---
title: 'CaZrO3/KTaO3 (111) Interface: 2DEG & Rashba Effects'
url: https://www.emergentmind.com/topics/cazro3-ktao3-111-interface
type: topic
---

# CaZrO3/KTaO3 (111) Interface: 2DEG & Rashba Effects

Searching arXiv for the specified interface and closely related KTaO\(_3\) (111) papers to ground the article in current literature.
arXiv search query: "CaZrO3 KTaO3 (111) interface KTaO3 (111) 2DEG Rashba superconductivity"
CaZrO\(_3\)/KTaO\(_3\) (111) is an epitaxial oxide heterointerface in which a CaZrO\(_3\) film is grown on a (111)-oriented KTaO\(_3\) substrate and a two-dimensional electron gas (2DEG) forms on the KTaO\(_3\) side. Reported CaZrO\(_3\)/KTaO\(_3\) (111) heterostructures combine a confined interfacial metallic state, two-dimensional superconductivity, strong inversion asymmetry, substantial Rashba spin–orbit coupling, and pronounced nonlinear transport responses, including giant light-tunable nonreciprocal transport and a sign-reversible nonlinear Hall effect [2403.04515; 2507.14476]. Because the interface is buried, its low-energy electronic structure is usually interpreted by reference to angle-resolved photoemission and tight-binding studies of KTaO\(_3\) (111) 2DEGs, which establish the Ta \(5d\) \(t_{2g}\)-derived subband structure, anisotropic Fermi surfaces, and nontrivial spin textures expected on the KTaO\(_3\) side [2311.08230; 1903.06077; 2502.15080].

## 1. Heterostructure, crystallography, and interfacial charge accumulation

Reported CaZrO\(_3\)/KTaO\(_3\) (111) devices are epitaxial heterostructures grown by pulsed laser deposition on single-crystal KTaO\(_3\) (111) substrates. One study used 50 nm CaZrO\(_3\) films grown at \(750\,^\circ\mathrm{C}\) and \(10^{-5}\) mbar oxygen pressure with a 248 nm KrF excimer laser at a fluence of \(\approx 2~\mathrm{J\,cm^{-2}}\) and 1 Hz [2403.04515]. Another used 10 nm CaZrO\(_3\) films on \(5 \times 5 \times 0.5~\mathrm{mm^3}\) KTaO\(_3\) (111), grown at \(750\,^\circ\mathrm{C}\) and \(p_{\mathrm{O}_2}=5\times10^{-3}\) Pa with a 248 nm KrF excimer laser at 2 Hz and a fluence of \(\sim 2~\mathrm{J/cm^2}\) [2507.14476]. The reported lattice mismatch is small, \(\approx 0.6\%\) or \(\sim 0.58\%\), enabling coherent or high-quality epitaxy [2403.04515; 2507.14476].

Structural characterization identifies atomically sharp and chemically sharp interfaces. In one report, \(\theta\)–2\(\theta\) x-ray diffraction and STEM-HAADF established coherent epitaxy and a flat interface, while STEM-EDX found no discernible interdiffusion [2403.04515]. In another, AFM showed an atomically flat surface with RMS roughness \(\sim 2.2~\text{\AA}\), consistent with layer-by-layer growth [2507.14476].

The KTaO\(_3\) (111) side sets the interfacial symmetry. KTaO\(_3\) is cubic perovskite, but along (111) the stacking is polar and the surface or interface belongs to \(C_{3v}\). The (111) projection of the B-site network yields a triangular lattice of Ta atoms, while a KTaO\(_3\) (111) slab can also be described as a buckled honeycomb arrangement of Ta\(^{5+}\) ions, with three successive Ta (111) planes forming a hexagonal arrangement with three inequivalent Ta sites [2311.08230; 2502.15080; 2507.14476]. This symmetry is fundamental for the trigonal Fermiology, anisotropic spin texture, and tensor form of nonlinear and spin-galvanic responses.

