Magnetocapacitance and transport measurements on HgTe-based 3D topological insulators

Outline Collaborators HgTe as a 3D topological insulator Sample design Transport measurements Capacitance measurements Summary Firstly i will give a short general introduction to Tis and will explain why hgte is an 3d ti Then i will show the structure of my sample After that i will present my transport and capacitance measurements. Collaborators Johannes Ziegler Dieter Weiss (Regensburg) Dima Kozlov Nikolai Mikhailov Sergey Dvoretsky (Novosibirsk)

HgTe as a 3D topological insultor Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. Hasan, Kane. Rev. Mod. Phys. 82(4), 3045 (2010). 2D 3D So first: What are TI? Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting surface states on their edge or sample In the 2d case we have a 2d layer with conducting edge states and in the 3d case we have a bulk with conducting surfaces. In the 3D TI each surface acts like an 2DEG. Kong, Cui. Nat. Chem. 3(11), 845–849 (2011).

HgTe as a 3D topological insulator HgTe unstrained To get a ti we need an inverted band structure. Hgte has an inverted band structure becaus the gamma 8 band lies over the gamma 6 band. If we bring this material together with one which has a normal band structure for example cdte, due to topological reasons the band needs to close at the interface. And this leads to 2D Dirac like surface states. but hgte is a semimetal and therefore it has no bandgap HgTe has an inverted band structure But HgTe is a semimetal -> no bandgap S.C. Wu, B. Yan, C. Felser, EPL, 107 (2014) 57006

HgTe as a 3D topological insulator HgTe unstrained HgTe strained when we grow hgte on cdte the hgte gets strained because of the lattive mismatch between hgte and cdte. Due to that strain a small gap opens. So now we have a bandgap in the bulk and due to the inverted band structure surface states This can be visulaised by a calculation of the density of states In this picture we can well see the surface states in and out of the gap. So this was the short introduction and now we come to the sample structure By growing HgTe on CdTe the HgTe layer is strained due to the lattice mismatch between HgTe and CdTe -> A small gap opens S.C. Wu, B. Yan, C. Felser, EPL, 107 (2014) 57006

Sample design The wafer consists a 80nm hgte layer between two cdhgte layer grown on the cdte subrate. A simple hallbar with ten contacts was etched Into the wafer. Then the insulator was made which consits a layer of about 20 nm sio2 and 100nm alox And on top a ti gold gate was deposited to be able to tune the gate voltage from the valence band over the gap to the conduction band. Kozlov, Kvon, Olshanetsky, Mikhailov, Dvoretsky, Weiss. Phys. Rev. Lett. 112(19), 196801 (2014).

1 1 2 Before is how the experimental results i will shortly explain the different regions of the sample between them we can switch by the gate voltage. This picture shows our sample structure with the bulk and the 2D surface states at the interfaces. If we apply a gate voltage with that we are in the valence band, we are in a region where holes from bulk and dirac electrons from the surface states coexist. When we raise the gate voltage so that the fermi energy lies in the bulk gap, there are only the electrons of the top and the bottom surface. If we further increase the gate voltage, we reach the conduction band and now bulk electrons and dirac electrons exist. So this leads us to the transport measurement. Kozlov, Kvon, Olshanetsky, Mikhailov, Dvoretsky, Weiss. Phys. Rev. Lett. 112(19), 196801 (2014).

Transport measurements Here you can see simply the longitudinal resistance and the hall voltage was measured in a magnetic field sweep. As i already said in the beginning, each surface state acts like an 2DEG. So we can identify shubnikov the haas oscillations and the quantum hall effect. Due to the fact that the QHE originates from the two surfaces, it differs a bit from that when it comes from only a single 2DEG. The total hall conductance is given by the sum of the coductivities of the two surfaces. If we now try to calculate the carrier density from the distance of the sdh oscillations by plotting the filling factor and 1/B, we mention two different slopes from which we can calculate the carrier density. So we get one carrier density from the high field oscillations and one from the low field oscillations. This can be explained by the effect of screening. Quantum-Hall Effect is formed by two surfaces σ𝑥𝑦 𝑡𝑜𝑡𝑎𝑙 =ν 𝑒 2 ℎ = σ𝑥𝑦 𝑡𝑜𝑝 + σ𝑥𝑦 𝑏𝑜𝑡𝑡𝑜𝑚 = (νt + νb ) 𝑒 2 ℎ σ𝑥𝑦 𝑡𝑜𝑝 and σ𝑥𝑦 𝑏𝑜𝑡𝑡𝑜𝑚 𝑎𝑟𝑒 𝑞𝑢𝑎𝑛𝑡𝑖𝑠𝑒𝑑 𝑖𝑛 𝑒 2 2ℎ

