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Room Temperature Gate Tunable Non Reciprocal Charge Transport in Lattice Matched InSb/CdTe Heterostructures

The manipulation of symmetry provides an effective way to tailor the physical orders in solid-state systems. With the breaking of both the inversion and time-reversal symmetries, non-reciprocal magneto-transport may emerge in assorted non-magnetic systems to enrich spintronic physics. Here, we report the observation of the uni-directional magneto-resistance (UMR) in the lattice-matched InSb/CdTe film up to room temperature. Benefiting from the strong built-in electric field of $0.13 \mathrm{~V} \cdot \mathrm{nm}^{-1}$ in the hetero-junction region, the resulting Rashba-type spin-orbit coupling and quantum confinement warrant stable angular-dependent second-order charge current with the non-reciprocal coefficient 1-2 orders of magnitude larger than most non-centrosymmetric materials at 298 K. More importantly, this heterostructure configuration enables highly-efficient gate tuning of the rectification response in which the enhancement of the UMR amplitude by 40% is realized. Our results advocate the narrow-gap semiconductor-based hybrid system with the robust two-dimensional interfacial spin texture as a suitable platform for the pursuit of controllable chiral spin-orbit devices and applications.

semiconductor-based hybrid system with the robust two-dimensional interfacial spin texture as a suitable platform for the pursuit of controllable chiral spin-orbit devices and applications.
Symmetry, which lies at the heart of the universal laws, serves as a fundamental degree of freedom to define the intrinsic properties of a material 1 . Together with spin-orbit coupling (SOC), the breaking of inversion symmetry modifies the Hamiltonian of the charge carriers with anti-symmetric momentum operators, thus leading to non-reciprocal transport phenomena featured by unidirectional I-V characteristics 2 .
In order to realize such rectification effect, it requires the magneto-chiral anisotropy that originates from either the non-centrosymmetric band structures or hetero-interfaces 3-5 . In this context, the inherent bulk/interfacial Rashba-type SOC would lift the spin degeneracy and trigger the current-induced spin polarization 6-11 . By further applying an external magnetic field to break the time-reversal symmetry, the regulation of the asymmetric spin splitting can be represented by the non-reciprocal electrical response where the longitudinal resistance exhibits unique current direction-dependent signature and its second-order harmonic component scales linearly with both the applied current and the magnetic field 2,4,5,12-23 . Governed by the spin-momentum locking mechanism, this unidirectional magnetoresistance (UMR) can be established without invoking additional magnetic order, hence unfolding a reliable approach to explore the spin-orbit dynamics in a variety of low crystalline symmetry systems including topological insulators/semimetals (e.g., Bi2Se3 19 , WTe2 20 ), polar semiconductors (e.g., BiTeBr 5 , -GeTe 21 ) and heterostructures (e.g., LaAlO3/SrTiO3 4, 22 , Ge/Si 23 ).
Considering the amplitude of the Rashba-type UMR signal is closely linked to the spin splitting energy Δ ~ R ⋅ (Δ ×̂) • (where R is the Rashba coefficient, k stands for momentum vectors,  is the Pauli operator, and the mirror symmetry is broken along the ̂ direction), the spin relaxation time , and the Fermi energy F, the key to facilitate the aforementioned non-reciprocal charge transport relies on the optimization of the internal polarization/electrical field as well as the tunability of the Fermi level 4,5, 21,22 . Accordingly, with appropriate design of heterostructures, the band bending at the interface can introduce the built-in electric field that ensures strong Rashba-type spin-orbit interaction, and the well-developed quantum well also helps to confine the electron conduction within the two-dimensional channel (i.e., which secures a long phasecoherent/scattering length). In addition, such band engineering allows for the direct modulation of the Rashba SOC strength and the Fermi level through the gate bias, which may cultivate versatile voltage-controlled nonreciprocal functionalities.
Inspired by the above design rules, in this work, we demonstrate the use of the InSb/CdTe heterostructures to achieve the electric field control of non-reciprocal charge transport up to room temperature. As illustrated in Fig. 1a, the integration of the narrow-bandgap InSb thin film with the wide-bandgap CdTe buffer layer takes full advantages of the type-I hetero-junction with a large conduction band offset of EC = 0.31 eV to generate strong built-in electric field and Rashba coefficient, both of whose values hold the record among reported III-V semiconductor-based heterostructures. Moreover, the nearly identical lattice constants between the two adjacent layers guarantee the formation of an atomically-sharp interface so that the spin-polarized electrons can move through with high carrier mobility. As a result, the giant Rashba field-induced spin splitting energy installed in the InSb/CdTe system gives rise to the enhanced unidirectional magnetoresistance and a gate-tunable non-reciprocal coefficient  in the entire temperature range of 1.5 K < T < 298 K. Our observations showcase the importance of the heterostructure engineering on preserving the non-reciprocal responses at room temperature, and offer feasible strategies for energy-efficient spin-state manipulation.

