Universiteit van AmsterdamVan DerWaals-Zeeman Institute

Faculty of Science

Report of Bachelorproject Physics- and Astrophysics, content 15 EC, conductedbetween 30-03-2015 and 03-07-2015

Photocurrent manipulation in topological insulators with lightpolarisation

Author:Noor Veenhoven

StudentID:10247572

Supervisor:Dr. Erik van Heumen

Second Reviewer:Dr. Jasper van Wezel

July 18, 2015

Abstract

Topological insulators (TIs) are materials that have a spin polarized photocurrentresponse to electromagnetic radiation, due to the presence of a unique surfaceelectronic structure. Such helicity dependent photocurrents have recently beenobserved by McIver et al. [2011]. The goal of this experiment is to build a setupthat can be used to detect such photocurrents. I have build a fully automatizedsetup that can map the photocurrent response as function of position on the sampleand as function of the incident polarisation state of a HeNe laser. I have detectedphotocurrents in a 1% Sn doped Bi2Te2S e sample that show a similar response aswas observed by McIver et al. [2011]. At the same time, I have also found cleardifferences with the results obtained by McIver et al. [2011]. In particular, I haveobserved photocurrents that may have a pure surface state origin. These resultsneed to be further verified in future experiments. The sample gave a current dueto the laser, which alternated under change of polarisation in a similar way as inthe experiment executed by McIver et al. [2011].

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Populaire samenvatting

Topologische isolatoren (TIs) zijn isolerende materialen die een geleidend opper-vlak hebben. Deze nieuwe materialen hebben unieke eigenschappen die uitzichtbieden op toepassingen in de elektronica. Een van die eigenschappen is dat elek-tronen in het materiaal niet makkelijk naar een hogere energietoestand kunnenverstrooien, zoals geı̈lustreerd in het energie tegen snelheid diagram in figuur 1.

Figure 1: Energie tegensnelheid diagram vanelektronen op het op-pervlak (Junck et al.[2013])

In de figuur kun je zien, dat de lage energietoestandengevuld zijn (blauw) en de hogere energietoestandenleeg (wit). In geleidende materialen kunnen de elek-tronen van deze gevulde toestand naar een hogere en-ergie toestand springen als je er een stroom door heenlaat lopen. De elektronen uit deze stroom zullen tegende kernen van het materiaal aan botsen, waardoor deelektronen van het materiaal genoeg energie krijgenom naar een lege toestand te springen, waardoor hetmateriaal opwarmt. In topologische isolatoren kan ditniet. Dit komt doordat de spin (het magnetische mo-ment, of draairichting van het elektron) in het hogereenergieniveau omgekeerd is aan de spin in de bezetteenergietoestand. Een elektron kan alleen maar naareen hogere enrgietoestand gaan als de lege toestand dejuiste spin heeft. Doordat een elektron dus niet zonderde spin om te draaien naar hoger energieniveau zal erveel minder warmte ontwikkeling plaatsvinden (link-erkant van figuur 1). Omdat er minder warmte on-twikkeling is , verlies je zo minder energie. De hoopis dat op deze manier nieuwe elektronica (spintronica)ontworpen kan worden de veel energie zuiniger is. Inhet experiment dat we hebben gedaan hebben we gekeken naar een andere eigen-

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schap van een topologische isolator die hier zeker niet los van staat. We hebbenin ons experiment geprobeerd een stroom te laten lopen door het materiaal doorer licht op te schijnen. Niet zo maar licht, maar circulair en lineair gepolariseerdlicht. Circulair gepolariseerd licht zou namelijk kunnen doen wat ons elektroneerder niet kon, de spin van het elektron omdraaien (rechterkant van figuur 1).Rechtsom circulair gepolariseerd licht draait de spin op zo een manier dat de elek-tronen aan de rechterkant van figuur 1 de juiste spinrichting krijgen en naar eenhoger energie niveau kunnen, dit gebeurd echter niet aan de linkerkant. Door dezeonbalans in elektronen aan de linkerkant en elektronen aan de rechterkant gaateen stroom lopen. Die stroom hebben we geprobeerd te meten. We hebben eenopstelling gebouwd, waarbij een laser op een sample schijnt met daar tussen op-tische elementen die het licht van polarisatie kunnen laten veranderen. Door tekijken naar het verschil tussen stroom bij circulaire polarisatie en lineaire polar-isatie konden we zien dat er inderdaad een photostroom (stroom door licht) ginglopen.