Δ𝑁𝑡𝑜𝑝 Δ𝑁𝑏𝑜𝑡 = 1+ 𝑞 2 𝐷𝑡𝑑𝐻𝑔𝑇𝑒 ε𝐻𝑔𝑇𝑒ε0 Screening Δ𝑁𝑡𝑜𝑝 Δ𝑁𝑏𝑜𝑡 = 1+ 𝑞 2 𝐷𝑡𝑑𝐻𝑔𝑇𝑒 ε𝐻𝑔𝑇𝑒ε0 1 Top and bottom surface have different carrier densities and mobilities 1 Higher mobility is connected to a smaller Landau level broadening -> Shubnikov de Haas oscillations at lower magnetic fields If we apply a gate voltage to a system of two 2deg the top surface screens a part of the voltage from the bottom surface. So a change in the gate voltage has a larger effect on the top surface than on the bottom surface. This leads to a higher carrier density and higher mobility on the top surface than on the bottom surface. The higher mobility is connected to a smaller landau level braodening which causes that sdh oscillations can be seen at lower magnetic field. This can be seen in this picture. The green line show the dos with a large landau level broadening and the red line show the dos with a small landau level broadening at a small magnetic field range. So as you can see the transport curve in the low field region is dominated by the red line which means in our case the top surface. And only at higher magnetic fields also the bottom surface oscillations contribute. Kozlov, Kvon, Olshanetsky, Mikhailov, Dvoretsky, Weiss. Phys. Rev. Lett. 112(19), 196801 (2014).

Transport measurements Period of low field oscillations arise top surface carrier density Period of high field oscillations arise from total carrier density That means that we ar able to calculate the carrier density of the top surface from the low field oscillations at different gate voltages. Furthermore the carrier density was been calculated from the slope of the linear hall curves in this region and this is in good agrrement with the carrier densities calculated from high field sdh oscillations. That means that the period of the high field sdh oscillations is given by the total carrier density. One feature i should mention is that the slope of the blue dots changes at about 1.8V. This is a hint that the conduction band starts here. The slope of the total carrier density N is constant over the whole region. In the gap it is the sum of top and bottom surface carrier densities and this is zero. But if we enter the conduction additionally the bulk carrier density contribute to the total carrier density what results in a rduced slope of the top and bottom carrier densities.

Transport measurements Period of low field oscillations arise top surface carrier density Period of high field oscillations arise from total carrier density Slope changes That means that we ar able to calculate the carrier density of the top surface from the low field oscillations at different gate voltages. Furthermore the carrier density was been calculated from the slope of the linear hall curves in this region and this is in good agrrement with the carrier densities calculated from high field sdh oscillations. That means that the period of the high field sdh oscillations is given by the total carrier density. One feature i should mention is that the slope of the blue dots changes at about 1.8V. This is a hint that the conduction band starts here. The slope of the total carrier density N is constant over the whole region. In the gap it is the sum of top and bottom surface carrier densities and this is zero. But if we enter the conduction additionally the bulk carrier density contribute to the total carrier density what results in a rduced slope of the top and bottom carrier densities. Reduced slope 𝑑𝑁𝑡𝑜𝑝 𝑑𝑉𝑔𝑎𝑡𝑒 reflects EF entering the conduction band 𝑑𝑁 𝑑𝑉𝑔𝑎𝑡𝑒 = 𝑑𝑁𝑡𝑜𝑝 𝑑𝑉𝑔𝑎𝑡𝑒 + 𝑑𝑁𝑏𝑢𝑙𝑘 𝑑𝑉𝑔𝑎𝑡𝑒 + 𝑑𝑁𝑏𝑜𝑡 𝑑𝑉𝑔𝑎𝑡𝑒 ≈ const.

