We demonstrate that measurements of the photo-electromagnetic effect using terahertz laser radiation provide an argument for the existence of highly conductive surface electron states with a spin texture in Dirac semimetals (Cd₁-xZnx)₃As

Drozdov, K. A.

Galeeva, A. V.

Knjazev, A. F.

Krylov, I. V.

Zakhvalinskii, V. S.

English

DSpace at Belgorod State University

167Electron energy relaxation under terahertz excitation in(Cd1−xZnx)3As2 Dirac semimetalsAlexandra V. Galeeva1, Ivan V. Krylov1, Konstantin A. Drozdov1, Anatoly F. Knjazev2,Alexey V. Kochura3, Alexander P. Kuzmenko3, Vasily S. Zakhvalinskii4,Sergey N. Danilov5, Ludmila I. Ryabova6 and Dmitry R. Khokhlov*1Letter Open AccessAddress:1Physics Department, M.V. Lomonosov Moscow State University,Leninskie Gory 1 bld.2, 119991 Moscow, Russia, 2Kursk ConstructionCollege, Sovetskaya str. 14, 305016 Kursk, Russia, 3South-WestState University, 50 Let Oktyabrya str. 94, 305040 Kursk, Russia,4Belgorod National Research University, Pobedy str. 85, 308015Belgorod, Russia, 5Faculty of Physics, University of Regensburg,Universitaetstr. 31, 93053 Regensburg, Germany, and 6ChemistryDepartment, M.V. Lomonosov Moscow State University, LeninskieGory 1 bld.3, 119991 Moscow, RussiaEmail:Dmitry R. Khokhlov* - khokhlov@mig.phys.msu.ru* Corresponding authorKeywords:Dirac semimetal; photo-electromagnetic effect; terahertz radiation;topological insulatorBeilstein J. Nanotechnol. 2017, 8, 167–171.doi:10.3762/bjnano.8.17Received: 27 October 2016Accepted: 06 January 2017Published: 17 January 2017This article is part of the Thematic Series "Physics, chemistry and biologyof functional nanostructures III".Guest Editor: A. S. Sidorenko© 2017 Galeeva et al.; licensee Beilstein-Institut.License and terms: see end of document.AbstractWe demonstrate that measurements of the photo-electromagnetic effect using terahertz laser radiation provide an argument for theexistence of highly conductive surface electron states with a spin texture in Dirac semimetals (Cd1−xZnx)3As2. We performed astudy on a range of (Cd1−xZnx)3As2 mixed crystals undergoing a transition from the Dirac semimetal phase with an inverse elec-tron energy spectrum to trivial a semiconductor with a direct spectrum in the crystal bulk by varying the composition x. We showthat for the Dirac semimetal phase, the photo-electromagnetic effect amplitude is defined by the number of incident radiationquanta, whereas for the trivial semiconductor phase, it depends on the laser pulse power, irrespective of wavelength. We assumethat such behavior is attributed to a strong damping of the interelectron interaction in the Dirac semimetal phase compared to thetrivial semiconductor, which may be due to the formation of surface electron states with a spin texture in Dirac semimetals.FindingsThe theoretical prediction of the existence of topological insula-tors [1,2] and their further experimental observation [3-7] haveled to the significant growth of scientific interest in this area ofresearch. Topological insulators form a class of materialspossessing a different electron energy spectrum at the surface ascompared to the bulk. The bulk energy spectrum of a topolog-Beilstein J. Nanotechnol. 2017, 8, 167–171.168ical insulator is typically observed for a semiconductor, where-as spin-polarized gapless electron states with a Dirac lineardispersion relation exist on the surface of a topological insu-lator.Recently, another topological state of matter – a Dirac semi-metal – was theoretically predicted [8] and then experimentallyobserved through the ARPES measurements in Cd3As2 [9-11].In a Dirac semimetal, the bulk conduction and valence bandsare inverted and touch each other at two points of the Brillouinzone, the Dirac points. The dispersion relation is linear in theproximity of the Dirac points in all three dimensions of themomentum space. The high Fermi velocity of the Dirac elec-trons is most likely the reason for extremely high values ofthe electron mobility observed in Cd3As2, which is up to107 cm2/(V·s) [9,11].The question concerning formation of spin-polarized surfaceelectron states in 3D Dirac semimetals remains open. Accord-ing to [9,11], the surface states of Cd3As2 do not possess anyspin texture. However, the authors do not exclude the possibili-ty that the spin-polarized surface states may be formed, but thesensitivity of the method used does not allow discriminatingthese states.In this paper, we show that there is an indirect confirmation forthe formation of spin-polarized electron states with highmobility on the surface of the Dirac semimetal solid solutions(Cd1−xZnx)3As2 with the inverted energy spectrum in the bulk.Our experimental approach is based on measurements of thephoto-electromagnetic (PEM) effect induced