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Acknowledgements

I would like to thank Erik van Heumen for supervising me during this projectand helping me write my thesis. I want to thank Hugo Schlatter for helping meprepare the sample and taking me to AMOLF to make the contacts. I would alsolike to thank Gerrit Hardeman for programming labview, Hans Ellermeijer forbuilding our first mount and Johan Mozes for building the automated mount. Ialso want to thank them for helping with all the other technicalities that Erik andI couldn’t do ourselves. Further, I want to thank Yu Pan for helping me put wireson our sample. At last I would like to thank Alona Tytarenko for answering myquestions and giving me advice when Erik was not around.

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Contents

1 Introduction 6

2 Theory 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Previous experimental work . . . . . . . . . . . . . . . . . . . . 82.3 Theoretical interpretation . . . . . . . . . . . . . . . . . . . . . . 9

3 Experimental Setup and Method 113.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.4 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Results 20

5 Discussion and Conclusion 29

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Chapter 1

Introduction

In recent years topological insulators have arrived as a hot topic in condensedmatter physics. These materials are bulk insulators with metallic surfaces. Whatmakes them different from ordinary band insulators? The surface states in aTI stay metallic, even under strong disorder because the states are protected bytime-reversal symmetry. They are also helical, which means that each surface-momentum state has a unique spin direction. Due to this helical property of thesurface states, a photocurrent can be observed in response to electromagnetic ra-diation (McIver et al. [2011]). Theorists have proven that there indeed should bea photocurrent in this case.[Junck et al., 2013]The goal of this bachelor thesis’ experiment is to investigate photocurrents gen-erated in topological insulator materials. The earlier experiments showed that thecurrent response is determined by several effects that occur simultaneously (bulkeffects, surface effects, effect due to light and effects due to temperature). Startingfrom the theoretical predictions we will try to provide a recipe to disentangle thephotocurrent associated with the topological surface states from the other sourcesmentioned above. Such a recipe could provide us with a new tool to investigate ordetect topological surface states.This thesis will describe the development of a new setup that was used to in-duce and measure photocurrents in the topological insulator S n0.01Bi1.99Te2S e. InChapter 2 the theory will be described, Chapter 3 describes the sample prepa-ration, the experimental setup and the method. The results are represented inChapter 4 and these results will be discussed in Chapter 5.

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Chapter 2

Theory

2.1 Introduction

Figure 2.1: Dirac cone in k-space, theelectron spin points perpenidcularly tothe momentum. Adapted from Qi andZhang [2011]

As was said in the introduction, topo-logical insulators are states of mat-ter with insulating bulk and conduct-ing surface states that are invariant un-der time-reversal. The topological pro-tected surface states consist of Diracfermions (massless, charged, spin 1/2particles). Due to the strong spin-orbitinteraction in these materials the topo-logical surface states are helical, thismeans that the electron spin points per-pendicularly to the momentum, form-ing a left handed helical structurein k-space (figure 2.1). The spin-momentum locking prevents the he-lical edge states from backscattering.This helical structure presents itselfas a Dirac cone, which has been ob-served in many materials using angleresolved photoemission spectroscopy(ARPES). Materials with helical surface states are expected to have a ratherunique photocurrent response to electromagnetic radiation. This is due to spin-

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selection rules: Looking at a 2D Dirac cone (figure 2.2) you can see clearly, thatfor an electron to excite to the top level of the cone, a spin needs to be flipped.When the material is illuminated with circularly polarised light, an electron on oneside of the cone will be able to make a transition, while the electron on the otherside of the cone will not be able to do this for the same handedness of the circularpolarisation. As a result this imbalence in the momentum distribution leads to acurrent. [Junck et al., 2013]

