Abstract
Robustness to disorder is the defining property of any topological state. The ultimate disorder limits to topological protection are still unknown, although a number of theories predict that even in the amorphous state a quantized conductance might yet reemerge. Here we report that in strongly disordered thin films of the topological material Sb2Te3 disorder-induced spin correlations dominate transport of charge—they engender a spin memory phenomenon, generated by the nonequilibrium charge currents controlled by localized spins. We directly detect a glassy yet robust disorder-induced magnetic signal in films free of extrinsic magnetic dopants, which becomes null in a lower-disorder crystalline state. This is where large isotropic negative magnetoresistance (MR)—a hallmark of spin memory—crosses over to positive MR, first with only one e2/h quantum conduction channel, in a weakly antilocalized diffusive transport regime with a 2D scaling characteristic of the topological state. A fresh perspective revealed by our findings is that spin memory effect sets a disorder threshold to the protected topological state. It also points to new possibilities of tuning spin-dependent charge transport by disorder engineering of topological materials.
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Introduction
Electronic disorder1 and elementary excitations in quantum condensed matter are fundamentally linked and it is well established that spatially fluctuating potentials tend to promote decoherence and localization of fermions, i.e., the formation of Anderson insulators2. The interplay of interactions and disorder often leads to new quantum behaviors; disorder typically boosts interparticle correlations both in charge and in spin channels, and that could either aid or suppress the motion of charge3. Spin effects related to disorder are particularly important when spin-orbit coupling (SOC) is strong4, and when spin-dependent charge transport can be electrically manipulated for uses, e.g., in spin-based electronics5.
Strong SOC is a hallmark of three-dimensional (3D) topological insulators6, where 2D gapless spin-polarized Dirac surface states are robust against backscattering. Most topological materials are known to contain a natural population of charged defects7 that do not cause a destruction of the topological Dirac states; indeed, they can be compensated8, although Dirac puddle disorders9 may remain. Under weak disorder, a coherent interference of electron waves survives disorder averaging10, and strong SOC enhances conductivity by a quantum weak antilocalization (WAL) correction related to the topological π-Berry phase6 when magnetic impurities are absent. With increasing disorder the 2D WAL channels can be outnumbered by the weak localization (WL) channels11—this is a precursor of Anderson localization2, which occurs at strong disorder. Under strong disorder, theory and numerical simulations12,13,14 predict an emergence of a new topological state, dubbed ‘topological Anderson insulator’, in which conductance G0 = e2/h is quantized. Indeed, recent theoretical demonstrations of topological phases in amorphous systems15 point to promising new possibilities in engineered random landscapes. Strong disorder, however, is not trivial to install, quantify and control, and topological matter under such conditions has not yet been experimentally tested.
Here we implement an extensive range of site disorder—from amorphous to crystalline state—in Sb2Te3, the material which is a known second generation topological insulator16,17, and report that under strong structural and electronic disorder conditions dynamic spin correlations dominate charge transport over a surprisingly large range of magnetic fields. These correlations imprint spin memory on the electrons hopping via localized spin sites. Predicted to be small18 and thus practically unobservable in the conventional materials, the effect found here is large; it persists over a surprisingly wide range of disorder and well within the disordered crystalline topological phase, as long as variable range electron hopping (VRH)19 is at play. It eventually transitions into the characteristic 2D WAL regime when a conductance channel quantized to G0 = e2/h, characteristic of the topological state, is established. The spin memory uncovered in this work is not an orbital effect; it is isotropic (3D) and thus distinctly different from the 2D conductance enhancement by the WL interference effects observed in the magnetically doped topological insulators20. It originates from the presence of disorder-induced localized spins3 and, as witnessed by the characteristically non-analytic negative magnetoresistance (neg-MR), is governed by the distribution of very large spin g-factors that widens with decreasing localization length ξ in a way akin to an assembly of quantum wells21.