by terahertz laserpulses. Previously, it has been demonstrated that in the range of(Bi1−xInx)2Se3 solid solutions which exhibit a transition fromthe topological insulator phase with the inverted electronicenergy spectrum at low x to the trivial insulator with the directspectrum at higher indium content there is a substantial differ-ence in the radiation power dependence of the PEM effectamplitude for the two phases [12]. In the trivial insulator case,the PEM effect amplitude is defined by the incident radiationpower, irrespective of wavelength, whereas for the topologicalinsulator phase, it depends on the number of incident radiationquanta per unit time. In this paper, we apply this approach to thesolid solutions of Dirac semimetals (Cd1−xZnx)3As2 under-going an analogous transition from the inverted to the directspectrum in the bulk at x > 0.08 [13].The samples  under  s tudy were  s ingle  crys ta ls  of(Cd1−xZnx)3As2 grown from the vapor phase. The sample com-position was measured by energy dispersive X-ray analysis(EDA). According to the dataset available [13], the transitionfrom the inverted electronic spectrum to the direct one occurs in(Cd1−xZnx)3As2 at x ≈ 0.08. In view of that, we have selectedthree samples for detailed study. Two of them correspond to theinverted spectrum composition region x < 0.08, the third onehas x = 0.25 and has a direct spectrum. The main electrophys-ical parameters of the samples are summarized in Table 1. Allsamples were of the n-type. The free electron concentrationmeasured using the Hall effect did not change in the tempera-ture range 4.2–300 K. The resistivity temperature dependence istypical for degenerate semiconductors: the resistivity decreasewith decreasing temperature from 300 K to 20 K is followed bya further saturation at T < 20 K. Since the free electron concen-tration does not change, this resistivity variation is completelydetermined by the mobility temperature dependence. It is im-portant to note that the free electron concentration in thesamples studied differs by a factor of four. The low tempera-ture mobility absolute values are very high and exceed105 cm2/(V·s).Table 1: The values of resistivity, ρ, free electron concentration, n, andmobility, μ, for (Cd1−xZnx)3As2 samples at T = 4.2 K.x ρ, mΩ∙cm n, 1017 cm−3 μ, 105 cm2/(V∙s)0.012 0.064 1.8 5.650.045 0.157 4.0 1.010.25 0.061 3.4 3.05The main tool of the study was the measurement of the PEMeffect induced by terahertz laser pulses at the wavelengths 90and 148 μm in a magnetic field up to 3 T. The pulse power wasup to 10 kW, and the sample temperature was T = 4.2 K. Theexperimental details can be found elsewhere [12,14-19].The PEM effect manifests itself as the appearance of a voltagedecrease across the sample in the direction normal to the mag-netic field and to the incident radiation flux. The experimentalgeometry is shown in the insert of Figure 1. The effect origi-nates from the Lorentz force action to the diffusive electron fluxwhich is due to excitation of the surface layer of a sample bythe incident terahertz radiation. The voltage sign is definedsolely by the direction of the net charge carrier flux either to orfrom the surface and does not depend on the charge carrier sign.The PEM effect was observed in all samples at both laser wave-lengths used. The kinetics of the PEM effect signal follow thesignature of the time profile of the laser pulse (see insert inFigure 1). The effect occurs only under a nonzero magneticfield, and its amplitude is odd under the magnetic field. Themagnetic field dependence of the PEM effect amplitude UPEMis shown in Figure 1. For all samples, the effect is linear underlow fields B < 1.5 T with a tendency for saturation under higherBeilstein J. Nanotechnol. 2017, 8, 167–171.169Figure 1: Dependence of the PEM effect amplitude on the magnetic field B applied for (Cd1−xZnx)3As2 samples for alloy compositions x = 0.012,0.045 and 0.25. The laser wavelength was λ = 90 μm and T = 4.2 K. The experimental geometry is shown in the upper left inset. Typical shape of thelaser pulse and PEM response are shown in the lower right inset.Figure 2: (a) Dependence of the PEM effect amplitude UPEM on the incident laser radiation power P at T = 4.2 K for laser wavelengths 90 and 148μm for a (Cd0.75Zn0.25)3As2 sample in trivial insulator phase. Inset: The same data plotted as PEM effect amplitude versus number of incident quantaN. (b) Dependence of the PEM effect amplitude on the flux of incident radiation quanta N at T = 4.2 K for laser wavelengths 90 and 148 μm for a(Cd0.955Zn0.045)3As2 sample in the Dirac semimetal phase. Inset: The same data plotted as PEM effect amplitude versus incident radiation power P.The lines in the panels (a) and (b) are the guides for the eye.fields. It is important to note that the PEM effect sign corre-sponds to the net electron flux from the sample surface to itsbulk.The effect of the radiation intensity variation on the PEM effectamplitude is shown in Figure 2. For the direct spectrum samplewith x = 0.25 (Figure 2a), the effect scales up as a function ofBeilstein J. Nanotechnol. 