2.2 Previous experimental workExperimentally, we can use a polariser and a λ

4 wave plate to provide circular po-larised light. This wave plate (or phase retarder) will change the polarisation of thelight from left handed circular to right handed circular, with linear polarisation inbetween. When the polarisation is vertical (or 0◦) and the the wave plate is rotatedover an angle α, the light will change from linear (α = 0◦), to right handed circu-lar (α = 45◦), to linear (α = 90◦), to left handed circular (α = 135◦) etc.. When

Figure 2.2: Dirac cone in k-space. Circularly polarised light will excite the elec-tron on the left side of the cone, but not on the right, inducing a current. Adaptedfrom Junck et al. [2013]

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the polarisation is horizontal this will be the same except that the order of left andright circular polarisation is reversed. In McIver et al. [2011] the current was mea-sured in the x- and y-direction and (with the y-direction perpendicular to the planeof incidence), with an 56◦angle of incidence and normal incidence. For currentin the y-direction was also measured for normal incidence. The polarisation wasP-polarised, which means that the polarisation is parallel to the plane of incidence.The current they measured could be described by the following function.

j(α) = D + C sin(2α) + L1 sin(4α) + L2 cos(4α) (2.1)

In this function, C and L1 are helicity dependent and thus responsible for the pho-togalvanic effect (utilizing the generation of a potential difference between twoelectrodes by illumination). D and L2 are terms with bulk origin, probably orig-inating in the photon drag effect (effective mass increase of conduction electronsor valence holes due to interactions with the crystal lattice in which the electronmoves). The measurement in the y direction gave a current with a large positiveC term and the other term negative, but approximately the same size. They alsomeasured the current in the x-direction, which gave a current twice as small asthe one measured in the y-direction. The dominating term (after D) was L2 whichmeans that the current generated in this direction has almost no surface origin.When the light is normally incident, C vanishes completely. From this they con-cluded that the C-term arises from the asymmetric optical excitation of the helicalDirac cone. [McIver et al., 2011]

2.3 Theoretical interpretationC and L1 originating from the surface is also supported by a theoretical article byJunck et al. [2013]. In this article the equation given for photocurrent for the idealDirac spectrum in the y-direction is,

jy(α) = C sin(2α) + L1 sin(4α) (2.2)

(reference frame and constants changed to match McIver et al. [2011]). For pho-tocurrent for the ideal Dirac spectrum in the x-direction another equation wasused,

jx = L2 cos(4α) (2.3)

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where L2 is a constant. This means that measurements of current in the x-directionshould give the same value for left circular polarised light as for right circularpolarised light. From the same article also followed that p-polarised light won’tgive a photocurrent, but s-polarised will.[Junck et al., 2013]

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Chapter 3

Experimental Setup and Method

3.1 Sample preparationThe sample that was used was S n0.01Bi1.99Te2S e. It was approximately 6 mmin length, 2.5 mm in width and 1 mm in thickness. S n0.01Bi1.99Te2S e is a likelycandidate material to be a topological insulator, since it’s a close relative of theknown TI Bi2Te2S e.To make well-defined contacts on the sample, the middle of the the sample wascovered with a piece of plastic. The whole surface was subsequently covered witha 100 nm layer of gold by sputtering. By removing the plastic, two clear Aucontacts remained on the sides of the sample. The wire contacts were glued withsilver paint on these contacts as seen in figure: 3.1.

(a) Schematic

(b) Foto

Figure 3.1: Sample with nano-layer gold on the sides and two contacts glued withsilver paint.

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3.2 SetupThe setup of this experiment is shown in Figure 3.2. A 50mW/cm2 laser beamwas sent through a polariser, a λ

4 wave plate and a lens, before hitting the samplewith an angle of incidence of 45◦. The sample was connected to ground and toan amplifier, which was connected to the lock-in amplifier. A signal generatorwas used to modulate the laser intensity with a sine wave reference frequency.The λ

4 wave-plate and the sample holder were both equipped with a stepper motor.This enabled automated rotation of λ

4 and high precision x, y movement of the

Figure 3.2: Setup of experiment. Laser was sent through a polariser, a λ4 wave plate

(automated with a stepper motor) and a lens before hitting the sample at variableangle of incidence. The sample holder was equipped with a x-y stepper motor andconnected to an amplifier. This amplifier connected to the lock-in amplifier. Thecontroller of the stepper motors and the lock-in were both connected to a pc.

laser spot over the sample. The laser that was used was 90% linearly polarised.