Results and Discussion
Giant Built-In Electric Field in InSb/CdTe Heterostructures. Experimentally, high-quality InSb/CdTe thin films were grown on the 3-inch semi-insulating GaAs (111)B wafer by molecular beam epitaxy (MBE) 24 , and detailed growth information and sample characterizations are discussed in Supplementary Fig. S1. Figures 1b reveals the cross-sectional high-angle annular dark field (HAADF) profile of the as-grown sample which confirms the absence of macroscopic threading dislocations in the examined region. Meanwhile, the structural characteristics near the InSb/CdTe junction are visualized by the atomic-resolution X-ray energy dispersive spectroscopy (EDS) mapping in Fig. 1c. It is clearly seen that all the [In, Sb, Cd, Te] atoms rigorously follow the zinc-blende configuration along the [111] direction, and the defect-free hetero-interface is well-defined with negligible inter-mixing among the constituent elements, hence validating the epitaxial growth of the single-crystalline heterostructures. Furthermore, the built-in electric field due to the interfacial band bending is quantified through the off-axis electron holography. Owing to the non-magnetic property of the InSb/CdTe sample, the phase shift of the incident electron beam is only affected by the electric field signal inside the sample. Therefore, the distribution of the internal electric potential is attained from the relevant phase diagram (see Supplementary Fig. S2) 25 . As emphsized in Fig. 1d, the peak position of the electric field is indeed found to locate at the InSb/CdTe interface, and its corresponding maximum intensity (Emax = 0.13 Vnm 1 at T = 298 K) is much higher than both the conventional GaAs/AlxGa1-xAs quantum wells (0.015 ~ 0.045 Vnm 1 ) and the InAs/GaSb superlattice (0.08 Vnm 1 ) 26 . In the meantime, the full width at half maximum (FWHM) of the electric-field spectrum is about 8 nm, and the electric potential energy difference of 0.3 eV is obtained by integrating the electric field within the hetero-junction region. These results are in a good agreement with the band diagram simulated by technology computer-aided design (TCAD) 27 , again validating the existence of the giant Rashba effect in the lattice-matched InSb/CdTe system.

