This project aims at combining electron-phonon and electron correlation effects into a unified formalism allowing us to accurately compute electro/thermal properties of materials.

Correlated electron materials are building blocks fornext-generation multi-functional materials. Contrary to conventional metals orsemiconductors used in today’s MOSFE-Transistors, emergent properties of correlatedelectron systems can be designed from a large class of competing interactionsamong the charge, spin, orbital, and lattice degrees of freedom. Indeed, recentbreakthroughs in materials science such as high temperature superconductivityand colossal magnetoresistance are related to strong electron correlationeffects. Novel thermal properties in such materials are expected to come fromthe nontrivial interplay between electron-phonon coupling and electron-electroncorrelation.

Understandingthe physics of electron-phonon coupling (EPC) not only is of fundamentalimportance, but also has wide-ranging technological implications. Inconventional superconductors such as elemental metals, EPC is the dominantmechanism of superconductivity. While it is likely that superconductivity incuprates and pnictides, the so-called high-*T*csuperconductors, originates from strong electron correlation, there is evidencethat the EPC may still play an important role. On the other hand, the causeof superconductivity in a large third class of high-*T*csuperconductors remains unclear. It has been suggested that EPC enhancedby strong electron correlations might be the key to their superconductivitymechanism. The interplay between the EPC and electron correlation alsoplays a crucial role in the transport and thermoelectric properties ofcorrelated materials. In fact, the large Seebeck coefficients that have beenobserved in several transition-metal compounds cannot be explained using effectivesingle-particle DFT methods or even correlated Dynamical Mean-Field Theory(DMFT) methods. Perhaps the most prominent example is the colossal Seebeck coefficientof 50 mV/K observed in the correlated system FeSb2 [5], where evencorrelated DMFT calculations resulted in Seebeck values no more than1.2 mV/K. While some works have shown the importance of electron correlationsin understanding the origin of the huge thermopower in FeSb2,other researchers have suggested the phonon drag mechanism, a transportphenomenon due to a strong EPC. We believe that only a unifying approachthat treats EPC, electron correlation, and phonon transport consistently willshed light on this intriguing phenomenon.

### Desired outcomes

To incorporate the correlation effect into thelattice dynamics calculation, we will adopt the variational Gutzwiller method, whichhas been shown to capture intriguing correlation physics such asmetal-insulator transition. In particular, since first-principles phonondynamics calculation is a rather expensive calculation, the Gutzwiller methodoffers an efficient yet accurate approach for our purpose. In thisproposal, we will extend and apply our lattice dynamics method to theDFT+Gutzwiller calculation. Inparallel, we will develop codes to also extract electron-phonon couplingconstants (EPC) and use the latter to compute relaxation rates of electronswhich will be used in our electron Monte Carlo (MC) Boltzmann solver.

The ** goal at theend of this funding period** is to validate force and EPC calculationsfor a simple model Hamiltonian, which will be later changed to a realistic onewith more degrees of freedom in order to simulate a real material. Thiscalculation, will illustrate the effect of correlations on the electronic andphononic band structures and thermal and thermoelectric properties of a “toy”model, and will lead to a preliminary publication. We are then in a position todiscuss to what extent these properties are sensitive to correlation effects,and under what conditions one would expect to see notable changes inproperties. Namely, in the case of FeSb2, we will clarify theinterplay between EPC and correlations and shed light on the reason for such ahigh thermopower. This understanding will allow us a rational design of newmaterials with unprecedented thermoelectric properties, and make our case verystrong for obtaining further funding from NSF and DOE-BES to apply this approach to real materials.

### Student engagement

100% of the funding will be used to supportgraduate students. Two Graduate students will implement force calculation in the existing Gutzwillercodes according to the formalism which will be developed by the PIs (Chern &Esfarjani). One graduate student who has already startedlearning MC coding, will implement the full-band structure and correlatedscattering rates into the electron MC code (Zebarjadi) and compute electronic transportproperties.

Joint group meetingamong three groups will be held monthly to ensure timely interactions betweengraduate students and faculty members, where the graduate students will report their progress.

The PIs have complementary expertise in DFTcalculations (KE), correlated systems (GWC), and Monte Carlo Transport (MZ).Thus they enable the students to see the problem from different viewpoints and benefitfrom the multidisciplinary nature (as a collaborative work between physics, mechanicalengineering, electrical engineering and materials science and engineeringdepartments) of the work.