The microscopic origin of the 2DEG is attributed primarily to oxygen vacancies at or near the KTaO\(_3\) surface or interface, together with interfacial polarity and band alignment. One study states that the interfacial conduction is attributed primarily to oxygen vacancies at the KTaO\(_3\) surface, which provide in-gap donor states with two main distributions around 2.3 eV and 3.1 eV below the conduction band and electron-dope the Ta \(5d\) \(t_{2g}\) conduction band [2403.04515]. Another states that, in combination with polar discontinuity and oxygen-vacancy-related in-gap states, electrons are transferred or accumulated on the KTaO\(_3\) side because the Ta \(5d\) conduction-band minimum lies below the relevant higher-lying CaZrO\(_3\) states [2507.14476]. A common misconception is that the conducting channel is a CaZrO\(_3\) metallic layer; the reported interpretation instead places the low-energy carriers in a KTaO\(_3\)-side interfacial quantum well.

## 2. KTaO\(_3\) (111) electronic structure as the reference normal state

Direct band mapping of buried CaZrO\(_3\)/KTaO\(_3\) (111) interfaces is not available from standard VUV ARPES, so the reference normal-state electronic structure is taken from KTaO\(_3\) (111) 2DEGs studied at surfaces and ultrashallow interfaces [2311.08230; 1903.06077]. These studies establish that the relevant conduction states are Ta \(5d\) \(t_{2g}\)-derived and, at experimentally relevant energies, are entirely derived from the bulk \(J=3/2\) manifold, with the \(J=1/2\) band lying about 400 meV higher in bulk KTaO\(_3\) [1903.06077].

Quantum confinement along [111] produces multiple subbands. ARPES on superconducting KTaO\(_3\) (111) 2DEGs reveals multiple dispersive conduction bands crossing the Fermi level and a subband structure fitted by four spin-split band pairs within the measurement window, including three Ta \(5d\) \(t_{2g}\)-derived pairs and an additional confined subband represented by a second copy of the \(t_{2g}\) manifold [2311.08230]. Earlier ARPES on surface-stabilized KTaO\(_3\) (111) 2DEGs resolved two main electron-like subbands with a bandwidth of \(\approx 130\) meV and a third low-density band near \(k_\parallel=0\) [1903.06077].

The Fermi surface is strongly noncircular. ARPES studies report a star-shaped outer contour centered at \(\Gamma\) together with inner sheets that are hexagonal or more isotropic [2311.08230; 1903.06077]. In one superconducting KTaO\(_3\) (111) 2DEG, the outer star-shaped Fermi surface has a major diameter of \(\sim 0.47~\text{\AA}^{-1}\) along \(\Gamma\)-M and a minor diameter of \(\sim 0.35~\text{\AA}^{-1}\) along \(\Gamma\)-K; inner contours are described as star-like, nearly hexagonal, and nearly circular [2311.08230]. In an earlier surface 2DEG, the outer star extends to \(|k|\sim 0.3~\text{\AA}^{-1}\) along \(\Gamma\)-M and the inner hexagon to \(|k|\sim 0.14~\text{\AA}^{-1}\) [1903.06077]. Reported ARPES-derived 2D carrier densities for these KTaO\(_3\) (111) 2DEGs are \(n_{2D}\approx 1.2\times10^{14}~\mathrm{cm^{-2}}\) and \(n_{2D}\approx 1.25\times10^{14}~\mathrm{cm^{-2}}\) [1903.06077; 2311.08230].

Orbital character is strongly hybridized. Unlike KTaO\(_3\) (001), where \(d_{xy}\) and \(d_{xz/yz}\) can often be separated, the KTaO\(_3\) (111) 2DEG does not exhibit a simple pure orbital character for individual bands; instead, the \(t_{2g}\) orbitals are strongly mixed, although large-\(k\) segments of the star-like contour can become locally dominated by \(d_{xy}\), \(d_{yz}\), or \(d_{xz}\) character [2311.08230; 1903.06077]. This suggests that CaZrO\(_3\)/KTaO\(_3\) (111) should be treated as a multi-orbital, symmetry-constrained quantum well rather than as a single-band Rashba electron gas.