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Since we want to make use of horizontal and vertical polarised light, the laserwas mounted with it’s main axis of polarisation under 45◦. This allows us toobtain both horizontal and vertical polarised light with equal intensity using asingle rotatable polariser. The λ

4 wave plate changed the polarisation of the laserbeam from linear to circular and back. If the polariser was vertical (θ = 0◦) and thewave plate started with it’s fast axis vertical (let’s say α = 0◦), the polarization waschanged from vertical polarised (α = 0◦), to right circularly polarised (α = 45◦), tovertical polarised again (α = 90◦), to left circular (α = 135◦) and that would repeatitself for the rest of the rotation. For horizontal polarisation this was of course thesame only with a phase difference of 90◦, and horizontal linear polarised light(so, horizontal, left circular, horizontal, right circular, etc.). After the λ

4 waveplate a lens was placed to focus the beam. The sample was mounted in a smallaluminium box (Figure 3.3a) in order to reduce electromagnetic interference inthe photocurrent circuit. A small slit in the box provided optical acces to thesample. Inside the box one side of the sample was connected to the ground (ascrew in contact with the outside of the box), the other side of the sample wasconnected to an output for a coax cable. The wires of the sample were connectedto these by means of a printed circuit board. In the sample box several resistorsand other outputs where present, these were not necessary in this experiment, butmight be of use in future experiments. The sample was attached to the box byfastening the top part between two plastic plates that were screwed to the box, sothat the sample is not in contact with the ground (figure 3.3b). The sample boxwas attached to a mount that could move in the x- and y-direction controlled bystepper motors, that could change the position with an accuracy of 2µm. For mostmeasurements the step size was 10µm or 100µm. The stepper motors were allcontrolled by a computer program in Labview, this will be dealt with in Section3.3. A current amplifier was used to convert the current to a voltage with a 106

amplification factor. The lock-in amplifier further amplified the signal and filteredaway a large part of the noise using a modulation- demodulation technique. Thiswill be explained in detail in Section 3.3.

3.3 ApparatusLock-in amplifiers are used to detect and measure very small AC signals usingphase-sensitive detection to single out the component of the signal at a specificreference frequency and phase. The lock-in amplifies the signal it measures andmultiplies it by the lock-in reference. The output of the phase-sensitive detector

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(a) Outside of sample box. (b) Inside the sample box.

Figure 3.3: Sample with nano-layer gold on the sides and two contacts glued withsilver paint.

will be the following: [Stanford Research Systems, 2002]

Vpsd = VsigVL sin(ωrt + θsig) sin(ωLt + θre f )

=12

VsigVL cos([ωr − ωL]t + θsig − θre f )−

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VsigVL cos([ωr + ωL]t + θsig + θre f )

(3.1)

When signal is passed through a low pass filter, the AC signals are removed. Nosignal will be left except when ωr equals ωL, the difference frequency componentwill be a DC signal. The output of the phase sensitive detector (PSD) becomes:

Vpsd =12

VsigVL cos(θsig − θre f ) (3.2)

This way the noise will be filtered out; the PSD and low pass filter only detect sig-nals whose frequencies are very close to the lock-in reference frequency filteringout disturbances for whisch ωR not close to ωL. θ is the phase difference betweenthe signal and the lock-in reference oscillator. By adding a second PSD the phasedependency can be eliminated and two outputs arise. One proportional to cos(θ)and one to sin(θ),

X = Vsig cos(θ) (3.3)

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Y = Vsig sin(θ) (3.4)

The phase dependency is removed by computing the magnitude (R) of the signal,

R = (X2 + Y2)1/2 = Vsig (3.5)

The phase difference between the lock-in reference and the signal can be calcu-lated using:

