Topological Heterostructures by Molecular Beam Epitaxy

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1 Topological Heterostructures by Molecular Beam Epitaxy Susanne Stemmer Materials Department, University of California, Santa Barbara Fine Lecture, Northwestern University February 20, 2018

2 Stemmer Group Research Molecular Beam Epitaxy of Novel Materials Quantitative STEM RHEED Screen Bayard-Alpert ion gauge As cracking source Cd As effusion cell 3 2 Heater Manipulator for sample transfer Substrate manipulator 300 Insulator T (K) R = Gd (a) 100 FL-like metal 2 ~ T 10 FM # (SrO layers) 300 (b) 250 T (K) R = Sm n 200 NFL metal 150 FL-like metal n 2 ~T 100 ~ T CDW / SDW? Pseudogap # (SrO layers) 10 3D Dirac Semimetal Heterostructures Sb cracking source Cryo shroud Residual gas analyzer Correlated and Functional Oxide Heterostructures ~ Sample Electron gun for RHEED Ga effusion cell

3 Outline q Introduction into topological materials q 3D Dirac semimetal: Cd 3 As 2 q Topological state engineering using heterostructures q MBE of Cd 3 As 2 q Probing electronic states in thin films of Cd 3 As 2 q Outlook

4 Acknowledgements Dr. Luca Galletti David Kealhofer Manik Goyal Dr. Timo Schumann Funding: Vannevar Bush Faculty Fellowship (DOD) Army Research Office Omor Shoron Dr. Honggyu Kim

5 Classification of Materials Insulators, Semiconductors Metals Si Conduction Band Conduction Band E F Cu Energy Band Gap Valence Band E F Energy Valence Band Momentum Momentum Topological Materials?

6 Topology in Materials Quantum Hall Effect B Conduction Band Energy Valence Band Conducting edge states Momentum q 2D electron gas in a high magnetic field q Skipping orbits at the edge of the sample 1D edge states q Dissipation-less, no backscattering q Topologically protected edge states Moore & Kane, Topological Insulators, Physics World, Feb. 2011

7 2D Topological Insulators Topologically Protected States Without an External Magnetic Field? 2D Topological Insulators O. A. Pankratov et al., Solid State Comm. 61, 93 (1987). Experiment: M. Koenig, et al. Science, 318, 766 (2007). p-type s-type Hg x Cd 1-x Te HgTe Hg x Cd 1-x Te s-type p-type q No external magnetic field q Contact between two semiconductors with mutually inverted bands q Band inversion is due to strong spin-orbit coupling

8 2D Topological Insulators Quantum Spin Hall Insulator Energy Conduction Band Valence Band Edge states C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, (2005). M. Koenig, et al. Science, 318, 766 (2007). Momentum q No external magnetic field (spin-orbit coupling takes that role) q Spin up and spin down states feel opposite effective magnetic fields q Edge states with spin up and spin down channels propagating in opposite direction q Edge states are protected by time reversal symmetry

9 3D Topological Insulators Surface Energy k y k x Experimental observation by ARPES D. Hsieh, et al. Nature 452, (2008). Fu, Kane, & Mele, Phys. Rev. Lett. 98, (2007). Moore & Balents, Phys. Rev. B 75, R (2007). Jozwiak, et al. Nat. Phys. 9, (2013). q Surface states have linear dispersion and obey the Dirac equation q Electron momentum and spin are locked

10 Dirac Materials T.O. Wehling et al., Adv. Phys. 63, 1 (2014).

11 Dirac and Weyl Semimetals Graphics: Claudia Felser q Crystal rotational symmetries protect against opening of a band gap q Three-dimensional Dirac or Weyl nodes q Linear (Dirac) energy dispersion in all three dimensions q Unique surface states q Theoretically predicted q S. M. Young et al., Phys. Rev. Lett. 108, (2012); Z. J. Wang et al., Phys. Rev. B 85, (2012); Z. J. Wang et al., Phys. Rev. B 88, (2013). q Experimentally (ARPES) confirmed in 2014: Cd 3 As 2, Na 3 Bi

12 Dirac and Weyl Semimetals Weyl Semimetal Dirac Semimetal Surface Fermi arcs Surface Fermi arcs Bulk Weyl nodes Bulk Dirac nodes Broken timereversal OR broken inversion symmetry Time-reversal and inversion symmetry are both present TaAs L. X. Yang, et al., Nat. Phys. 11, 728 (2015).