## 3. Interfacial transport and two-dimensional superconductivity

CaZrO\(_3\)/KTaO\(_3\) (111) interfaces are metallic at low temperature and support a confined conduction channel. In a 50 nm-film study, the sheet carrier density is \(n_s \approx 4.6\times10^{13}~\mathrm{cm^{-2}}\) at 300 K and decreases to \(\approx 3.8\times10^{13}~\mathrm{cm^{-2}}\) at low temperature because of carrier freeze-out from in-gap states; the mobility is \(\mu \approx 140~\mathrm{cm^2\,V^{-1}\,s^{-1}}\) at 2 K and \(\sim 14~\mathrm{cm^2\,V^{-1}\,s^{-1}}\) at 250 K [2403.04515]. In a 10 nm-film study, the interface remains metallic from 2 to 300 K with \(n_s \approx 5.0\times10^{13}~\mathrm{cm^{-2}}\), \(\mu \approx 212~\mathrm{cm^2\,V^{-1}\,s^{-1}}\), and \(R_s \sim 500~\Omega/\square\) at 2 K [2507.14476].

The conduction is two-dimensional. Angular magnetoresistance was used to estimate a conduction thickness of \(\sim 4.35\) nm via
\[
t = \frac{h}{e^2 k_F R_s \alpha},\qquad k_F = \sqrt{\pi n_s},
\]
and the resulting metallic channel was described as confined to the interface region [2403.04515]. In the dark, Hall transport is linear and negative, consistent with a dominant electron-like band [2403.04515].

A superconducting transition is observed at low temperature. For the 50 nm CaZrO\(_3\)/KTaO\(_3\) (111) interface, the sheet resistance drops to zero with a critical temperature \(T_c \approx 0.43\) K, defined at 50% of the normal-state resistance [2403.04515]. The superconducting state is described as two-dimensional and localized at the interface, comparable to epitaxial LaVO\(_3\)/KTaO\(_3\) (111) and lower than some non-epitaxial KTaO\(_3\) interfaces [2403.04515]. Within the broader KTaO\(_3\) literature, the (111) orientation is singled out as hosting the highest \(T_c\) among KTaO\(_3\) orientations [2403.04515].

Reference superconducting KTaO\(_3\) (111) 2DEGs also display strong in-plane anisotropy. In Eu-oxidized KTaO\(_3\) (111), \(T_c \approx 0.82\) K for current along \([1\bar{1}0]\) and \(T_c \approx 0.58\) K for current along \([\bar{1}12]\), while the normal-state mobilities are \(\mu_{\langle -1\,1\,2\rangle} \approx 111~\mathrm{cm^2/Vs}\) and \(\mu_{\langle 1\,\!-\!10\rangle} \approx 33~\mathrm{cm^2/Vs}\) [2311.08230]. This suggests that the anisotropic Fermi surface and spin texture established for KTaO\(_3\) (111) are relevant to superconductivity at CaZrO\(_3\)/KTaO\(_3\) (111) as well.

## 4. Rashba spin–orbit coupling, spin texture, and spin-to-charge conversion

Broken inversion symmetry along the interface normal, combined with strong Ta \(5d\) spin–orbit coupling, gives rise to Rashba physics. A standard phenomenological form used for KTaO\(_3\) (111) interfaces is
\[
H_R = \frac{\alpha_R}{\hbar} (\boldsymbol{z} \times \mathbf{p}) \cdot \boldsymbol{\sigma},
\]
or equivalently
\[
H_\mathrm{R} = \alpha_R (\sigma_x k_y - \sigma_y k_x),
\]
but band-structure studies show that the actual splitting is multi-orbital, momentum-dependent, and strongly anisotropic [2502.15080; 2403.04515; 2311.08230].