θ = arctan(Y/X) (3.6)

In Labview a program was made that recorded the lock-in outputs X and Y andstored them into a text file. It was programmed to measure a specified numberof points, then move over the sample or rotate the wave-plate (or both), and startmeasuring again. Other than just storing some measurements, the program had alot more capabilities. In Figure 3.4 a screenshot can be seen of the program. In theyellow framed box all settings that are also on the lock-in amplifier are present.These settings can be changed before and during a measurement. From the mo-ment the program is started, the values that the lock-in measures can be followedin the purple framed windows. The top one with the X values and the bottom onewith the Y values. Having these windows is very convenient when you want tocheck if what you are measuring makes sense without having to put the data filesinto the analysing program. The scan selector is framed in green, it is a drop downmenu in which a scan can be selected, choices can be made between scanning x,y (of the sample) and rotate (of the wave plate), in all possible combinations. Thered framed part is where the sort of scan can be further specified; which part ofthe sample you want to scan (in µm) and how much you want to rotate the λ

4 plate(in ◦) in a certain amount of steps. The small boxes above the red frame indicatenumber of measuring points per step and the time that is measured per point. Onthe bottom of the screen, framed by a blue line, there is a set position option. Withthe three variables (x, y, and angle) the sample can be moved, and the wave platerotated.The data is analysed using a routine programmed in Igor (screenshot figure: 3.5).

This program averages over the points measured for one position (or rotation)and calculate the current J. It could do this using al three degrees of freedom thatthe stepper motors used and create 2D and 3D graphs. The program also fits thecurrent to the following function:

j = D + C sin(2α) + L1 sin(4α) + L2 cos(4α) (3.7)

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Figure 3.4: Screenshot of Labview program: Yellow, options that are also presenton the lock-in amplifier. Green, scan selector and start/stop sweep button. Red,range in which the measurement takes place, and the distance between steps. Blue,Set position. Purple, monitor window.

Which is the same equation as was used in the article of McIver et al. [2011]. Inthe screenshot in figure 3.5 a scan over the x-direction can be seen, while rotatingthe wave plate for every step in that scan. In the graph in the top left cornerthis data is plotted as position versus rotation, with the colours indicating whatthe value of the current is (blue is the lowest value and red the highest). Thered lines in the graph indicate the cut that can be seen in the other two graphs.The horizontal line can be seen in the top right corner and shows current versusrotation. The vertical line can be seen in the bottom right corner and shows currentversus position. The data is loaded into the program using the indicators framedby the green box. These indicators are the same as the ones used to start the

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measurement in Labview (Figure: 3.4, red box). In the yellow frame it is possibleto change the cuts of the measurement, so basically changing the position of thered lines in the top left graph. The orange framed part is were the data can befitted. The values for D,D1,D2,C, L1 and L2 can be put in and fixed if necessary.It is also possible to fit more cuts of the data at the same time by inserting a startand an end position, and hitting ’fit all’. The values of D,D1,D2,C, L1 and L2 willbe stored in a table, so it will be easy to compare them with each other.

Figure 3.5: Screenshot of Igor program. Top right corner, graph of position versusrotation versus current (blue being the lowest current and red the highest). Top leftcorner, cut of the data, plotting current versus rotation. Bottom left corner, cut ofthe data, plotting current versus position. Green framed, indicators of the range inwhich the data was measured and the step size. The data can be loaded by hitting’Load data’. Yellow framed, way to browse trough the data and take other cuts(for the graphs top right and bottom right). Orange framed, indicators to fit thedata to equation 3.7. Indicators can be locked if deemed necessary and more cutscan be fitted at the same time.