2017, 8, 167–171.170the incident radiation power for both laser wavelengths used(the main panel), whereas the dependence of UPEM on the num-ber of radiation quanta is different for different laser wave-lengths (insert in Figure 2a). Instead, the inverse spectrum sam-ple with x = 0.045 demonstrates a completely opposite behav-ior (Figure 2b): the UPEM dependence on the number of inci-dent quanta is the same for both wavelengths (the main panel),and the UPEM dependence on the terahertz radiation powerdiverges for different wavelengths (insert in Figure 2b).As it has been shown in [12,18], the diffusive electron flux fromthe surface to the bulk of degenerate semiconductors may ariseonly as a result of formation of conductive surface electronstates with the mobility higher than in the bulk. These kind ofsurface states are apparently present both in the inverse anddirect gap phases of (Cd1−xZnx)3As2 solid solutions. The effectamplitude, however, scales up differently as a function of theincident radiation flux in the two cases. It was suggested in [12]that this difference in the case of topological insulators(Bi1−xInx)2Se3 is due to the different relation between the char-acteristic thermalization τth and diffusion τdif times of free elec-trons excited by the incident terahertz radiation. In the trivialinsulator case, τth << τdif, so the excited electrons first ther-malize and then start to diffuse, thus the effect depends on thepower absorbed. In the case of a topological insulator, thereverse relation τth >> τdif is realized, so the diffusion startsfirst, and then the number of diffusing electrons depends on thenumber of incident quanta. The thermalization of electronsexcited by the incident terahertz radiation occurs mainly via theinterelectron interaction since the optical phonon energy ishigher than the laser quantum energy used. Consequently, thestrong enhancement of the thermalization time in topologicalinsulators compared to the trivial insulators is likely to result inthe reduction of the number of electrons that interact effec-tively with a given one. As it was suggested in [12], this reduc-tion may be due to the locking of the spin direction to themomentum direction of surface electron states in topologicalinsulators. Therefore, the surface electrons may effectivelyinteract only with other electrons possessing the same spin and,respectively, the momentum direction, and not with the wholeFermi sphere, as in the case of trivial insulators. Therefore, thisenhancement of the thermalization time is an indication of theappearance of the spin texture of surface electron states. Theresults of the present experiment demonstrate that this kind ofspin texture appears not only in topological insulators, but in theDirac semimetals as well.In conclusion, we have demonstrated through the measure-ments of the photo-electromagnetic effect that the thermaliza-tion time is strongly enhanced in the Dirac semimetals(Cd1−xZnx)3As2, which is an indirect confirmation for forma-tion of spin-polarized highly conductive electron states at theirsurface.AcknowledgementsThe research described in this paper was supported by the grantof the Russian Science Foundation #16-12-10071.References1. Kane, C. L.; Mele, E. J. Phys. Rev. Lett. 2005, 95, 146802.doi:10.1103/PhysRevLett.95.1468022. Fu, L.; Kane, C. L.; Mele, E. J. Phys. Rev. Lett. 2007, 98, 106803.doi:10.1103/PhysRevLett.98.1068033. König, M.; Wiedmann, S.; Brüne, C.; Roth, A.; Buhmann, H.;Molenkamp, L. W.; Qi, X.-L.; Zhang, S.-C. Science 2007, 318,766–770. doi:10.1126/science.11480474. 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Technol. 2015, 5, 659–664.doi:10.1109/TTHZ.2015.2436712License and TermsThis is an Open Access article under the terms of theCreative Commons Attribution License(http://creativecommons.org/licenses/by/4.0), whichpermits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly cited.The license is subject to the Beilstein Journal ofNanotechnology terms and conditions:(http://www.beilstein-journals.org/bjnano)The definitive version of this article is the electronic onewhich can be found at:doi:10.3762/bjnano.8.17

Electron energy relaxation under terahertz excitation in (Cd1−xZnx)3As2 Dirac semimetals

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Electron energy relaxation under terahertz excitation in (Cd1−xZnx)3As2 Dirac semimetals

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