13 3D Dirac Semimetal: Cd 3 As 2 x x Antifluorite structure As Cd Tetragonal unit cell (I4 1 acd) M. N. Ali et al., Inorg. Chem. 53, 4062 (2014) Journal of Applied Physics 30, 1621 (1959). a = b = Å c = Å

14 3D Dirac Semimetal: Cd 3 As 2 ARPES Z. J. Wang et al., Phys. Rev. B 88, (2013). S. Borisenko, et al. Phys. Rev. Lett. 113, (2014). M. Neupane et al., Nat. Commun. 5, 3786 (2014). Z. K. Liu et al., Nat. Mater. 13, 677 (2014). q q Semimetal with band crossing at the Fermi level Band crossing protected by four-fold symmetry axis

15 Topological State Engineering 3D Dirac semimetal Four-fold degenerate Inversion symmetry breaking (4 Weyl nodes) Time-reversal symmetry breaking (2 Weyl nodes) Gapped state for broken rotational symmetry or quantum confinement B Three-dimensional Dirac semimetals are in proximity to a wide range of unique topological/trivial electronic states S. M. Young et al., Phys. Rev. Lett. 108, (2012).

16 Topological State Engineering q 3D Dirac semimetals are in proximity to a wide range of unique electronic states q Use heterostructure engineering to tune between these states q Bulk materials no need to control an atomically thin layer 3D Dirac SM 3D Dirac SM Gate 3D Dirac SM Superconductor 3D Dirac SM Substrate Substrate Substrate Substrate Strain engineering: break rotational symmetries Confinement: film thickness, quantum wells Need high-quality, high mobility thin films of 3D Dirac semimetals Electric field effect: charge carrier modulation, inversion symmetry breaking Proximity effects: topological superconductivity, time reversal symmetry breaking

17 Topological State Engineering Predictions from theory Bulk Thin film Na 3 Bi A. Narayan, et al. Phys. Rev. Lett. 113, (2014) q Gap opens in the bulk Dirac nodes for thin films q Surface states remain protected to very low thicknesses (~ 5 nm)

18 Topological State Engineering Predictions from theory q Very thin films q Cross-over between trivial and non-trivial 2D insulators q 2D topological insulator/qsh 2D TI QSH Z. J. Wang et al., Phys. Rev. B 88, (2013).

19 Topological State Engineering Predictions from theory Electric field effect to switch between trivial insulator and QSH state. H. Pan et al., Sci. Rep. 5, (2015). Need for high-quality, high mobility thin films of 3D Dirac semimetals

20 Prior Work on Cd 3 As 2 Thin Films Method Reference Mobility (cm 2 /Vs) Thermal evaporation on glass H. Matsunami et al., Jpn. J. Appl. Phys. 10, 600 (1971). Thermal evaporation on mica L. Żdanowicz et al., Thin Solid Films 29, 177 (1975); L. Żdanowicz et al., Thin Solid Films 34, 41 (1976). 3,600 No 10,000 No Pulsed laser deposition on quartz J.J. Dubowski et al., Can. J. Phys. 63, 815 (1985). 9,000 No Pulsed laser deposition on glass M. Din et al., Appl. Surf. Sci. 252, 5508 (2006). No Molecular beam epitaxy (MBE) on mica Y. Liu et al., NPG Asia Mater. 7, e221 (2015). 8,000 No MBE on mica P. Cheng et al., New J. Phys. 18, (2016). B. Zhao et al., Sci. Rep. 6, (2016). 2,600 9,000 (2K) MBE on mica C. Zhu et al., Nat. Comm., 1411 (2017). 3,300 No Epitaxial? No No epitaxial films and only modest mobilities.