Results
Magnetotransport under strong disorder
The experiments were performed on 20-nm thin films of Sb2Te3, in which extreme positional disorder (amorphous state) is possible to obtain without finetuning the deposition parameters (Supplementary Note 1). Sb2Te3, in addition to being a canonical topological material16 in a crystalline state, is also a well known phase-change material (PCM)22 (Supplementary Fig. 1), that undergoes amorphous-to-crystalline transformation with the concurrent orders-of-magnitude resistive drop, and hence a huge range of disorder and its effect on the topological properties could be controllably explored.
Our first key finding is shown in Fig. 1a. The change in the longitudinal magnetoresistance ΔRxx in the amorphous Sb2Te3 films at low magnetic fields is with a remarkable fidelity impervious to the tilt of magnetic field. It is relatively large and negative (i.e., charge transport becomes less dissipative with increasing field) up to a field \({H}_{\max }\) (Fig. 1a and Supplementary Fig. 2). The as-deposited films are highly resistive and obey Anderson scaling1 (Fig. 1b) consistent with electron localization (Supplementary Note 2), which can be induced either by increasing system size for fixed disorder or decreasing disorder for fixed system size. Robust in 3D, such scaling is marginal in 2D unless there is a strong SOC, hence a 2D localization in our thin films is not precluded. The field isotropy of the low-field dissipation ‘quench’ naturally suggests a spin-dominated 3D mechanism rather than orbital effect, and so the pertinent question to ask is how such behavior can proceed in a system where electronic states are localized and the extrinsic spinfull impurities are absent (see Supplementary Table 1).
Direct detection of ‘glassy’ magnetic signal
To start we note that in the presence of disorder a finite population of singly occupied states below the Fermi energy EF has been discussed as long as 20 years back by Sir Neville Mott3. Magnetic response from randomly localized spins in such ‘Fermi glass’ state was expected to be weak and, as far as we know, has never been experimentally demonstrated. So our second surprising finding was a very robust magnetic signal from the disordered Sb2Te3 films directly detected using a custom-designed μHall sensors (Fig. 1c, d), with the thin film flakes mechanically exfoliated from their substrates and transferred onto the active sensor area (“Methods”, Supplementary Fig. 3, Supplementary Note 4). We surmise that here the observed effective moment per atom is significantly amplified by the large effective Landé g-factor4 in Sb2Te3, where SOC is strong16. The detected signal depends on the magnetic history (field-cooling vs. zero-field cooling), which, together with slow magnetic relaxation (Supplementary Fig. 3c) reflects a glassy nature of the localized state. We emphasize that magnetic signal crucially depends on the level of disorder; indeed, it becomes barely detectable in the crystalline phase as disorder in the same film is reduced by thermal annealing (Fig. 1d).
Spin memory effect
Under strong disorder charge transport is a complex electron hopping process that at low temperatures proceeds via quantum tunneling between localized states assisted by phonons10,19. While considerations of magnetotransport have mainly focused on the orbital effects, a recently proposed idea18 takes note of putative nonequilibrium spin correlations in the localized regime created by the flowing current when electron hopping times τ are short relative to the spin relaxation times τs. These time scales determine the magnetic field range over which spin-correlation-driven neg-MR (positive magnetoconductance) ought to be present.
The idea is illustrated in Fig. 1e. When the current is injected, an electron with spin S attempting to hop to an available empty site can do it in two ways: directly or via an intermediate site occupied by a localized spin s. It may take several attempts for the indirect hops to succeed and the return probability will depend on history, i.e., on whether the tunneling electron can form a triplet or a singlet state with s. For example, in the absence of disorder a triplet state would remain so in the presence of applied magnetic field and no reduction of magnetoresistance (increase of magnetoconductance) is expected. Under strong disorder (such as shown in Fig. 1b), however, spin g-factors will be spatially random so that localized spins at different sites will precess incoherently and spin correlations will be destroyed by the field. Accordingly, in a simple model18 the change in magnetoconductance ΔGxx arising from such spin correlations should follow not a power law25 but a unique non-analytic form:
where \(A=\frac{{G}_{{\rm{xx}}}(H\;\to\;\infty )\,-\,{G}_{{\rm{xx}}}(0)}{{G}_{{\rm{xx}}}(0)}\), ds = 4/3 is the spectral dimension of the percolation cluster26 (which is the relevant dimension in the hopping process), l is an index for the diffusing spin, \(\Gamma (-\frac{{d}_{{\rm{s}}}}{2})\) is the gamma function ≅ −4, and \({H}^{\star \star }=\frac{\hslash }{{\mu }_{{\rm{B}}}\tau \Delta g}\) is the limiting magnetic field range set by the hopping rate 1/τ and the disorder-induced spread Δg of spin g-factors.
