Electric-field controlled nonlinear anomalous Nernst effect in two-dimensional time-reversal symmetric systems

TL;DR

This work shows that in 2D time-reversal symmetric crystals with high crystal symmetry, a dc electric field can lift symmetry constraints and enable a nonlinear anomalous Nernst effect (NANE) driven by Berry connection polarization (BCP) and field-modified nonequilibrium distributions. Using a Boltzmann-transport framework, the authors derive the second-harmonic NANE response to an alternating temperature gradient and decompose the field-induced NANCs into Berry-connection-polarization contributions and anomalous-velocity–modified distribution contributions, with symmetry dictating which terms survive. In 2D systems with both $ ext{T}$ and $ ext{P}$ symmetries, the NDF-AV part vanishes, leaving BCP as the sole origin of the field-induced NANE, a result concretely illustrated for monolayer graphene with $C_{6v}$ where the second-harmonic Nernst signal follows $j^{ ext{nl},2oldsymbol{ extomega}}_{ ext{N}}=oldsymbol{ ext{ξ}}^{ ext{BCP}}_{yxxy}( ilde{oldsymbol{ abla}T})^{2}E$ and is maximized when $oldsymbol{E}^{ ext{dc}}ot ilde{oldsymbol{ abla}T}$. The study provides both qualitative and quantitative predictions, including angular dependences $oldsymbol{ ext{ξ}}_{ ext{N}}( heta,oldsymbol{oldsymbol{ extvarphi}})$ and order-of-magnitude estimates for graphene, offering a practical route to detect and control NANE in high-symmetry 2D materials via electric-field engineering.

Abstract

It's established that the nonlinear anomalous Nernst effect (NANE), originating from Berry curvature near the Fermi energy, is symmetry-permitted only when a single mirror symmetry exists in the transport plane of two-dimensional (2D) materials. Here, we show that an applied direct electric field can lift this symmetry constraint, enabling an electric-field-induced NANE emerge in time-reversal symmetric 2D systems with higher crystallographic symmetries. This electric-field-induced NANE arises from both Berry connection polarization, rooted in the electric-field-corrected Berry curvature, and the anomalous-velocity-modified nonequilibrium Fermi distribution function. Additionally, we propose an alternating temperature gradient as a driving force instead of the conventional steady one, ensuring experimental detection of NANE via second-harmonic measurement techniques. The behaviour of electric-field-induced NANE in the monolayer graphene has been theoretically and systematically investigated.

Figures (3)

• Figure 1: Schematic of the measurement setup for electric-field-induced NANE, showing the complex amplitude vector $\tilde{\boldsymbol{\nabla}T}$ of the alternating temperature gradient $\boldsymbol{\nabla} T^{\omega}$ and direct electric field $\boldsymbol{E}^\text{dc}$ in the same plane. $\boldsymbol{\nabla} T^{\omega}$ is generated by passing an alternating current $I^{\omega/2}_\text{heater}$ with frequency $\omega/2$ to a microheater electrode. $\theta$ ($\varphi$) represents the polar angle of $\tilde{\boldsymbol{\nabla}T}$ ($\boldsymbol{E}^\text{dc}$) with respect to $x$-axis, which is taken as a crystal axis (e.g. the zigzag direction in graphene).
• Figure 2: Schematic of the Berry connection polarization elements $\tilde{\mathcal{G}}_{xx}$ [(a)], $\tilde{\mathcal{G}}_{xy}$ [(b)], $\tilde{\mathcal{G}}_{yx}$ [(c)] and $\tilde{\mathcal{G}}_{yy}$ [(d)] of the conduction band for the $K$ valley of monolayer graphene. Momenta are measured in units of the inverse of the lattice constant $\alpha$ and $\tilde{\mathcal{G}}_{ab}$ is measured in units of $e\alpha^{2}/t_{0}$
• Figure 3: (a) The dependence of $\xi_{\text{N}}(\theta,\varphi)$ on the relative orientation (i.e., $\varphi-\theta$) of dc electric field $\boldsymbol{E}^{\mathrm{dc}}$ with respective to temperature gradient. (b) $\xi^\text{BCP}_{yxxy}$ versus the Fermi energy $E_{f}$ for different temperature $T$. (c) $\xi^\text{BCP}_{yxxy}$ vs $T$ for different $E_{f}$ . (d) $\xi^\text{BCP}_{yxxy}$ as a function of $E_{f}$ and $T$. The relative angle $\varphi-\theta=\pi/2$ is fixed in (b)-(d). The typical scale $\xi_{0}$ is defined as $\xi_{0}=2\tau e^{2}k_{B}^{2}\alpha^{2}/[(1+i\omega\tau)\hbar^{2}t_{0}]$.