Transport measurements 1 The evaluation of the carrier density in the lower gate voltage region is more difficult. Starting between 1 and 0.5V the hall curves become non linear. This behaviour can be explained that we now come to the region were electrons and bulk holes coexist. So the transport curves must be fitted to the two carrier drude model, which says that the total conductivity is a sum of the conductivy of the holes and that of the electrons. And if we do so, we obtain this behaviour for the surface electrons and bulk holes. Now we go on with the capacitance measurements. Fitted by the two-carrier drude model (i=2)

Capacitance measurements Equivalent cicuit for EF in the gap: Total capacitance depends also on quantum capacitance The capacitance is measured with a capacitance bridge between the gate and the TI layer. The equivalent circuit when Efermi lies in the gap, can be seen as a three plate condensator. Not only the geometrical capacitances of the insulator cgt and of the ti layer cbt goes in, also the quantum capacitance of the surface contributes, which is given by e^2 times the DOS of the surface. So capacitance measurements are a method to determine the dos of the surfaces. The calculation of the whole capacitance of the system leads to this formula. If we calculate the derivative of the capacitance over the dos and compare them, we see that this fraction is always bigger than one. So we would expect that the capacitance is more sensitive to the top surface than to the bottom surface. And if the capacitance between the top and bottom surface goes to zero, we get to this simple formula, and this is the same as we know from capacitance measurements of a single 2deg measured capacitance most sensitive to top layer usual result for conventional 2DES

Capacitance measurements In the magnetic field we can see the oscillation of the density of states and from that we can calculate the carrier density like we did with the shubnikov de hass oscillation in transport. Now here we get only one slope from which we can evaluate the carrier density.

Capacitance measurements If we do so for the same gate voltages like in transport, we mention that the carrier densities which we get from capacitance measurements are well agree with that what we got from low field sdh oscillations. To remeber: the low field sdh arised only from the top surface. So that means that capacitance measurements are also measures only or mainly the top surface in and out of the gap. And this was also expected by the calculation i showed before. Ne extracted from capacitance measurements matches well with Ne from low field SdH oscillations -> Capacitance measurements are most sensitive to the top surface

Capacitance measurements C-CB=0[10-13F] Here you can see capacitnace measurements with a gate voltage from -1 to 3 volts and magnetic fields up to 5 tesla. You can recognize the landau fan. From the previous results i show, we know that this shows the landau fan of the top surface. And you can also see that there is again a change in the slope which shows the entering of the conducting band. From the previous results i show, we know that this shows the landau fan of the top surface. Reduced slope dB/dVG reflects EF entering the conduction band

Transport measurements σxx [10-5S] If we do the same measurements for the transport by plotting sigma xx, we mention that the landau fan, mainly at higher fields looks a bit different. To compare the two color plots, i put the dots now in the same picture, and now even up to 10 tesla.

Comparison Here you can see that at low fields the landau levels of tranport and capacitance are the same, This is what we expect due to the effect of screening. At higher fields they starting to differ, because now also the bottom surface oscillations contribute and the landau fan of the transport measurements is now probably somehoe of an overlap of the top and bottom surface landau fan.

Transport measurements Summary Transport measurements Quantum Hall Effect is formed by two surfaces Period of high field oscillations arise from total carrier sensity Low field oscillations arise from top surface Ne of the top surface Capacitance measurements Ne from capacitance matches with Ne from low field oscillations Capacitance measurements probes mainly the top surface Possibility to disentangle contributions from top and bottom surface by comparing transport and capacitance

Thank you!

HgTe as a 3D topological insulator Calculation of the local density of states: Demonstration of the surface states Good agreement with experimental ARPES measurement S.C. Wu, B. Yan, C. Felser, EPL, 107 (2014) 57006

Transport measurements Folie löschen Vgate [V]

Capacitance measurements The first capacitance measurement i show, is a gate sweep. You can see the gap between 0.8V and 1.8V, and this is similar to that what we expecte from transport. In the magnetic field we can see the oscillation of the density of states and from that we can calculate the carrier density like we did with the shubnikov de hass oscillation in transport. Now here we get only one slope from which we can evaluate the carrier density.

HgTe as a 3D topological insulator To get a ti we need an inverted band structure, which has its origin in a strong spin orbit interaction In An inverted band structure the conduction band is ptype and valence band is stype. In contrast to the normal band structure with an p type valence band and stype conduction band Band inversion due to strong spin-orbit interaction B.A.Volkov, O.A. Pankratov, JETP Letters (1985); L.G. Gerchikov, A.V. Subashev, phys. stat. sol. (b) 160, 443 (1990)

HgTe as a 3D topological insulator If we now bring a material with inverted band structure together with one which has a normal band structure, due to topological reasons the band needs to close at the interface. And this leads to 2D Dirac like surface states. At the interface the band gap needs to close ->2D Dirac-like surface states B.A.Volkov, O.A. Pankratov, JETP Letters (1985); L.G. Gerchikov, A.V. Subashev, phys. stat. sol. (b) 160, 443 (1990)

Transport measurements