The strongly localizing behavior we observe in the longitudinal resistance Rxx (Fig. 2a) at low temperatures (below ~10 K) follows variable range hopping (VRH) law \({R}_{{\rm{xx}}}(T)={R}_{0}\exp {(\frac{{T}_{0}}{T})}^{1/2}\) of Efros-Shklovskii (E-S) kind10, see Fig. 2b. The E-S energy scale T0 characteristic of the hopping process (Supplementary Fig. 1b) is tracked on decreasing disorder by a well controlled thermal annealing schedule (“Methods”); it is inversely proportional to the electron localization length19ξ, which we will show controls the g-factor distribution width Δg. We remark that in this regime (at low T) the detected magnetic moment appears ‘flat’ in temperature (Fig. 1d).
In the VRH regime, the fit of conductance to Eq. (1) for two states of disorder is illustrated in Fig. 2c. As seen in the figure, at low magnetic fields the characteristic non-analytic behavior is accurately followed; here the ratio of hopping time to spin relaxation time τ/τs and the hopping field scale H⋆⋆ were used as fitting parameters (“Methods”). The fits at different disorder levels controlled by the anneals at different temperatures Ta are shown in Supplementary Fig. 4. The ratio τ/τs strongly depends on the level of disorder (Fig. 2d), with the hopping and spin relaxation rates, 1/τ ∝ H⋆⋆ and 1/τs ∝ Hs, in close correspondence with the disorder dependence of Rxx all the way through crystallization transition. The hopping time τ can be independently extracted from the E-S energy (Supplementary Fig. 5a), and, as expected for the hopping conductivity τ increases exponentially on decreasing temperature (Supplementary Fig. 5b). This allows us to consistently obtain the evolution of spin-relaxation time τs (Fig. 2e) and Δg (Fig. 3a) with decreasing disorder (increasing Ta), and hence that of the low-field spin-relaxation scale \({H}_{{\rm{s}}}=\frac{\hslash }{{\mu }_{{\rm{B}}}{\tau }_{{\rm{s}}}\Delta g}\) (Supplementary Fig. 6); Hs marks a crossover from the concave-up field shape associated with τs to concave-down behavior at higher fields, see Fig. 2c.
An intriguing question arises as to what controls the unexpectedly large (Tesla-range) field scale where neg-MR, the hallmark of dynamic spin memory, is found. For the systems with small spin-orbit coupling where g-factor ~2, the expected field range would be in the 10−4–10−5 Tesla range. In theory18, this range is set by the competition between the magnetic energy gμBH and either thermal energy or the exchange J between neighboring spins—it ought to be well below the competing effects. Here, however, with large effective g value27, gμBH/kB ~ 20 K is comparable to the spin-memory range. This brings us back to disorder-induced spin correlations. Fig. 1d shows that under extreme disorder the onset of magnetic response is rather abrupt and at a remarkably high temperature Ts ~200 K. While the details of spin correlations in this Anderson-like-localized glassy state clearly deserve further experimental and theoretical studies, a rough estimate of J ~ kBTs/z ≈ 70 K, using local coordination number22 z ~3 expected in Sb2Te3, implies that here short range interactions between localized spins play the key role.