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3.4 MethodThe goal of this experiment is to measure photocurrent and build a setup that canreproduce the experiment of McIver et al. [2011]. Unfortunatly photocurrents arenot the only thing that will arise when illuminating the sample, but also thermo-electric currents. These thermoelectric currents emerge because when the sampleis illuminated by a laser, it will only partly warm up, creating thermoelectric cur-rents. In the paper of McIver et al. [2011] they tackled this problem by scanningover the sample with the laser while measuring the current. The results of this areshown in figure 3.6a. The current goes from positive to negative close to the mid-dle of the sample. In the middle of the sample thermoelectric currents should bezero, since the thermoelectric currents from both sides of the sample will canceleach other. The current in the article of McIver et al. [2011] shows a non-zerocurrent in the centre, indicating a that there is an additional contribution. This isthe location were they measured the current with the rotation of the λ

4 wave plate.The result of this measurement (under a 56◦angle of incidence in the y-direction)can be seen in figure 3.6b. The sample used in the article of McIver et al. [2011]was Bi2S e3 and was 3µm by 5µm by 120nm (figure3.6c). They also used a laserbigger than the sample (100µm), constantly illuminating the whole sample. Weused a different sample (S n0.01Bi1.99Te2S e) because Bi2S e3 has a relatively largebulk conduction. At the WZI a large effort has been made to make TIs with ahigh bulk resistivity resulting in samples including ours. It is hoped that the sur-face state contribution will be larger than the bulk contribution because of the

(a) Position scan over the sam-ple.

(b) Current measured under ro-tation of λ

4 wave plate.

(c) The sample, 3µmby 5µm by 120nm

Figure 3.6: The position scan, rotation measurement and the sample of McIveret al. [2011]

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improved bulk resistivity. This may make the identification of surface state cur-rents more clear.In the following chapter we will follow the same procedure to try to identify pho-tocurrents.

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Chapter 4

Results

The first measurement that was done was the position scan of the sample. Sinceour sample was bigger than the sample of McIver et al. [2011] and our laserspotsmaller than the sample, we made an XY-scan over the sample surface, while mea-suring the current for every 10µm, as can be seen in figure 4.1b. The data in thisfigure looks slightly more complicated than the data in the article of McIver et al.[2011], but a laser induced current can be seen, which was the first goal of thisexperiment. The figure shows a map of the sample where red and blue give themaxima and minima of the current. Most minima and maxima can be observedon a diagonal line over the sample where also an irregularity can be seen (figure4.1c). These minima and maxima might be seen in this position because the irreg-ularity causes this part of the sample to have a larger effective surface area. Sincewe don’t have a simple picture with the current going from zero, to negative, topositive and again to zero as can be seen in figure 3.6a (McIver et al. [2011]),we didn’t know on which position it was best to do a photocurrent measurement.That’s why we chose to measure over a small range of positions on the sample,where the current went from positive to negative (just like in the article of McIveret al. [2011]). In the figure 4.2, the first exploratory measurement can be seen. Inthis measurement we chose a position with maximum current close to x = 2 mmand y = 0,8 mm in figure 4.1b. We used horizontal polarised (p-polarised) lightand measured with the contacts in the y-direction. This measurement correspondsclosest to the geometry used by McIver et al. [2011] underlying figure 3.6b.After the exploratory measurement, a rotation scan was conducted over a smallrange (200µm) in position over the sample as was explained above. This mea-surement was executed for vertical and horizontal polarisation with contact ori-entated along the x- and y-direction. In figure 4.3 and 4.4 the results of these

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(a) Sample with contacts.(b) Map of the sample where red and blue givethe minima and maxima of the current.

(c) Picture of the sample and the map of the sample on top of each other. The green dotindicates the the the size of the of the laserspot. The scale is in mm.

Figure 4.1: Figure 4.1c shows that the top peaks of the current are present inparticular on the left contact and on the diagonal scratch on the sample.

measurements can be seen. Figure 4.3a shows a wide range scan of the current,for current measured in the y-direction. Also indicated are two coloured areas(red, blue) corresponding to the panels shown in 4.3b and 4.3c. Figure 4.4a alsoshows a wide range scan of the current, but with contacts orientated along thex-direction. Here the coloured areas (green and dark blue) correspond to figure4.4b and 4.4c. The top figures of figure 4.3b, 4.3c, 4.4b and 4.4c show the pho-tocurrent for linear polarisation measured over a narrow range along the sample.