Room-Temperature Rashba-Type Unidirectional
Magnetoresistance. From our previous study, we have detected distinct spin-torque ferromagnetic resonance (ST-FMR) signals from the hybrid Py-InSb/CdTe films at T = 298 K 28 , which suggest productive spin polarization in the InSb/CdTe channel up to room temperature.
To further investigate the inversion asymmetry-related effects, we performed angular-dependent magnetotransport measurements on the m-size six-probe Hall-bar device patterned from the MBE-grown InSb(30 nm)/CdTe(400 nm) sample (see Methods). Given that the interfacial Rashba SOC-induced pseudo-magnetic field Beff is tightly locked to the product of the momentum operator and the built-in electric field (i.e., = ⋅ ( ×̂)), it would influence the in-plane spin-dependent scattering. In this regard, by applying the lowfrequency AC current I = I0sin(t) along the +x direction while rotating the external magnetic field in the xyplane (i.e., the angle between B and I is defined as ), the 2 nd -harmonic components of both the longitudinal ( 2 ) and vertical ( 2 ) voltages were recorded using the standard lock-in technique. Figure  To understand the interplay between the Rashba-type spin splitting and  UMR 2 ( , ), it is firstly recalled that the Fermi level position within the InSb/CdTe junction region resides above the conduction band 6 of InSb (see Supplementary Fig. S4) 27,29 . By applying the current along the +x-axis, the interfacial conducting electrons are spin-polarized toward the +y direction, and the 2D Rashba Hamiltonian under an in-plane magnetic field is thus given by: where ℏ is the reduced Planck constant, * = 0.03 me is the electron effective mass 30 , = 42 is the inplane g-factor 31,32,33 , is the Bohr magneton, and the Rashba coefficient R = 0.4 eVÅ is deduced from the weak anti-localization data 17 . In reference to such database, a semi-empirical energy band dispersion with | R | = 9 meV and Δ = = 34 meV is shown in the top panel of toward the x direction. Consequently, a high (low) resistance state is expected when the magnetic field is parallel (anti-parallel) to the spin polarization direction, consistent with the UMR results of Fig. 2b.
Additionally, it is noted that ∆ UMR 2 evolves non-monotonously from T = 1.5 K to 298 K (inset of Fig. 2b curves exhibit sinusoidal angular dependence with a period of 360, and the normalized peak amplitude ratio of ∆ UMR 2 ( )/∆ UMR 2 ( = 90°) follows the sin relation (Fig. 3d). Comparing with the in-plane reference data re-captured from Fig. 2b (red line), we may conclude that the non-reciprocal response in our sample mainly stems from the two-dimensional conduction channel at the hetero-interface where the spinmomentum locking nature of the Rashba effect only produces spin polarization strictly orthogonal to × (i.e., counter-clockwise spin chirality of the outer branch in the k-space), and there is no out-of-plane spin component since the UMR 2 contours in the xy and yz-planes are identical to each other (Fig. 3a). Besides, we have also carried out the angular-dependent second-order harmonic measurements on a series of Hall-bar devices fabricated along different crystal orientations, and the same obtained UMR results disclose the isotropic feature of the energy band (see Supplementary Fig. S5).
In order to evaluate the strength of the non-reciprocal charge transport, here we choose the non-reciprocal  (Fig. 4a). The gate-dependent UMR results of the fabricated device at T = 1.5 K are presented in Fig.   4b. By changing the gate voltage (Vg) from -4 V to 6 V, the normalized norm 2 = UMR 2 ( g ) curves all retain the original sin line-shape while the non-reciprocal amplitude  UMR 2 ( g ) successively shrinks from 0.67  to 0.47  (i.e., 40% gate-voltage modulation efficiency), and the same negatively-correlated norm − g trend can be observed from 1.5 K up to 298 K, as shown in Fig. 4c.
According to the TCAD-simulated spatial distribution profile of the electron density across the Al2O3/InSb/CdTe structure (Fig. 4d), it is seen that the top-gate configuration enables a highly-effective charge InSb/CdTe device, hence making the gate-voltage modulation less effective at higher temperatures (Fig. 4c).
In addition to the UMR effect arisen from the second-order charge current, the first-order anisotropic magneto-resistance (AMR) of our InSb/CdTe heterostructures also unveils a unique gate-dependent trait. As identified in Fig. 4e, the AMR amplitude of the Al2O3(50 nm)/InSb(30 nm)/CdTe(400 nm) device gets boosted significally with the increase of the applied gate voltage (i.e., corresponding to the transition from the twodimensional hetero-junction conduction to the bulk InSb transport). Concurrently, more pronounced AMR signals are also discovered in thicker InSb samples (see Supplementary Fig. S6), which implis the origin of this W-shape AMR effect may be associated with the bulk property of the InSb(111) material [36][37][38][39][40] .

Conclusion
In conclusion, we have investigated the non-reciprocal magneto-transport phenomenon induced by the interfacial Rashaba SOC in the InSb/CdTe heterostructures. The achievements of large Rashba coefficient, long phase-coherent length, and adjustable Fermi energy altogether contribute to the remarkable UMR response whose coefficient ~0.52 −1 −1 is well-maintained up to room temperature. Furthermore, the systematic angular-and gate-dependent measurements not only manifest the isotropic spin-momentum locking energy band with and in-plane counter-clockwise spin texture, but also excel at salient gate-controlled capability on tuning the UMR (InSb/CdTe hetero-junction transport) and AMR (InSb bulk conduction) components. Our results highlight the indispensable role of band engineering on strengthening the spin-orbit interaction, and the lattice-matched material integration concept may set up a general framework for the design of gate-controllable low-power spin-orbitronics applications.

Sample Growth and structural characterization. The InSb/CdTe heterostructures growth was carried out
in an ultra-high vacuum DCA dual-chamber MBE system with the base pressure of 3  10 -11 Torr. Semiinsulating ( > 10 6 •cm) 3-inch GaAs (111) B wafers were pre-annealed in the growth chamber at up to 570 C in the Te-protected environment to remove the native oxide. Subsequently, a two-step growth procedure was adopted for the CdTe growth with relatively low growth rate of 1.1 Ås -1 to obtain a smooth surface morphology. After a moderate post-annealing at 355 C, the CdTe film was exchanged onto another substrate holder and later transferred in the III-V chamber. For the subsequent InSb layer growth, the substrate temperature was kept at 300 C and the growth rate was fixed as 3.5 Ås -1 . During the entire epitaxial growth, the beam flux monitor was used to calibrate element flux rate and in-situ RHEED was applied to monitor the real-time growth conditions. After sample growth, atomic force microscopy(AFM) were performed to observe surface morphology of as-grown InSb/CdTe sample. In addition, XRD and HRSTEM were applied to check crystal phase and quality.      Unlike the norm 2 − g behavior, the AMR amplitude gradually enlarges as Vg changes from 4 V to 6 V, reflecting a different mechanism related to the InSb bulk property.