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The exceptional magnetoresistance of semimetals

The exceptional magnetoresistance of semimetals. October 9, 2017. Why is this interesting?. 1856: Lord Kelvin discovers ordinary magnetoresistance (OMR) 1879: Edwin Hall discovers the Hall effect 1985: Nobel Prize for Quantum Hall effect 1998: Nobel Prize for fractional QHE

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The exceptional magnetoresistance of semimetals

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  1. The exceptional magnetoresistance of semimetals October 9, 2017

  2. Why is this interesting? 1856: Lord Kelvin discovers ordinary magnetoresistance (OMR) 1879: Edwin Hall discovers the Hall effect 1985: Nobel Prize for Quantum Hall effect 1998: Nobel Prize for fractional QHE 2007: Nobel prize for Giant Magnetoresistance (GMR) Colossal (CMR), extraordinary (EMR), etc. History of magneto-transport

  3. Brief equations for a single charge carrier Equation of motion of an electron in a uniform magnetic field: Classical magnetoresistance Leads to the static magnetoconductivity tensor: Hall conductivity:

  4. Changes for a two-carrier model Electron and hole model gives a conductivity as such: Classical magnetoresistance Equal electron and hole populations (n=p): Otherwise: Classically, magnetoresistance scales with B2 if the carriers are equal. Otherwise, it saturates to a constant value.

  5. How does QM change things? Intuitively, quantum effects are non-negligible when: Quantum effects Another “extreme” quantum limit is when: What happens in strong magnetic fields? Landau quantization nist.gov *Landau levels lead to quantum Hall effect

  6. Differences from the classical picture It was found that the quantum MR follows: Quantum magnetoresistance Abrikosov, A. “Quantum magnetoresistance” Phys. Rev. B. 58, 5 1998. Linear dependence on field, no saturation Magnetic field necessary to pull all the electrons into the lowest Landau Level? For some 2DEG: ~10 T

  7. Why MR in semimetals? Semimetals Classical: Two carrier transport may give higher MR (n=p) Quantum: “dilute” semimetals make it easier to access the quantum limit. DOS at the Fermi-level is low, carrier density is low.

  8. Summarizing the last few slides… Magneto-transport is a host to many rich physical phenomena which have led to real world applications. This talk will focus on the magnetoresistance found in semimetals. Classically, in a semimetal, the MR will rise as B2 if n=p and will otherwise saturate. Applying a large enough B-field will introduce Landau quantization. Quantum MR predicts a linear dependence with B in zero gap materials. Brief Interlude

  9. Vastly different MR phenomena in semimetals Quadratic XMR Linear XMR Cd3As2 Dirac semimetal Nat. Mater. 14, 280 (2015). TaAs Weyl semimetal Phys. Rev. X 5, 031023 (2015). NbP Weyl semimetal Nat. Phys. 11, 645 (2015). TmPn2 (Tm=Ta/Nb, Pn=As/Sb) Phys. Rev. B 93, 195119 (2016). LnX (Ln=La/Y, X=Sb/Bi) Nat. Phys. 12, 272 (2015). ZrSiS arXiv: 1602.01993. WTe2 Nature 514, 205 (2014). List of examples

  10. Electron-hole resonance compensation Nature 514, 205 (2014). Forbidden backscattering at zero field Phys. Rev. Lett. 115, 166601 (2015). Field-induced Fermi surface changes Sci. Rep. 4, 7328 (2014). Nontrivial band topology Nat. Phys. 12, 272 (2015). XMR mechanisms

  11. Lanthanum Antimony Unsaturated magnetoresistance Fit well by three-band model Zeng. L. –K., et al. “Compensated semimetal LaSb with unsaturated magnetoresistance” Phys. Rev. Lett.117 (2016).

  12. Lanthanum Antimony Carrier imbalance? ne/nh~100 ARPES reveal no observable changes of the FSs with temperature in LaSb. Zeng. L. –K., et al. “Compensated semimetal LaSb with unsaturated magnetoresistance” Phys. Rev. Lett.117 (2016).

