequency of the excitonic peaks. In the left panel of Fig. 2 we show the generated carrier density upon pumping at the A, B, C exciton energies and off-resonance close (+0.1 eV) to the C peak. As expected, the carrier density is proportional to the intensity of the optical susceptibility at the pumping frequency, and this is clearly shown in the right panel of Fig. 2 where the carrier density is renormalized by the optical susceptibility value.
Once the excited carrier population is known, TA spectrum can be calculated at different levels of sophistication. At low pumping, i.e. low carrier densities regime, the excitation energies of the system (the poles of the response function) could in principle be considered fixed at their equilibrium values.
Figure 2: Carrier population
Figure 3: Mo2TA spectra including only the effect of Pauli blocking. Left panel: pump A; center panel:
pump B; right panel: pump C.
In this way we describe and isolate the, so called, Pauli Blocking effect (PBE). Within the PBE the TA features are ascribed to a different availability of electronic states that quenches possible excitations thus changing the way the systems absorbs light. In the left panel of Fig. 3 we show the TA spectra at the three pumping frequencies including the PBE. We see that there is a bleaching (negative signal) only at the pumping energy, and no photoinduced absorption (positive signal) appears.
Figure 4: Mo2 TA spectra including the variation of excitation energies. Left panel: pump A; center
panel: pump B; right panel: pump C.
We next take into account the possibility that also the excitation energies are affected by the excited state carrier population. We found that the excitation energies change is mainly affected by the change in the electronic screening. The increased screening capability of the system reduces the binding energy of the excitons and, at the same time, it reduces the quasi-particle gap. These two effects only partially compensate each other and the absorption of the system changes. When we include these effects we obtain the results shown in the right panel of Fig. 4. In this case we recover a stronger agreement with experiments: a bleaching of all the peaks appears, and also photoinduced absorption is present.