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Berry Curvature Dipole-induced Non-linear Hall Effect in Oxide Heterostructures

Nesta Benno Joseph, Arka Bandyopadhyay, Ajit C. Balram, Awadhesh Narayan

Abstract

The observation of non-linear Hall effects in time-reversal invariant systems has established the intriguing role of band topology beyond Berry curvature in determining transport phenomena. Many of these non-linear responses owe their origin to the Berry curvature dipole (BCD), which, like the Berry curvature (monopole), is also an electronic band structure effect, but is routinely strongly constrained by crystalline symmetries. Here, we propose non-centrosymmetric transition metal oxide heterostructures as promising platforms for realizing and tuning BCD-induced non-linear Hall effects. Specifically, we investigate superlattices of the form $(\mathrm{Ba(Os,Ir)}\mathrm{O}_3)_n/(\mathrm{BaTiO}_3)_4$ ($n{=}1, 2$), comprising metallic perovskite layers ($\mathrm{BaOsO_3}$ or $\mathrm{BaIrO_3}$) sandwiched between insulating ferroelectric $\mathrm{BaTiO_3}$ (BTO). The ferroelectric distortion in BTO breaks inversion symmetry of the superlattice, giving rise to a finite BCD with two symmetry-allowed components of equal magnitude and opposite sign. Our first-principles calculations demonstrate that the magnitude of the BCD -- and consequently the nonlinear Hall response -- can be effectively tuned by varying the number of metallic layers or the choice of the B-site cation in these $\mathrm{ABO_3}$ perovskites. Since Rashba splitting and ferroelectric distortion in these systems are readily controllable via an external electric field or strain, the non-linear Hall response in these materials can be directly engineered. Our findings establish non-centrosymmetric oxide perovskite heterostructures as a versatile platform for exploring and manipulating BCD-driven non-linear transport phenomena.

Berry Curvature Dipole-induced Non-linear Hall Effect in Oxide Heterostructures

Abstract

The observation of non-linear Hall effects in time-reversal invariant systems has established the intriguing role of band topology beyond Berry curvature in determining transport phenomena. Many of these non-linear responses owe their origin to the Berry curvature dipole (BCD), which, like the Berry curvature (monopole), is also an electronic band structure effect, but is routinely strongly constrained by crystalline symmetries. Here, we propose non-centrosymmetric transition metal oxide heterostructures as promising platforms for realizing and tuning BCD-induced non-linear Hall effects. Specifically, we investigate superlattices of the form (), comprising metallic perovskite layers ( or ) sandwiched between insulating ferroelectric (BTO). The ferroelectric distortion in BTO breaks inversion symmetry of the superlattice, giving rise to a finite BCD with two symmetry-allowed components of equal magnitude and opposite sign. Our first-principles calculations demonstrate that the magnitude of the BCD -- and consequently the nonlinear Hall response -- can be effectively tuned by varying the number of metallic layers or the choice of the B-site cation in these perovskites. Since Rashba splitting and ferroelectric distortion in these systems are readily controllable via an external electric field or strain, the non-linear Hall response in these materials can be directly engineered. Our findings establish non-centrosymmetric oxide perovskite heterostructures as a versatile platform for exploring and manipulating BCD-driven non-linear transport phenomena.
Paper Structure (8 sections, 5 equations, 4 figures)

This paper contains 8 sections, 5 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Computational Details
  3. Results and Discussion
  4. Conclusions
  5. Acknowledgements

Figures (4)

  • Figure 1: Centrosymmetric and non-centrosymmetric$\mathbf{n{=}1}$ heterostructures of (Ba(Os,Ir)O3)$_n$/(BTO)4. The heterostructure (a) without and (f) with the ferroelectric distortion. The green, blue, brown, and red atoms represent Ba, Ti, Ir/Os, and O, respectively. Electronic band structure of the centrosymmetric and non-centrosymmetric structures of (b)-(c) (BaOsO3)1/(BTO)4 and (d)-(e) (BaIrO3)1/(BTO)4. The broken inversion symmetry leads to a large Rashba splitting of the bands. The bands around the Fermi level (red dashed line) arise predominantly from the $d$ orbitals of Os/Ir.
  • Figure 2: Berry curvature and BCD of $\mathbf{n{=}1}$ heterostructures. Berry curvature components $\Omega_x$ and $\Omega_y$, superimposed on the band structure along high-symmetry $\Gamma-M$ direction, associated with (a) (BaOsO3)1/(BTO)4 and (c) (BaIrO3)1/(BTO)4. The red and blue colors represent positive and negative values of the Berry curvature components, respectively. The two equal and opposite components, $D_{xy}$ and $D_{yx}$, of the BCD as a function of the energy with respect to the Fermi level associated with (b) (BaOsO3)1/(BTO)4 and (d) (BaIrO3)1/(BTO)4. The inset shows the components magnified around $E{-}E_F{=}0$.
  • Figure 3: Berry curvature and BCD of $\mathbf{n{=}2}$ heterostructures. The Berry curvature components $\Omega_x$ and $\Omega_y$, superimposed on the band structures along $\Gamma-M$ direction of (a) (BaOsO3)2/(BTO)4 and (c) (BaIrO3)2/(BTO)4. The red and blue colors represent positive and negative values of the Berry curvature components, respectively. (b), (d) The non-zero BCD components $D_{xy}$ and $D_{yx}$ associated with the $n{=}2$ heterostructures, plotted as a function of energy with respect to the Fermi level. The inset shows a magnified region of BCD around $E-E_F=0$. Sandwiching two layers of (Ba(Os, Ir)O3) between the BTO layers significantly enhances the BCD around the Fermi level.
  • Figure 4: A comparison of the distribution of the derivative of the Berry curvature. The distribution of the quantity $\partial_x\Omega_y$ on the Fermi surface of (a) (BaOsO3)1/(BTO)4, (b) (BaIrO3)1/(BTO)4, (c) (BaOsO3)2/(BTO)4, and (d) (BaIrO3)2/(BTO)4. The red and blue colors indicate the positive and negative values, respectively. Note that the value of $\partial_x\Omega_y$ for $n{=}2$ heterostructures is two orders of magnitude higher than the $n{=}1$ case.