Linear thermal noise induced by Berry curvature dipole in a four-terminal system

TL;DR

The paper addresses how Berry curvature dipole (BCD) geometry shapes linear thermal noise in a four-terminal Hall device. It develops a gauge-invariant, current-conserving NEGF framework for linear noise in multi-terminal transport and connects terminal-resolved noise to direction-resolved bulk noise, revealing symmetry-imposed selection rules. The results show that auto-correlations scale as $2 k_B T$ when the driving field is perpendicular to the BCD and vanish when parallel, while cross-correlations scale as $k_B T$, with pronounced band-edge peaks. Dephasing reduces noise at higher temperatures, indicating an optimal low-temperature regime for observing BCD-induced linear thermal noise.

Abstract

In this work, we numerically investigate linear thermal noise in a four-terminal system with a finite Berry curvature dipole (BCD) using the nonequilibrium Green's function formalism. By comparing with the semiclassical results for bulk systems, we establish a one-to-one correspondence between terminal-resolved linear noise in multi-terminal systems and direction-resolved noise in bulk transport. Specifically, the auto-correlation function scales as $2 k_B T$ when the driving field is perpendicular to the BCD and vanishes when they are parallel, whereas the cross-correlation scales as $k_B T$. Both the auto- and cross-correlation functions exhibit pronounced peaks near the band edges, consistent with BCD-induced features. In addition, the linear thermal noise increases approximately linearly with $T$ at low temperatures and is suppressed by dephasing effect at high temperatures. Our work bridges semiclassical bulk theory and quantum multi-terminal theory for linear thermal noise, highlighting the symmetry(geometry)-selection rule in quantum transport.

Figures (5)

• Figure 1: Schematic of a two-dimensional(2D) four-terminal Hall setup for measuring quantum noises. The voltage profile ${\cal{V}}=(V_1,V_2,V_3,V_4)$ describes the bias voltages applied to each terminal. (a) In setup I, ${\cal{V}}=(0,0,V/2,-V/2)$, corresponding to a driving electric field along the $y$ direction. (b) In setup II, ${\cal{V}}=(V/2,-V/2,0,0)$, corresponding to a driving field along the $x$ direction. The four-terminal system is modeled by the tight-binding Hamiltonian in Eq. (\ref{['Ham2']}). Here $\mathcal{M}_x$ denotes the mirror symmetry in the $x$ direction, and $\mathcal{D}_x$ is the pseudovector representing the Berry curvature dipole. $S_{11}$ and $S_{33}$ are the auto-correlation function of the current in Terminal-1 and Terminal-3, respectively. $S_{13}$ and $S_{31}$ are the cross-correlation between currents in Terminal-1 and Terminal-3.
• Figure 2: Band structures of the tight-binding Hamiltonian in Eq. (\ref{['Ham2']}) along the $k_x$ direction in (a) and along the $k_y$ direction in (b). $p_1$ and $p_2$ label the first and second conduction bands in $k_x$, respectively.
• Figure 3: Linear thermal noises as a function of the Fermi energy at $T=10$$\text{K}$. Panel (a) corresponds to setup I with a bias in $x$ direction, while panel (b) is for setup II with a driving electric field in $y$ direction. $p_1$ and $p_2$ label the first and second band edges along $k_x$.
• Figure 4: Linear thermal noises as a function of the temperature at $E_f=0.12$. (a) $S^{(1)}_{11}$, $S^{(1)}_{13}$ and $S^{(1)}_{14}$ for setup I. (b) $S^{(1)}_{31}$ for setup II.
• Figure 5: Dephasing effect on the linear thermal noise. (a) $S^{(1)}_{11}$ for setup I. (b) $S^{(1)}_{31}$ for setup II.