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3.8

3.6

3.4

3.2curr

ent (

nA)

3002001000rotation (°)

data fit

C = 0.14L1 = 0.02L2 = 0.33

Figure 4.2: Current versus rotation, fittedto equation 3.7. The current was mea-sured for horizontal polarisation in the y-direction.

The bottom figures show an (y,α) map(or (x,α) map depending on orien-tation of the contacts) with a colorscale ranging from −3nA (blue) to 5nA(red). The figure in the middle of ev-ery framed box is the most interesting.It shows the values of the C, L1 and L2

terms of equation 3.7 for every posi-tion in the measured range. A compar-ison of these four experiments displaysan interesting recurrence. In the loca-tion where the photocurrent becomes 0for linear polarisation, a finite currentappears for circularly polarised light.In the article of McIver et al. [2011],only measurements with horizontal polarisation where done, but they did do ex-periments with contacts along the x- and y-direction. They showed that a mea-surement of the current in the y-direction should give a clear photocurrent, withthe C term large and positive, and L1 and L2 approximately the same magnitudebut negative. Our measurement gave us similar results for some positions on thesample. In the same article it was also shown that for contacts in the x-direction,all three of these terms should become at least 4 times smaller. This result was ab-sent from our measurements. However, in order to change the contacts the sampleneeds to rotate and we are not sure that we have located the same position. Mostlikely not given figure 4.3a and 4.4a.The current for the rotation of the λ

4 wave plate on the position where the currentis very close to zero and the fit can be seen in figure 4.5. The figure shows the cur-rent for horizontal polarisation with contacts orientated in the x- and y-direction(the current for vertical polarisation looks similar). In these two data figures itcan be clearly seen that the sin(2α) is dominant (C) and that the sin(4α) and thecos(4α) are almost absent (L1 and L2). This sin(2α) is characteristic for a pho-tocurrent in the y -direction, but in combination with the other two terms. In thex-direction there shouldn’t be a sin(2α) term at all for a photocurrent (Junck et al.[2013]). Another observation is a 45◦phase difference between current in the x-and y-direction. Although it is tempting to assign the photocurrent in figure 4.5ato the TI surface states, the result of 4.5b may cost some doubt on this conclusion.This sin(2α) is supposed to become very small for a small angle of incidence if ittruly belongs to the photocurrent of the surface state (McIver et al. [2011]). To see

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(a) Big range (1mm) position scan in the middle of thesample in the y direction, horizontal polarisation.

(b) Horizontal polarisation. (c) Vertical polarisation.

Figure 4.3: Current in the y-direction under horizontal (framed blue) and vertical(framed red) polarisation. From top to bottom: First, small range (200µm) positionscan. Second, position versus rotation, the colorscale ranges form −3nA (blue) to5nA (red) and at the bottem the values of C, L1 and L2 if the data is fitted toequation: 3.7.

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if the result in 4.5a is really a surface state photocurrent we decided to also mea-sure under a smaller angle of incidence (15◦). These results can be seen in figure4.6 and 4.7. Figure 4.6a and 4.6b show again the current against position mea-surement, and figure 4.6c and 4.6d show the (y,α) maps with a color scale rangingfrom −3nA (blue) to 5nA (red). In contrast to figure 4.4 and 4.3 the fit coefficientsL1 and L2 in figure 4.6f and 4.6e are now zero over the entire measured range ,while C shows an oscillatory behaviour. In figure 4.7 the fitted data can be seenfor a position on the sample with high current. There is again a phase differencebetween horizontal en vertical polarisation, but this time of approximately 15◦.These results are quite similar to the results seen in figure 4.5.

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(a) Big range (2mm) position scan in the middle of thesample in the x direction, hotizontal polarisation

(b) Horizontal polarisation. (c) Vertical polarisation.

Figure 4.4: Current in the x-direction under horizontal (framed green) and vertical(framed dark blue) polarisation. From top to bottom: First, small range (200µm)position scan. Second, position versus rotation, the color scale ranges form −3nA(blue) to 5nA (red) and at the bottem the values of C, L1 and L2 if the data is fittedto equation: 3.7.