Tight-binding fits to superconducting KTaO\(_3\) (111) 2DEGs use a Ta \(t_{2g}\) basis on a 2D triangular lattice with \(a=4.0~\text{\AA}\), \(t_\pi=-0.65\) eV, \(t_\delta=-0.05\) eV, onsite energies \(\Delta\epsilon=1.946\) and \(2.011\) eV for two effective subband copies, atomic spin–orbit coupling \(\lambda=0.4\) eV, and inversion-breaking orbital mixing \(g=3\) and \(1\) meV [2311.08230]. In these fits, the Rashba-like splitting emerges from the combination of \(H_{\text{hop}}\), on-site \(H_{\text{SOC}}\), and inversion-breaking \(H_{\text{mix}}\), rather than from a single explicit Rashba term [2311.08230].

Band-resolved Rashba parameters near \(\Gamma\) are reported as \(\alpha_R \approx 20\) meV\(\cdot\)\AA\ for the outer pink band pair and \(\alpha_R \approx 8\) meV\(\cdot\)\AA\ for the orange pair, while the green and cyan pairs are anisotropic with \(\alpha_R=0\) along \(\Gamma\)-M and \(\alpha_R \approx 14\) and \(4\) meV\(\cdot\)\AA\ along \(\Gamma\)-K, respectively [2311.08230]. Earlier ARPES-based analysis defined an effective \(\alpha_R^{\mathrm{eff}}(\mathbf{k})=\Delta E(\mathbf{k})/(2k_\parallel)\) and reported \(\alpha^{\text{KTO}}_{\Gamma M}\sim 2~\mathrm{meV\cdot\AA}\) and \(\alpha^{\text{KTO}}_{\Gamma K}\sim 21~\mathrm{meV\cdot\AA}\), with corresponding momentum splittings of \(\sim 2\times10^{-3}~\text{\AA}^{-1}\) and \(\sim 5\times10^{-3}~\text{\AA}^{-1}\) [1903.06077]. These values show that no single isotropic \(\alpha_R\) characterizes KTaO\(_3\) (111).

The spin texture is equally nontrivial. Calculations for KTaO\(_3\) (111) find that spin-momentum locking holds only on high-symmetry directions, while a strong out-of-plane spin component renders the spin texture threefold symmetric [1903.06077]. In the superconducting KTaO\(_3\) (111) 2DEG, the outer star-shaped contour exhibits helical-like spin winding with strong warping; spins are purely in-plane at the star tips along \(\Gamma\)-M, but acquire large out-of-plane components between tips, and inner sheets can show both orthoradial and radial orientations with local helicity reversals near band intersections [2311.08230].

Spin-to-charge conversion has been measured directly in AlO\(_x\)/KTaO\(_3\) (111) 2DESs by spin pumping. There, the Hall sheet density is \(n_{2D}\approx 3.2\times10^{13}~\mathrm{cm^{-2}}\) at 300 K and \(n_{2D}\approx 2.8\times10^{13}~\mathrm{cm^{-2}}\) at 3–4 K, the mobility at 3 K is \(\mu \approx 60~\mathrm{cm^2/Vs}\), and the mean free time is \(\tau \approx 0.02\) ps [2502.15080]. The inverse Rashba–Edelstein length is defined by
\[
\lambda_{\mathrm{IREE}} = \frac{J_c^{2D}}{J_s^{3D}},
\]
and reaches \(\lambda_{\mathrm{IREE}} \approx 0.6\) nm at 10 K. Using
\[
\lambda_{\mathrm{IREE}} = \frac{\alpha_R \tau}{\hbar},
\]
an effective \(\alpha_R \approx 2~\mathrm{meV\cdot\AA}\) was inferred [2502.15080]. The angle dependence deviates from simple \(\cos\phi\) behavior and is fitted by
\[
V(\phi) = A \cos\phi \cos(3\phi) + C \sin\phi \cos(3\phi),
\]
with \(A/C \approx 1.9\) at 10 K and \(2.8\) at 70 K [2502.15080]. An important clarification is that stronger atomic SOC does not automatically imply stronger spin-to-charge conversion: the KTaO\(_3\) analysis attributes the modest IREE partly to multi-orbital compensation and to \(J=3/2\) states near \(\Gamma\) with nearly vanishing magnetic moment [2502.15080].