21 Epitaxial Cd 3 As 2 Cd 3 As 2 (112) Zinc blende (111) Cleavage plane (112) Cd 3 As 2 (111) GaSb (111) GaAs (112) Cd 3 As 2 (111) CdTe Band Gap (ev) ZnSe GaP CdSe AlAs ZnTe AlSb CdTe GaAs InP GaSb InSb InAs Lattice constant (Å) Cd 3 As 2

22 Molecular Beam Epitaxy of Cd 3 As 2 q High-purity sources and UHV growth environment q Low energetic deposition q Produces highest quality films

23 Epitaxial Cd 3 As 2 (112) Cd 3 As 2 (111) GaSb (111) GaAs Intensity (arb. units) CdAs GaAs GaSb Intensity (arb. units) ~80 nm CdAs 224 GaSb 111 ~180 nm 1.5 nm 1 x 1 μm Θ (degree) Θ (degree) 26 q Single phase Cd 3 As 2 q Smooth surface with atomic steps T. Schumann et al., APL Mater. 4, (2016). T. Schumann et al., Phys. Rev. B 95, (R) (2017).

24 Intensity (arb. units) Molecular Beam Epitaxy of Cd 3 As 2 Cd Cd (vac.) As Distance (nm) 3 4 Atomic resolution STEM shows that films grow in the vacancy-ordered Dirac phase T. Schumann et al., APL Mater. 4, (2016).

25 Transport Properties 160 C 5 5 µm2 180 C 170 C 20 nm 5 5 µm2 5 nm 5 5 µm2 190 C 10 nm 5 5 µm2 15 nm

26 Quantum Confinement Cd 3 As 2 20 nm 3D Dirac SM Substrate GaSb Topological state of ultrathin Cd 3 As 2? Confinement: film thickness, quantum wells GaAs T. Schumann, et al., Phys. Rev. Lett. 120, (2018).

27 Quantum Hall Effect in Very Thin Films R xx (kω) ν = ν = ν = ν = 1 ν = nm Cd B (T) 3 As B (T) 2 GaSb 10 nm Cd 3 As 2 (111) GaAs (111) CdTe R xy (kω) q Ultrathin films show the quantum Hall effect q Independent of substrate T. Schumann, et al., Phys. Rev. Lett. 120, (2018); M. Goyal et al., APL Mater. 6, (2018). R xx (kω) R xy (kω)

28 Quantum Hall Effect in Very Thin Films q Ultrathin films show the quantum Hall effect q Origin of the two-dimensional states that give rise to the QHE? q q Quantum confined bulk states? Topological surface states? N ( cm -2 ) Mobility N (Hall) N (SdH) µ (m 2 /Vs) q q Two sets of carriers, one that does not freeze out and one that does At low temperatures, only carriers in the two-dimensional states remain 20 nm Cd 3 As 2 GaSb (111) GaAs T (K) 0.0 T. Schumann, et al., Phys. Rev. Lett. 120, (2018).

29 Quantum Hall Effect in Very Thin Films q Ultrathin films show the quantum Hall effect q Origin of the two-dimensional states that give rise to the QHE? q q Quantum confined bulk states? Topological surface states? x nm Cd 3 As 2 (111) CdTe R xy ( 10 3 Ω) nm 120 nm 70 nm 60 nm 10 nm 2 4 B (T) 6 8 Carrier density ( cm -2 ) Hall SdH 100 M. Goyal et al., APL Mater. 6, (2018). 200 Thickness (nm) 300 q q q Onset of QHE at 70 nm Two-dimensional states give rise to quantum oscillations already in thick films QHE develops as bulk states are gapped out with decreasing thickness

30 Quantum Hall Effect in Very Thin Films q Ultrathin films show the quantum Hall effect q Origin of the two-dimensional states that give rise to the QHE? q q Quantum confined bulk states? Topological surface states? Thick film Surface Fermi arcs Thin film Bulk Dirac nodes? Surface Gapped Bulk Fermi arcs Robust surface states predicted by theory.

