MUlogo Group of Carsten A. Ullrich
Department of Physics and Astronomy, University of Missouri-Columbia

 

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RESEARCH

The research in our group is in theoretical and computational condensed-matter physics. A major focus is on the charge and spin dynamics in semiconductors (bulk and nanostructures) in a variety of settings. We are particularly interested in exploring the intricacies of electronic many-body effects in collective excitations such as excitons, plasmons and spin waves.

Most of our work uses density-functional theory (DFT) for static and time-dependent systems. DFT is the most important first-principles method for calculating the electronic structure of materials, and its time-dependent version, TDDFT, is becoming increasingly popular to describe electronic excitations.

My group is pursuing the following research projects, which have been supported by grants from the National Science Foundation, the Department of Energy, and Research Coporporation::

1. Exciton binding energies in semiconductors and insulators

exciton             LiFLiF

Excitons in a periodic insulating crystal can be viewed as bound electron-hole pairs, whose average size can extend over many lattice constants. Calculating excitonic properties from first principles is usually done with many-body techniques such as GW + BSE (Bethe-Salpeter Equation). Our goal is to develop an alternative approach based on TDDFT. Over the past few years we have systematically explored various TDDFT approaches to obtain accurate exciton binding energies and optical spectra that compare well to experimental results.

Most recently, we performed a detailed comparative study of the family of so-called "long-range corrected" exchange-correlation kernels, see
Young-Moo Byun and C. A. Ullrich, Phys. Rev. B 95, 205136 (2017) . We proposed an empirical scaling method to produce accurate exciton binding energies for a variety of materials.

In another recent paper we showed that hybrid approaches such as screened exact exchange (SXX)  can be a promising (and cheaper) alternative to the BSE, see Zeng-hui Yang, Francesco Sottile, and C.A. Ullrich, Phys. Rev. B 92, 035202 (2015).

2. Visualization of charge-transfer excitations

PHM1PHM2

In electronic excitations, electrons move to different locations, leaving holes behind. To characterize an excitation, it is of great interest to know where electrons and holes are coming from and where they are going to; however, in complex molecular systems this is not always easy to figure out. We have developed a new visualization tool which allows a simple and intuitive way  to track the origins and destinations of electrons and holes: the particle-hole map (PHM).

The PHM can easily be implemented as a post-processing tool with standard electronic structure codes, using the output of a TDDFT calculation for a given electronic excitation. As shown in the pictures above, we obtain two-dimensional maps or contour plots that give a clear characterization of charge-transfer excitations (here for the C2H4 - C2F4 molecular complex).

This work was recently published in
Yonghui Li and C. A. Ullrich, J. Chem. Phys. 145, 164107 (2016) .

3. Spin waves in chiral electron gases: interplay of spin-orbit coupling and electronic many-body effects

spinwaves

The two-dimensional electron gas (2DEG) is a paradigm of an electronic many-body system. The physics of the 2DEG has been studied for decades, but new interesting effects continue to be discovered. We have studied 2DEGs confined in semiconductor quantum wells with Rashba and Dresselhaus spin-orbit coupling, and how the behavior of collective electronic modes (plasmons, spin waves is affected by this.

Most recently, we have focused on spin-wave excitations in paramagnetic 2DEGs in CdMnTe quantum wells, and we have found that the presence of spin-orbit coupling causes the spin waves to propagate as if they were in a moving, twisted reference frame. We have confirmed this in a joint experimental and theoretial study, see
F. Perez, F. Baboux, C. A. Ullrich, I. D'Amico, G. Vignale, G. Karczewski, and T. Wojtowicz, Phys. Rev. Lett. 117, 137204 (2016) .

As a follow-up study, we did a careful analysis of the dependence of the spin-wave dispersions on the direction of propagation. We found that our TDDFT calculations reproduce the angular modulation very well, see S. Karimi,  F. Baboux, F. Perez, C. A. Ullrich, G. Karczewski, and T. Wojtowicz, Phys. Rev. B 96, 045301 (2017).

modulation

4. Ensemble-DFT for excitation energies

TDDFT is not the only DFT-based method to calculate excitation energies. Going back to the work by Oliveira, Gross and Kohn in 1988, another formally exact approach is based on ensembles of excited states. However, at present the ensemble-DFT approach has not been very widely used, since it lacks the accuracy and convenience of TDDFT. But there has been a lot of activity in recent years in the field of ensemble-DFT for excited states, and much progress has been made.

beryllium
We have recently found a way to directly extract electronic excitation energies based on ensemble-DFT, see Zeng-hui Yang, Aurora Pribram-Jones, Kieron Burke, and C. A. Ullrich, Phys. Rev. Lett. 119, 033003 (2017). The approach is computationally cheap, and its accuracy is comparable to that of TDDFT. An additional great advantage is that it yields double excitations without any additional effort (in contrast with standard TDDFT), as shown here for the example of the beryllium atom, see the picture above. However, much work remains to be done: in particular, we need better exchange-correlation functionals for ensembles.