## 5. Light-tunable nonreciprocal transport

A defining result for CaZrO\(_3\)/KTaO\(_3\) (111) is the giant optical enhancement of nonreciprocal transport in the normal state [2403.04515]. Nonreciprocity is described phenomenologically by
\[
R(B,I) = R_0\left(1 + \beta B^2 + \gamma B I\right),
\]
with the experimentally extracted coefficient
\[
\gamma = \frac{\Delta R}{2 B I R_0},
\qquad
\Delta R = R(+I,B) - R(-I,B),
\]
in the linear regime \(|B|\le 0.7\) T [2403.04515].

In the dark at 5 K and \(I=40~\mu\)A, \(\gamma \sim 10^2~\mathrm{A^{-1}T^{-1}}\), already comparable with LaAlO\(_3\)/SrTiO\(_3\) and larger than many Rashba semiconductors [2403.04515]. Under 330 nm ultraviolet illumination, \(\Delta R/R_0\) reaches \(\approx 4\%\) at several tesla and \(\gamma \approx 10^{5}~\mathrm{A^{-1}T^{-1}}\), representing a three-orders-of-magnitude enhancement [2403.04515]. The signal decreases with increasing temperature and disappears around 40 K [2403.04515].

The optical response is wavelength dependent. Around 450–360 nm, photons excite electrons from oxygen-vacancy in-gap states into the conduction band; at 330 nm, slightly above the KTaO\(_3\) band gap of \(\approx 3.6\) eV, photoconductance is maximal because abundant electrons are pumped from the valence-band maximum into the Ta \(t_{2g}\) conduction band and into the interfacial well [2403.04515]. At 300 nm, the resistance increases again because photoexcited electrons occupy higher subbands, electron–phonon scattering and recombination increase, and weak localization competes with weak antilocalization [2403.04515].

Hall transport under illumination becomes nonlinear and is analyzed with a two-band model. For \(\lambda > 400\) nm, only intrinsic carriers are reported, with \(n_1 \sim 4\times10^{13}~\mathrm{cm^{-2}}\) and \(\mu_1 \sim 160~\mathrm{cm^2\,V^{-1}s^{-1}}\). At \(\lambda \lesssim 400\) nm, a second photocarrier channel appears and a Lifshitz transition occurs at \(\approx 400\) nm [2403.04515]. At 330 nm, \(n_1\) jumps to \(1.6\times10^{14}~\mathrm{cm^{-2}}\), \(n_2 \approx 0.3\times10^{13}~\mathrm{cm^{-2}}\), and \(\mu_2 \approx 1.54\times10^{4}~\mathrm{cm^2\,V^{-1}s^{-1}}\) [2403.04515].

Weak antilocalization analysis by modified Maekawa–Fukuyama theory yields a peak spin–orbit field
\[
B_\mathrm{so} \approx 14.7~\mathrm{T}
\]
at 330 nm, together with a maximum Rashba coefficient
\[
\alpha_R \approx 0.26~\mathrm{eV\ \AA}
\]
and a spin splitting energy
\[
\Delta \approx 168~\mathrm{meV}
\]
using \(m^* \approx 0.3m_0\) [2403.04515]. The reported microscopic scaling is
\[
\gamma \propto \frac{\alpha_R \tau}{E_F},
\]
and the interpretation is that UV illumination increases both \(\alpha_R\) and \(\tau\) by about an order of magnitude, so the product \(\alpha_R\tau\) dominates over the increase in \(E_F\) and drives the giant enhancement of \(\gamma\) [2403.04515].