31 Quantum Hall Effect in Very Thin Films q Ultrathin films show the quantum Hall effect q Origin of the two-dimensional states that give rise to the QHE? q q Quantum confined bulk states? Topological surface states? Surface Fermi arcs q QHE shows that these are two-dimensional states and there is little parasitic bulk conduction q It does not provide any information about the topological nature of these 2D states Bulk Surface? Dirac nodes Fermi arcs Gapped Bulk

32 Dirac Physics with Cd 3 As 2? In bulk Cd 3 As 2, high Fermi level (unintentional carriers) is claimed to prevent observation of Dirac physics: A. Akrap, et al., Phys. Rev. Lett. 117, (2016).

33 2D Dirac Physics: Landau Levels Conventional 2DEG 2D Dirac Fermions N = 3 N = 2 N = 1 Electrons DOS N = 0 Dirac point Holes E E Zero energy Landau level only present for Dirac electrons

34 2D Dirac Physics: Landau Levels Tune the Fermi level via a gate voltage Cd 3 As 2 Metal 2D#Dirac#Fermions N#=#3 N#=#2 N#=#1 N#=#0 Electrons Dirac#point Holes Top-gated Hall bar structure with ALD Al 2 O 3 Landau level spectroscopy E Zero#energy#Landau#level#only# present#for#dirac#electrons L. Galletti, T. Schumann, O. F. Shoron, M. Goyal, D. A. Kealhofer, H. Kim, and S. Stemmer, Phys. Rev. B, accepted (2018).

35 Tuning Through the Dirac Point R xx (h/e 2 ) T 3.6 T 7 T 10.6 T 13.8 T V G (V) (er H ) -1 ( cm -2 ) V G (V) 38 nm Cd 3 As 2 Cd 3 As 2 q Gate voltage tunes through the Dirac point of the 2D states q Depletion of electron-type carriers followed by hole accumulation as gate voltage is swept from positive to negative L. Galletti, et al., Phys. Rev. B, accepted (2018). Metal

36 Fan Diagram q Quantum oscillations shift to higher V G at higher magnetic fields indicating electron-type transport q Charge neutrality point in good agreement with that determined from R xx q Landau level for p-type carriers can be detected q All consistent with a Dirac point for the 2D carriers L. Galletti, T. Schumann, O. F. Shoron, M. Goyal, D. A. Kealhofer, H. Kim, and S. Stemmer, Phys. Rev. B, accepted (2018).

37 2D Dirac Physics: Density of States C (µf/cm 2 ) T 14 T V G (V) C (µf/cm 2 ) C q = D e 2 C ox C q C ox = 0.55 μf/cm 2 q The DOS of a 2D Dirac system depends linearly on the Fermi energy q CV measurements probe the DOS as a function of Fermi level L. Galletti, T. Schumann, O. F. Shoron, M. Goyal, D. A. Kealhofer, H. Kim, and S. Stemmer, Phys. Rev. B, accepted (2018).

38 2D Dirac Physics: Density of States C q (µf/cm 2 ) T 14 T C q (µf/cm 2 ) q The quantum capacitance, and thus the DOS, depends linearly on the Fermi energy q Note the CNP q With an applied magnetic field, the zero energy Landau level is present p 1/2 n 1/2 (10 6 cm -1 ) 4 2D Dirac Fermions in a Confined 3D Dirac Semimetal! " = ħ% " &' L. Galletti, T. Schumann, O. F. Shoron, M. Goyal, D. A. Kealhofer, H. Kim, and S. Stemmer, Phys. Rev. B, accepted (2018).

39 Summary q Transformed a 3D Dirac semimetal into a 2D gas of Dirac fermions q Topological state engineering! q Consistent with theoretical predictions of robust surface states q But: many open questions as to the nature of these states Surface Gapped Bulk Fermi arcs Data does not look like this. It looks like a single set of Landau levels. Screening? Hybridization of the two surfaces? Nature of the state at the CNP?

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