Large fluctuations of Landé g-factors
Let us now consider g-factor fluctuations in a strongly disordered state. The g distribution width naturally arising from our magnetoconductance data (Fig. 3a) within the model considered above is spectacularly wide at the highest level of disorder, Δg ≃ 40; it exceeds the effective g value of ~30 obtained, e.g., directly in the same topological insulator family from the electron spin resonance (ESR) experiments27. Such large g spread is uncommon but not unprecedented. Giant fluctuations of g-factors have been reported in, e.g., InAs nanowires where Δg > ∣geff∣ and the effective factor ∣geff∣ is also large24. Furthermore, in semiconducting quantum wells ∣geff∣ has been known to increase roughly linearly21 with quantum confinement energy EQ as ∣geff∣ ≃ g0 + βEQ, where β is a material-specific constant. Here we propose that in the strongly localized state (Supplementary Note 2), quantum confinement is enforced by the wells constrained by the localization length ξ (Fig. 3b). In this view, a simple particle-in-a-box approximation gives EQ ∝ ξ−2 that indeed fully scales with Δg (Fig. 3a). The expected linear ∣geff∣ vs. EQ would then set ∣geff∣ ~ Δg−α with α ~ 0.1, with ∣geff∣ approaching the ESR-determined value in the unconfined state, see Fig. 3c.
Mapping spin memory phase space
Our experiments reveal how positive ΔGxx(H) (neg-MR) evolves with decreasing disorder; it persists over a spectacularly large disorder range, all the way through the crystallization process and beyond (Fig. 4a). The large limiting field range set by \({H}_{\max }\) at strong disorder falls with increasing Ta (Fig. 4b) to pinch off ΔGxx(H) eventually to null. A clear visual of the field-disorder phase space is shown in Fig. 4c, where the strength of disorder is represented by EQ. H − EQ diagram shows that spin-memory region is restricted by H⋆⋆ to relatively low fields, but when the system is less localized the ‘envelope’ of the spin-memory space switches to \({H}_{\max }\).
The temperature range over which spin memory is evident is set by the VRH process (Fig. 2b), with ΔGxx(H) well described by Eq. (1). Above ~10 K, outside the VRH region, ΔGxx(H) becomes nearly ‘flat’ (Fig. 4d); there both τs (Supplementary Fig. 7a) and ∣geff∣ (see Supplementary Fig. 7b) appear to saturate, and spin-memory phenomenon is not expected. The typical field scale associated with the E-S energy T0 ~ 10–30 K is in the 1–2 T range, in close correspondence with H⋆⋆ at low T. As before, \({H}_{\max }\ncong {H}^{\star \star }\), and in the low-temperature localized state \({H}_{\max }\) becomes the limiting crossover field (Fig. 4e). Above Ta ≃ 180 ∘C (EQ ≈ 60 meV), in the strongly disordered crystalline state spin memory phenomenon is not detectable.
Transition to a 2D weak antilocalization regime
The exit from the spin-memory state at ≅180 ∘C is clearly evidenced by a transition from the negative MR (neg-MR) to a positive MR (pos-MR) ‘cusp’ characteristic of the WAL state (Fig. 5a). The WAL cusp29 scales with the transverse component of applied magnetic field \({H}_{\perp }=H\cos \theta\) (Fig. 5b), consistent with the 2D (orbital) character expected in a topological insulator8 under weak disorder. This 2D scaling should be contrasted with isotropic (3D) scaling of the neg-MR peak in the spin-memory state. Thus, unlike the WL-WAL transition driven by magnetic impurities20, the transition from spin-memory onto a WAL state is also a 3D-2D dimensionality transition at which the electron system rapidly delocalizes. We remark again that WAL onsets at ≃180 ∘C, way above the crystallization temperature of ≃140 ∘C (see inset in Fig. 5c), pointing to a disorder threshold for the gapless topological state.
Discussion
The emergence of WAL in the diffusive transport regime3 should be reflected in the evolution of the electron localization length ξ. Figure 5c shows that with increasing Ta, ξ first experiences a ’kink’ at the first order crystallization transition22. However, its largest change—an increase by orders of magnitude—initiates at the onset of WAL. We note that the electron mean free path is only limited by the film thickness and the grain size in the crystalline state at high Ta (Supplementary Fig. 8).