## 6. Nonlinear Hall effect, skew scattering, and Berry-curvature engineering

The CaZrO\(_3\)/KTaO\(_3\) (111) interface also exhibits a giant, light-tunable nonlinear Hall effect (NLHE) at zero magnetic field [2507.14476]. In a six-terminal Hall-bar geometry, an AC drive current \(I^\omega = I_0\sin(\omega t)\) generates a second-harmonic transverse voltage \(V_y^{2\omega}\), from which the second-order transverse conductivity is extracted as
\[
\sigma^{(2)}_{yxx} = \frac{\sigma_{xx} V_y^{2\omega} L^2}{(V_x^\omega)^2 W}.
\]
For current mainly along \([1\bar{1}0]\), the dark signal at 10 K is positive, with \(V_y^{2\omega}\approx +38~\mu\mathrm{V}\) at \(I_0=+100~\mu\mathrm{A}\); for current along \([11\bar{2}]\), the NLHE is much weaker [2507.14476].

The key symmetry point is that the standard Berry-curvature-dipole mechanism is forbidden. Because the nonmagnetic KTaO\(_3\) (111) interface retains in-plane threefold rotation \(C_3\), the Berry-curvature dipole vanishes by symmetry, even though inversion symmetry is broken and Berry curvature itself is nonzero [2507.14476]. The measured NLHE is instead assigned to extrinsic skew scattering, with side jump providing a subdominant contribution [2507.14476].

Optical excitation acts as an efficient gate. At \(\lambda=405\) nm and \(P\approx 0.1\) mW, the sign of \(V_y^{2\omega}\) reverses; at \(P=0.45\) mW, \(V_y^{2\omega}=-424~\mu\mathrm{V}\) at \(100~\mu\mathrm{A}\); at \(P=15\) mW and \(I_0=+60~\mu\mathrm{A}\), \(V_y^{2\omega}\approx -840~\mu\mathrm{V}\), compared with \(+13~\mu\mathrm{V}\) in the dark [2507.14476]. The corresponding \(|\sigma^{(2)}_{yxx}|\) increases from \(\approx 3.3\times10^{-5}~\mu\mathrm{m\,V^{-1}\,\Omega^{-1}}\) in the dark to \(\approx 2.4~\mu\mathrm{m\,V^{-1}\,\Omega^{-1}}\) under strong illumination, nearly five orders of magnitude larger [2507.14476].

The transport scaling analysis uses
\[
\frac{\sigma^{(2)}_{yxx}}{\sigma_{xx}} = \xi \sigma_{xx}^2 + \eta.
\]
Here the \(\propto \tau^3\) term is attributed to skew scattering and the \(\propto \tau\) term to side jump, since the Berry-curvature-dipole contribution is symmetry-forbidden [2507.14476]. In the low-\(\sigma\) regime, \(\xi \approx +3.51\times10^4~\mu\mathrm{m\,V^{-1}\,\Omega^2}\) and \(\eta \approx +0.03~\mu\mathrm{m\,V^{-1}}\); in the high-\(\sigma\) regime, \(\xi \approx -2.49\times10^6~\mu\mathrm{m\,V^{-1}\,\Omega^2}\) and \(\eta \approx +13.9~\mu\mathrm{m\,V^{-1}}\) [2507.14476]. The sign reversal is therefore driven by the skew-scattering term.

First-principles calculations connect this sign change to the Berry curvature triple
\[
T(E_F) = \frac{2}{(2\pi)^2 \hbar} \int d^2k\, \delta(E_F - E_\mathbf{k})\, k^2\, \Omega_z(\mathbf{k}) \cos 3\theta_\mathbf{k},
\]
the symmetry-allowed third angular moment of Berry curvature on the Fermi contour [2507.14476]. For a 6-unit-cell KTaO\(_3\) (111) slab, \(T(E_F)\) is positive for \(E_F<0.24\) eV, crosses zero at \(E_F\approx 0.24\) eV, and becomes negative above that value [2507.14476]. The experimental interpretation is that light raises the Fermi level toward a band crossing near M, changes the sign of the Berry curvature triple, and simultaneously introduces a high-mobility carrier channel with \(\mu_2\) increasing from 2403 to 9060 \(\mathrm{cm^2/V\cdot s}\) as power rises from 0.1 to 15 mW [2507.14476].