  13. Lanthanum Antimony No Dirac-like surface states are observed. LaSb is topologically trivial but with a linearly dispersive bulk band. Zeng. L. –K., et al. “Compensated semimetal LaSb with unsaturated magnetoresistance” Phys. Rev. Lett.117 (2016).

  14. Dirac semimetal (3D Graphene) Cadmium Arsenide Dirac semimetal is a bulk analogue to graphene Dirac cone in all dimensions Liu, Z.K., et al. “A stable three-dimensional topological Dirac semimetal Cd3As2” Nat. Mat. 13(2014).

  15. Dirac semimetal Cadmium Arsenide Liang, T., et al. “Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2” Nat. Mat. 14 (2015).

  16. Dirac semimetal Picture fits the “quantum” magnetoresistance for linear and non-saturating. Mechanism for the magnetoresistance is still not fully understood and being actively pursued at the moment. Recently the Weyl semimetal, TaAs, also demonstrated linear magnetoresistance. Cadmium Arsenide Zhang, C., et al. “Tantalum Monoarsenide: an Exotic Compensated Semimetal” arXiv.

  17. The “unstoppable” magnetoresistance Tungsten Ditelluride Anisotropic crystal structure (distorted hexagonal) Metallic chains along the “a” lattice direction No CDW phase? (TEM shows no additional peaks under B-field but at high T) Ali, M. N., et al. “Large, non-saturating magnetoresistance in WTe2” Nature. 514 (2014).

  18. The “unstoppable” magnetoresistance Tungsten Ditelluride Ali, M. N., et al. “Large, non-saturating magnetoresistance in WTe2” Nature. 514 (2014).

  19. The “unstoppable” magnetoresistance Near quadratic up to 60 T Tungsten Ditelluride Slope ~1.96 Ali, M. N., et al. “Large, non-saturating magnetoresistance in WTe2” Nature. 514 (2014).

  20. The basis for MR? Is the n=p compensation really perfect/protected for the first time? Tungsten Ditelluride Ali, M. N., et al. “Large, non-saturating magnetoresistance in WTe2” Nature. 514 (2014).

  21. The basis for MR? Tungsten Ditelluride Ali, M. N., et al. “Large, non-saturating magnetoresistance in WTe2” Nature. 514 (2014). Pletikosic, I., et al. “Electronic Structure Basis for the Extraordinary Magnetoresistance in WTe2” Phys. Rev. Lett. 113, 216601(2014).

  22. Classical vs. Correlated? Is there no other material which exhibits perfect n=p compensation? Or could this involve some QM/correlated phenomena? B-field induced phase transition? In TMDC: TiSe2 exhibits an excitonic insulator state which also requires n=p Tungsten Ditelluride 250 to 65 K a new band emerges and the gap opens from semimetal to insulator in the CDW TMDC TiSe2. Ali, M. N., et al. “Large, non-saturating magnetoresistance in WTe2” Nature. 514 (2014). Cercellier, H., et al. “Evidence for an Excitonic Insulator Phase in 1T-TiSe2” Phys. Rev. Lett. 99, 146403(2007).

  23. Conclusions and next steps Magnetoresistance is a very rich topic in semimetals due to the many observed effects as well as caused effects. This includes other magneto-transport effects such as WL/WAL New classes of Dirac and Weyl semimetals are interesting due to their topological properties, which contribute to their high observable mobilities and MR. These materials are becoming the next highly researched topic. Summary I

  24. Conclusions and next steps WTe2 has an amazing magnetoresistance never before observed. The exact mechanism for the non-saturating B2 MR is not fully understood. ARPES confirms from that the electronic structure that n=p, why other similar materials cannot demonstrate the same effect (Bukchornite, TiSe2)? The nature of the layered WTe2structure makes it natural to tune the MR with an electric field. Possibly some correlated phenomena or phase changes related to WTe2. Summary II

  25. Conclusions and next steps The physical properties of these 3D semimetal, Dirac semimetal, Weyl semimetal in 2D forms. Exotic Hall effects? Gate tunable XMR? Anisotropic transport? Summary III

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