To translate Ta into a disorder energy scale WD12 we use the annealing evolution of the full-width-half-max (FWHM) of the in-plane Raman \({E}_{{\rm{G}}}^{2}\) mode (Fig. 5c and Supplementary Fig. 1) as a metric of disorder30. A simple phenomenological scaling is derived by setting maximum disorder in the amorphous state at the energy corresponding to the bulk gap EG ~200 meV16 in the crystalline state and minimum disorder (at the highest Ta) to zero (Fig. 5d, Supplementary Note 11, and Supplementary Fig. 9). When the angular field-dependence of magnetoresistance ΔR is plotted as a function of WD (Fig. 5d), the 3D-2D transition from the spin-memory state to WAL at a surprisingly low (\({W}_{{\rm{D}}}^{{\rm{2D}}} \sim 10\ {\rm{meV}}\)) disorder level is strikingly apparent. Figure 5e shows that at \({W}_{D}^{2D}\) the low-temperature longitudinal conductance Gxx is with good precision equal to one conductance quantum \({G}_{0}=\frac{{{\rm{e}}}^{2}}{h}\). This suggests that at the transition only one topological channel is present. To test this we fit the field dependence of the WAL conductance to 2D localization theory28 of Hikami, Larkin and Nagaoka (HLN)
where f(x) ≡ lnx − ψ(1/2 + x), ψ is the digamma function, and field \({B}_{\phi }=\frac{\hslash }{4e{l}_{\phi }^{2}}\) is related to the dephasing length lϕ of interfering electron paths (Supplementary Note 12, Supplementary Fig. 10). The number nQ of quantum conduction channels contributing to WAL can be estimated from the coefficient α = nQ/2, which equals to 1/2 for a single 2D channel. The plot of α (insert in Fig. 5e) indeed confirms that maximum α ≅ 1/2 is at Ta ≅ 180 ∘C corresponding to \({W}_{{\rm{D}}}^{{\rm{2D}}}\) (see Supplementary Fig. 10a). The decrease of α at lower disorder is likely due to increased conductivity of the 2D electron gas states of bulk origin11.
To summarize, we directly detect a glassy spin response from thin films of Sb2Te3 under strong structural disorder, which vanishes in the same film when disorder is sufficiently reduced. Under strong disorder, the system develops spin-correlations that drive the spin-memory phenomenon controlling the transport of charge, with the key features well captured by a simple phenomenology. Both in magnetic field and in disorder strength, the parameter space where spin memory exists is unexpectedly broad—it persists well into a disordered crystalline state where, eventually, a 2D WAL quantum interference correction is recovered. We remark that in Sb2Te3 electron correlations at the transition are weak in the Mott sense3; taking the carrier density n ≲ 1020 cm−3 (Supplementary Fig. 8b) and Bohr radius aB ~ 60 nm31 we obtain n1/3aB ≃ 28, more than ~100 times the Mott criterion of 0.25. Strong charge screening in Sb2Te3 (large dielectric constant ϵ ~ 17031) renders the Coulomb energy (EC ≃ 4 meV) much smaller than the Fermi energy (EF ≃ 260 meV); with EC ≪ EF this points to the transition to be disorder-driven32.
Our findings show that spin-memory effect sets a disorder threshold at which topological protection of the surface states is reclaimed, although bulk channels may still contribute. Direct measurements of glassy spin response in materials other than Sb2Te3 are yet to be carried out; it is clear, however, that for spin memory the spin-lifetime τs has to be much longer than the hopping time τ. We expect spin memory to be visible in a broader family of strong SOC materials; it has been reported in SnSb2Te433, where crystal (and defect) structure is different34. The electrical control of this spin-dependent transport can, in principle, be achieved through electrostatic gating35, and by locally modifying spin correlations using currently practiced doping techniques.
