Transport in InAs-GaSb quantum wells Klaus Ensslin Solid State Physics the material system ambipolar behavior non-local transport inverted bandstructure Zürich Collaborators: S. Müller, M. Karalic, C. Mittag, A. Pal, T. Ihn, C. Charpentier, T. Tschirky, W. Wegscheider
Topological insulator in HgCdTe HgTe quantum well has to have exactly the correct width M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. Molenkamp, X.-L. Qi, and S.-C. Zhang,, Science 318, 766 (2007).
Band structure of InAs/GaSb quantum wells type-ii band alignement AlSb AlSb GaSb InAs hybridization gap due to tunneling between layers
Bandstructure calculations (not so new) Band gap can be tuned by electric field Y. Naveh and B. Laikhtman, Appl. Phys. Lett. 66, 1980 (1985)
Bandstructure calculations C. Liu, T. L. Hughes, X.-L. Qi, K. Wang, S.- C. Zhang, PRL 100, 236601 (2008) two regimes of band alignment have different topological invariants
Previous transport experiments See also Chang, Surf. Sci. 98, 70 (1980) Altarelli, PRB 28, 842 (1983) Altarelli, PRB 35, 9867 (1987) Mendez, PRL 55, 2216 (1985) Cooper, Patel, Drouot, Linfield, Ritchie, and Pepper, PRB 57, 11915 (1998)
Previous transport experiments
InAs/GaSb qws: edge states Du group: PRL 100, 236601 (2008), PRL 114, 096802 (2015), PRL115 136804 (2015), arxiv:1508.04509 Muraki group: PRB 87, 235311 (2013), PRBB 91, 245309 (2015), arxiv:1606.01710 Nichele, Kouwenhoven, Marcus: arxiv:1605.04818, arxiv:1605.01241, New J. Phys. 18, 083005 (2016)
InAs/GaSb qws: ambipolar behavior high mobility sample 50 μm Charge neutrality point Hall slope changes sign across the CNP CNP
InAs/GaSb qws: ambipolar behavior mobility density coexistence of electrons and holes at CNP
quantum Hall regime resistance peak at n=0 plateau at n=0
hybridization of Landau levels formation of gaps might be masked by disorder Chiang et al. Phys. Rev. Lett.77, 10 (1996) Takashina et al. Phys. Rev. B. 68, 235303 (2003)
hybridization of Landau levels no disorder disorder edge states
Non-local transport at B=0 additional Si-dopants Suzuki, Harada, Onomitsu, and Muraki PRB 87, 235311 (2013) PRBB 91, 245309 (2015) High mobility: no non-local transport at B=0 Du, Knez, Sullivan, and Du PRL 114, 096802 (2015)
questions: - How precise and reproducible is this quantized resistance? - What are the relevant length scales? Inelastic and elastic scattering? - Bulk conduction and edge conduction?
Introducing impure Ga Goal: Additional disorder localizes the bulk without affecting the edge states impure Ga μ=8'000cm 2 /Vs mobilities at n=8x10 11 cm -2 pure Ga μ=300'000cm 2 /Vs C. Charpentier et al, Appl. Phys. Lett. 103, 112102 (2013)
Reducing device size large intermediate L W 2 μm small W=25μm, L=50μm W=4.9μm, L=10μm W=2.2μm, L=5.1μm large R >> h/e 2 gate hysteresis e-h crossover R > h/e 2 R h/e 2 Resistance at CNP decreases and transforms into a plateau Plateau below quantized expectation value
Small device: local resistance Plateau value close to expected h/2e 2 Sample homogenous
Evidence for edge conduction R NL =V/I=h/6e 2 R NL =V/I=h/3e 2 Exp. value 67 % of theor. value non-local transport around the CNP with reduced resistance
Resistor model V1 R C V6 V5 R E V4 R E : edge resistance R C : center resistance V2 V3 Fit all non-local resistance configurations for a given sample with two parameters: R E, R C Result: R E : 15 kω to 22 kω (of order of h/e 2 ) R C : 65 kω to 340 kω (much larger than h/e 2 )
Plateau height and device size Small device W=2.2μm, L=5.1μm below expected quantized value Intermediate device W=4.9μm, L=10μm above expected quantized value Remaining bulk conduction => reduced edge current Bulk stays the same L edge > relaxation length => increased edge resistance
also edge transport in the trivial phase? F. Nichele et al. New J. Phys. 18, 083005 (2016)
Conductance quantization? Conductance value depends on sample geometry F. Nichele et al. New J. Phys. 18, 083005 (2016)
Well width dependence 12.5 nm InAs Inverted gap 10 nm InAs standard gap gap disappears with inplane B-field because of tilting in k-space gap increases with in-plane B-field because of diamagnetic shift See also Yang et al., Phys. Rev. Lett. 78, 4613 (1997)
effect of an in-plane magnetic field T.O. Stadelmann, PhD thesis, Oxford (2006)
Well width dependence 12.5 nm InAs low-field Hall effect electrons only electrons and holes Inverted gap holes and electrons holes only
Shubnikov-de Haas oscillations 12.5 nm InAs 10 nm InAs
Calculated Landau level spectrum inverted gap -> crossings and anticrossings of levels standard gap -> electron and hole-like Landau levels Kiryl Pakrouski Alexey Soluyanov Quasheng Wu Matthias Troyer arxiv:1606.03627
Conclusions QH Regime (high mobility) Helical and dissipative quantum Hall edge channels shorted by a small residual bulk conductivity PRL 112, 036802 (2014) B=0 (low mobility) Ambipolar behavior Non-local resistance Plateau values sample size dependent Different InAs well thicknesses Experimental evidence for inverted gap Strong SI PRB 92, 081303(R) (2015) arxiv:1606.03627 S. Müller, M. Karalic, C. Mittag, A. Pal, F, Nichele, T. Ihn, C. Charpentier, T. Tschirky, W. Wegscheider, K.Pakrouski, A. Soluyanov, Q. Wu, M. Troyer
Thomas Ihn Thank you Atin Pal Susanne Müller Matija Karalic Werner Wegscheider Thomas Tschirky Fabrizio Nichele Christopher Mittag