# Analytical expression of negative differential thermal resistance in a macroscopic heterojunction

## TL;DR

This paper derives analytical formulas for heat flux and differential thermal resistance in a macroscopic heterojunction, revealing conditions for negative differential thermal resistance crucial for thermal device applications.

## Contribution

It provides the first precise analytical expressions for heat flux and differential thermal resistance in heterojunctions, elucidating the NDTR effect.

## Key findings

- Analytical expressions for heat flux and resistance derived.
- Conditions for negative differential thermal resistance identified.
- Potential applications in thermal transistors and memory devices.

## Abstract

Heat flux ($J$) generally increases with temperature difference in a material. A differential coefficient of $J$ against temperature ($T$) is called differential thermal conductance ($k$), and an inverse of $k$ is differential thermal resistance ($r$). Although $k$ and $r$ are generally positive, they can be negative in a macroscopic heterojunction with positive $T$-dependent interfacial thermal resistance (ITR). The negative differential thermal resistance (NDTR) effect is an important effect that can realize thermal transistor, thermal memory, and thermal logic gate. In this paper, we examine analytical expressions of $J$, $k$, $r$, and other related quantities as a function of parameters related to thermal conductivity ($\kappa$) and ITR in a macroscopic heterojunction to precisely describe the NDTR effect.