Methods
Film growth and structural characterization
Films of Sb2Te3 with thicknesses ranging from 20 to 100 nm were sputter-deposited at room temperature in Ar gas at 4 mTorr and a flow of 46 sccm from a nominally stoichiometric target using 15 W DC power on Si3N4 (100 nm)/Si substrates. The stoichiometry was confirmed by Rutherford Backscattering (RBS) and particle induced X-ray emission (PIXE). RBS data were collected at NEC 3UH Pelletron using a Si surface barrier detector with He+ ions at 2.3 MeV. PIXE data was collected using a Si-Li detector with H+ ions at 1 MeV. Elemental analysis was done at Evans Analytical Group. X-ray diffraction characterization was performed using Bruker D8 Discover system with the da Vinci configuration using a monochromated beam (λCu = 1.5418 Å) and a scintillator detector with analyzer crystal (HR-XRD). The film morphology was characterized using the FEI Titan Themis 200 transmission electron microscope (TEM), 200 kV, with TEM resolution 0.9 Å and 4 k × 4 k Ceta 16 M CMOS camera. Disorder was characterized by Raman spectra using 633 nm linearly polarized excitation in a backscattering configuration30, with power kept below 2 mW to avoid heating effects.
Magnetic measurements
Magnetic measurements were performed using custom-designed on-chip μ-Hall sensors based on In0.15Ga0.85As heterostructures (SI). To measure magnetization, ~50 μm in lateral size thin Sb2Te3 film samples were exfoliated from their substrates and placed directly on the SiO2-passivated sensor using PDMS. At each temperature an empty twin sensor was used for background subtraction.
Transport measurements
Transport measurements were performed in a 14 Tesla Quantum Design PPMS system in 1 mTorr of He gas on many film samples, each subjected to the same annealing protocol used to tune the level of disorder. Lithographically patterned structures combining both Hall bar and van der Pauw electrical contact configurations with Ti/Au metallurgy were used (Fig. 2a). Measurements were performed on as-deposited films and on the same films after each 5 min annealing step in a box furnace in flowing nitrogen in the temperature range across crystallization at Ta ~ 140 ∘C. We used a numerical Monte Carlo technique to fit our transport data to Eq. (1).
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Abrahams, E., Anderson, P., Licciardello, D. & Ramakrishnan, T. Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979).
Evers, F. & Mirlin, A. Anderson transitions. Rev. Mod. Phys. 80, 1355–1417 (2008).
Mott, N. Metal-insulator Transitions (Taylor & Francis, New York, 1997).
Winkler, R. Spin-Orbit Coupling Effects in Two-dimensional Electron and Hole Systems (Springer-Verlag, Berlin-Heidelberg-New York, 2003).
Žutić, I., Fabian, J. & DasSarma, S. Spintronics: fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004).
Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Scanlon, D. et al. Controlling bulk conductivity in topological insulators: key role of anti-site defects. Adv. Mater. 24, 2154–2158 (2012).
Zhao, L. et al. Stable topological insulators achieved using high energy electron beams. Nat. Comm. 7, 10957 (2016).
Beidenkopf, H. et al. Spatial fluctuations of helical Dirac fermions on the surface of topological insulators. Nat. Phys. 7, 939–943 (2011).
Gantmakher, V. In Electrons and Disorder in Solids (Clarendon Press, Oxford, 2005).
Zhang, L. et al. Weak localization effects as evidence for bulk quantization in Bi2Se3 thin films. Phys. Rev. B 88, 121103 (2013).
Li, J., Chu, R.-L., Jain, J. & Shen, S.-Q. Topological Anderson insulator. Phys. Rev. Lett. 102, 136806 (2009).
Groth, C., Wimmer, M., Akhmerov, A., Tworzydło, J. & Beenakker, C. Theory of the topological Anderson insulator. Phys. Rev. Lett. 103, 196805 (2009).
Guo, H.-M., Rosenberg, G., Refael, G. & Franz, M. Topological Anderson insulator in three dimensions. Phys. Rev. Lett. 105, 216601 (2010).
Mitchell, N. P., Nash, L. M., Hexner, D., Turner, A. M. & Irvine, W. T. M. Amorphous topological insulators constructed from random point sets. Nat. Phys. 14, 380–385 (2018).
Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3, and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 5, 438–442 (2009).
Zhao, L. et al. Singular robust room-temperature spin response from topological Dirac fermions. Nat. Mater. 13, 580–585 (2014).
Agam, O., Aleiner, I. & Spivak, B. Spin-memory effect and negative magnetoresistance in hopping conductivity. Phys. Rev. B 89, 100201 (2014).