## 7. Modeling strategies, experimental constraints, and broader significance

Two complementary modeling frameworks are used for KTaO\(_3\) (111) and provide the natural starting point for CaZrO\(_3\)/KTaO\(_3\) (111). One is a self-consistent tight-binding supercell built from relativistic DFT and Ta \(t_{2g}\) Wannier functions, with a 30-unit-cell slab along [111], an on-site confinement potential \(V_i\), and self-consistent Poisson–Schrödinger solution with a field-dependent dielectric constant [1903.06077]. The other is a reduced 2D triangular-lattice tight-binding model with explicit \(H_{\text{hop}}\), \(H_{\text{SOC}}\), and inversion-breaking \(H_{\text{mix}}\) terms and parameters fitted to ARPES [2311.08230]. Both encode the essential point that Rashba-like splitting and spin texture emerge from confinement, inversion breaking, and multi-orbital Ta \(5d\) physics rather than from a minimal single-band model.

For CaZrO\(_3\)/KTaO\(_3\) (111), CaZrO\(_3\) can be treated as a wide-gap insulating overlayer that sets electrostatic boundary conditions, potential drop, strain, and orbital mixing on the KTaO\(_3\) side [2311.08230]. This suggests that interface-specific modeling should modify the confinement profile, subband occupancy, and inversion-breaking parameter rather than replace the KTaO\(_3\)-side \(t_{2g}\) framework. Strain may be incorporated as anisotropic changes in hopping or as crystal-field terms that distinguish the three \(t_{2g}\) orbitals [2311.08230].

A major experimental limitation is spectroscopic accessibility. Standard VUV ARPES probes only the top \(\sim 1\)–2 nm and is therefore suitable for surface 2DEGs or ultrashallow buried interfaces, but not for a buried CaZrO\(_3\)/KTaO\(_3\) channel. Soft x-ray ARPES can probe deeper, though with limited energy and momentum resolution near \(E_F\) [2311.08230]. As a result, buried CaZrO\(_3\)/KTaO\(_3\) interfaces are presently constrained primarily by transport, weak-antilocalization analysis, nonlinear response measurements, and theory guided by KTaO\(_3\) (111) electronic-structure benchmarks [2311.08230; 2403.04515; 2507.14476].

Several conceptual clarifications follow from the current literature. First, the KTaO\(_3\) (111) interface is not well described by an isotropic circular Rashba 2DEG; the actual Fermi surface is warped and multi-sheeted, and the spin texture includes substantial out-of-plane canting [1903.06077; 2311.08230]. Second, strong atomic SOC does not guarantee maximal spin-galvanic efficiency because spin and orbital channels can partially cancel [2502.15080]. Third, in the NLHE of CaZrO\(_3\)/KTaO\(_3\) (111), the canonical Berry-curvature-dipole mechanism is symmetry-forbidden, and the experimentally relevant quantity is the Berry curvature triple controlling skew scattering [2507.14476].

Taken together, the available work identifies CaZrO\(_3\)/KTaO\(_3\) (111) as a noncentrosymmetric, multi-orbital, Ta \(5d\)-electron interface in which the polar (111) geometry, strong spin–orbit coupling, and optically tunable band filling produce an unusual coexistence of two-dimensional superconductivity, anisotropic Rashba physics, giant nonreciprocal transport, and a sign-reversible nonlinear Hall effect [2403.04515; 2507.14476].

Source: https://www.emergentmind.com/topics/cazro3-ktao3-111-interface