Eccentricity valley Hall effect

Abstract

Valleytronics harnesses the valley degree of freedom -- energy-degenerate extrema in the electronic band structure -- for information storage and processing. Valley Hall effect (VHE) is a cornerstone of valleytronics, enabling electric generation of pure valley currents. While extensively studied in systems with valleys located at time-reversal-breaking points, here, we shift the paradigm to valleytronic platforms with time-reversal-invariant valleys (TRIVs), revealing a novel phenomenon: eccentricity VHE. Unlike conventional VHE, the valley Hall angle for eccentricity VHE is an intrinsic geometric property, governed solely by the eccentricity of the valley Fermi surface, rendering it highly robust against variations in temperature or carrier density. Eccentricity VHE emerges universally across all 25 layer groups supporting TRIVs. We demonstrate these distinctive features in monolayer GeS$_{2}$ via first-principles calculations, predicting a significant valley Hall angle of 0.74. This effect can be detected through nonlocal transport measurements exhibiting characteristic scaling behavior, or, in certain cases, through valley-layer coupling. Our findings reveal a critical overlooked facet of valley Hall physics, transcend the established VHE paradigm, and significantly broadens the scope of valleytronics.

Figures (4)

• Figure 1: Valley Hall effect and two categories of valleytronic systems.a, In VHE, a longitudinal charge current $j^c_\|$ drives a transverse valley current $j^v_\bot$. The blue and red spheres denote electrons from two different valleys $V_1$ and $V_2$. b, Conventional valleytronic systems, such as graphene and transition metal dichalcognides materials, have a pair of valleys located at $K$ and $K'$ points of the hexagonal Brillouin zone. The two valleys are related by time-reversal $\mathcal{T}$, yet each valley is at a $k$ point that does not preserve $\mathcal{T}$. c, Valleytronic system with time-reversal-invariant valleys (TRIVs). Each valley here resides at a $\mathcal{T}$-invariant momentum point. The two valleys are not related by $\mathcal{T}$ but by some crystalline symmetry $\mathcal{Q}$.
• Figure 2: Eccentricity valley Hall effect.a, The generic shape of a TRIV Fermi surface is an ellipse. Its geometry is characterized by the eccentricity $\mathfrak{e}$. Here, we illustrate the case of a TRIV Fermi surface with semi-major axis along $y$. b, Illustration of a pair of TRIVs connected by $\mathcal{Q}=C_{4z}$ symmetry. Under a driving electric field, the valley-contrasted current response leads to a VHE determined by eccentricity of valley Fermi ellipse. c, The resulting valley Hall angle as a function of $\mathfrak{e}$ and (inset) of the orientation of the applied electric field. d, The eccentricity VHE features a valley Hall angle independent of temperature and chemical potential.
• Figure 3: Results on monolayer GeS$_2$.a, Crystal structure of monolayer tetragonal GeS$_2$. b, Calculated band structures. The color map indicates the value of out-of-plane polarization of each state. c, Fermi surface at $\mu =-0.1$ eV. A pair of Fermi ellipses around the two valley centers at $X$ and $X'$ can be seen. d, VHE conductivity and valley Hall angle plotted as functions of chemical potential. The data points are the first-principles results, and the solid lines are results from Eqs. (\ref{['VHC']}) and (\ref{['VHA']}). In calculating $\sigma^v$, we take $\tau=0.1\,$ps.
• Figure 4: Nonlocal transport signature.a, Experimental setup for nonlocal measurement of VHE. A charge current is applied between contacts 1 and 2, and the resulting voltage is measured between contacts 3 and 4 at a distance $x$ along the sample strip. b, Eccentricity VHE features a nonlocal resistance $R_\text{NL}\propto \rho$, in contrast to the $R_\text{NL}\propto \rho^3$ scaling for conventional VHE.