Shklovskii, B. & Efros, A. Electronic Properties of Doped Semiconductors (Springer-Verlag, Berlin, 1984).
Liu, M. et al. Crossover between weak antilocalization and weak localization in a magnetically doped topological insulator. Phys. Rev. Lett. 108, 036805 (2012).
Chen, Z., Carter, S., Bratschitsch, R., Dawson, P. & Cundiff, S. Effects of disorder on electron spin dynamics in a semiconductor quantum well. Nat. Phys. 3, 265–269 (2007).
Shakhvorostov, D. et al. Evidence for electronic gap-driven metal-semiconductor transition in phase-change materials. Proc. Natl Acad. Sci. USA 106, 10907–10911 (2009).
Singh, J. Effective mass of charge carriers in amorphous semiconductors and its applications. J. Non-Cryst. Solids 299-302, 444–448 (2002).
Csonka, S. et al. Giant fluctuations and gate control of the g-factor in InAs nanowire quantum dots. Nano Lett. 8, 3932–3935 (2008).
Ioffe, L. & Spivak, B. Giant magnetoresistance in the variable-range hopping regime. J. Exp. Theor. Phys. 117, 551–569 (2013).
Havlin, S. & Ben-Avraham, D. Diffusion in disordered media. Adv. Phys. 51, 187–292 (2002).
Woloś, A. et al. g-factors of conduction electrons and holes in Bi2Se3 three-dimensional topological insulator. Phys. Rev. B 93, 155114 (2016).
Hikami, S., Larkin, A. & Nagaoka, Y. Spin-orbit interaction and magnetoresistance in the two-dimensional random system. Prog. Theor. Phys. 63, 707–710 (1980).
Garate, I. & Glazman, L. Weak localization and antilocalization in topological insulator thin films with coherent bulk-surface coupling. Phys. Rev. B 86, 035422 (2012).
Secor, J. et al. Phonon renormalization and Raman spectral evolution through amorphous to crystalline transitions in Sb2Te3 thin films. Appl. Phys. Lett. 104, 221908 (2014).
Heremans, J., Cava, R. & Samarth, N. Tetradymites as thermoelectrics and topological insulators. Nat. Rev. Mater. 2, 17049 (2017).
Siegrist, T. et al. Disorder-induced localization in crystalline phase-change materials. Nat. Mater. 10, 202–208 (2011).
Reindl, J., Volker, H., Breznay, N. & Wuttig, M. Persistence of spin memory in a crystalline, insulating phase-change material. npj Quantum Mater. 4, 57 (2019).
Menshchikova, T., Eremeev, S. & Chulkov, E. Electronic structure of SnSb2Te4 and PbSb2Te4 topological insulators. Appl. Surf. Sci. 267, 1–3 (2013).
Sandhu, J., Heberle, A., Baumberg, J. & Cleaver, J. Gateable suppression of spin relaxation in semiconductors. Phys. Rev. Lett. 86, 2150–2153 (2001).
Acknowledgements
We thank Igor Aleiner and Boris Spivak for their useful comments. We wish to acknowledge Roland Winkler for his key insights regarding g-factors. We are grateful to Andy Kellock for the RBS and PIXE analysis of the films. This work was supported by the NSF grants DMR-1312483-MWN, DMR-1420634, and HRD-1547830 (L.K.-E.).
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Experiments were designed by L.K.-E., I.K., and S.R. grew Sb2Te3 films. I.K. performed structural characterization. I.K., L.Z., and Z.C. fabricated devices for transport measurements performed by I.K., H.D., and Z.C. M.K. designed Hall-sensors for magnetic measurements performed by L.Z. and S.Z. Data analysis was done by I.K., H.D., L.Z., Y. D., and L.K.-E. L.K.-E. wrote the manuscript with input from I.K., H.D., and L.Z.
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Korzhovska, I., Deng, H., Zhao, L. et al. Spin memory of the topological material under strong disorder. npj Quantum Mater. 5, 39 (2020). https://doi.org/10.1038/s41535-020-0241-5
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DOI: https://doi.org/10.1038/s41535-020-0241-5
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