# DEPARTMENT OF PHYSICS DISSERTATION: Erik Kountz

**Ph.D. Candidate: Erik Kountz**

**Research Advisor: Aharon Kapitulnik**

**Date: **June 10, 2024 **Time:** 2 PM PST

**Location: **McCullough 335

**Zoom Link: ** https://stanford.zoom.us/j/92873610842

**Zoom Password: Email **physicsstudentservices [at] stanford.edu (**physicsstudentservices[at]stanford[dot]edu**)** for password. **

**Title: **Thermal Diffusivity and Conductivity in CDW Materials

**Abstract: **Photo-thermal microscopes can be used to take high resolution thermal diffusivity by measuring phase delay in local-temperature through measurements of optical differential reflectivity. Within kinetic theory, if specific heat is measured as well, thermal conductivity can be calculated as well using the Einstein relation kappa=cD. However, this so-called “thermal Einstein relation” can be directly tested if the thermal conductivity is measured independently.

Within kinetic theory, one can derive relations electrical and thermal conductivity including Fourier’s law of thermal conduction and Ohm’s law. These laws then give us Einstein relations for electrical and thermal transport. These Einstein relations connect the electrical (thermal) conductivity to the product of the electrical (thermal) diffusivity and the susceptibility (specific heat). Within kinetic theory, the ratio of the thermal and electrical conductivities gives the Weidemann-Franz law and shows how much of the total thermal conductivity is carried by electrons with the remainder carried by other excitations such as phonons. By independently measuring the thermal and electrical properties of materials with strong electron-phonon coupling, we can test where these relations break and where the assumptions of kinetic theory fail.

I present thermal diffusivity, direct thermal conductivity, specific heat, and resistivity data on two materials: CsV3Sb5, and ErTe3. Both these materials have a layered quasi-2D structure and have one or more charge density wave (CDW) transitions. CsV3Sb5 has a first order structural phase transition and commensurate 2D CDW at 94K. ErTe3 has two perpendicular second order incommensurate stripe ordered CDWs which onset at 265K and 160K.

For my measurements of CsV3Sb5, I will show a strong anomaly in thermal diffusivity where within two degrees of the CDW transition temperature, the diffusivity plummets by 90%. Additionally, there is a 70% increase in specific heat and no anomaly in directly measured thermal conductivity. I will explain this violation of the Einstein relation in the vicinity of the CDW transition as a result of a two-phase regime where strong resemblance between the specific heat and the resistivity derivative below the transition may point to a concurrent emergence of a secondary electronic order parameter.

For my measurements of ErTe3, I will show below the primary CDW transition temperature, there is a strong anomaly in the diffusivity along both axes of the planes while the conductivity and specific heat change less and more broadly. I will further discuss the relation between thermal and charge transport, and the applicability of Einstein relation kappa=cD and the Wiedemann-Franz law near the CDW transitions.

I will conclude by summarizing where the thermal Einstein relation and Weidemann-Franz law break down and the resulting assumptions of kinetic theory fail.