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0.2

0.1

0.0

-0.1curr

ent (

nA)

3002001000rotation (°)

data fit

(a) Current in the y direction, horizontal po-larisation.

0.30

0.20

0.10

0.00

curr

ent (

nA)

3002001000rotation (°)

data fit

(b) Current in the x direction, horizontal po-larisation.

Figure 4.5: Current versus rotation, fitted to equation 3.7. Location on the samplewith almost zero current.

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(a) Position scan vertical polarisation. (b) Position scan horizontal polarisation.

(c) Position versus rotation versus current,the color scale ranges form −3nA (blue) to5nA (red). Vertical polarisation.

(d) y-position versus rotation versus current,the color scale ranges form −3nA (blue) to5nA (red). Horizotal polarisation.)

0.100.080.060.040.020.00

valu

e

3002001000y position (µm)

C L1

L2

(e) Values the constants C, L1 and L2 fromequation: 3.7, versus rotation. Vertical po-larisation.

0.100.080.060.040.020.00

valu

e

3002001000y position (µm)

C L1

L2

(f) Values the constants C, L1 and L2 fromequation: 3.7, versus rotation. Horizontalpolarisation.)

Figure 4.6: Data for angle of incidence 15◦. Vertical polarisation and horizontalpolarisation.

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2.70

2.65

2.60

2.55curr

ent (

nA)

3002001000rotation (°)

data fit

(a) Horizontal polarisation

2.752.702.652.602.55

curr

ent (

nA)

3002001000rotation (°)

data fit

(b) Vertical polarisation

Figure 4.7: Data fits of current versus rotation in measurement with 15◦angle ofincidence.

28

Chapter 5

Discussion and Conclusion

In our experiment we have found three key observations:

• We have observed photocurrent, but with some deviations from the litera-ture.

• We found locations on the sample with similar polarisation dependence asMcIver et al. [2011], but also positions that seem to be dominated by purelyhelicity dependent photocurrent.

• We have not observed large differences between orientation/polarisation aswas predicted.

The positions on the sample which seemed to be dominated by purely helicitydependent photocurrent (figure 4.5a) look a lot like the photocurrent measuredunder a 15◦angle of incidence (figure 4.7a), which shouldn’t be helicity dependentat all according to McIver et al. [2011] and Junck et al. [2013].The photocurrent observed in the y-direction for p-polarisation (horizontal) and s-polarisation (vertical) under a 45◦angle of incidence didn’t differ much from eachother, while from the theory (Junck et al. [2013]) followed that there shouldn’t bea current for p-polarised light, there should be a current for s-polarised light whenmeasuring pure surface state photocurrent. Since there are also other effects thatcause current it is logical that we don’t see zero current for p-polarisation, but weshould at least see a difference between the two polarisations.Measurements with smaller sample might explain more , since it would give lessinfluence from the bulk. Moving the laser over the sample instead of moving thesample itself in respect to laser spot, will give a better accuracy in which can be

29

measured. The sample box is a lot heavier than the laser, which can cause thestepper motor to skip over points. These preliminary measurements do howevershow that this new setup can provide a good basis for further research.

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Bibliography

Junck, A., Refael, G., and Von Oppen, F. (2013). Photocurrent response of topo-logical insulator surface states. Physical Review B - Condensed Matter andMaterials Physics, 88(7):1–7.

McIver, J. W., Hsieh, D., Steinberg, H., Jarillo-Herrero, P., and Gedik, N. (2011).Control over topological insulator photocurrents with light polarization. NatureNanotechnology, 7(2):96–100.

Qi, X. L. and Zhang, S. C. (2011). Topological insulators and superconductors.Reviews of Modern Physics, 83(4).

Stanford Research Systems (2002). Sr830 Lock-in Amplifier Manual. 0(408).

Yuan, H., Wang, X., Lian, B., Zhang, H., Fang, X., Shen, B., Xu, G., Xu, Y.,Zhang, S.-c., Hwang, H. Y., and Cui, Y. (2014). Generation and Electric Controlof Spin-Coupled Valley Current in WSe2. Nature Nanotechnology, 9(10):21.

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