Helical Surface State in Multilayer Massless Dirac Fermion System

What is the ground state of massless Dirac fermion systems under a magnetic field? This question has attracted a great deal of attention, since several types of ν = 0 quantum Hall (QH) states, which emerge on the ν = 0 Landau level with spin and valley degeneracies, have been predicted. Examples of these include the QH insulator with no edge state that appears when the valley-splitting dominates the degeneracy breaking [1–3], the QH ferromagnet with the helical edge state that is realized when the spin-splitting is dominant [4,5], and the canted antiferromagnet with an intermediately gapped edge state [6,7].

The organic conductor α-(BEDT-TTF)₂I₃ exhibits a multilayer two-dimensional massless Dirac fermion system in bulk crystal. The interlayer magnetoresistance (MR), which rapidly decreases as the magnetic field increases, ensures the existence of the massless Dirac fermion system [8]. Although the MR begins to increase exponentially owing to the splitting of the ν = 0 Landau level as the magnetic field increases, this increase saturates in higher magnetic fields [9].

Osada [10] has shown that the saturation of the MR is well explained as the interlayer surface transport via the helical edge state by assuming that the ground state is the QH ferromagnet. The QH ferromagnet in a single-layer Dirac fermion system is accompanied by the helical edge state, i.e., a pair of edge states with opposite spin and chirality, as shown in Fig. 1(a). Osada [10] has studied interlayer tunneling between the helical edge states in the multilayer massless Dirac fermion system. It has been shown that interlayer tunneling with no energy change only occurs when the magnetic field is parallel to the edge surface shown in Fig. 1(b). The helical surface state is stabilized by this resonant inter-edge tunneling. It has been also shown that the interlayer surface conductivity is finite (but much less than e²/h), which indicates metallic surface transport. When the magnetic field is tilted away from the edge surface, the interlayer surface conductivity exhibits Lorentzian decay, because the resonant inter-edge tunneling is suppressed. Although the mechanism of low-temperature anomalies observed in NMR is still an open question, this lucid work accelerates exploration of the ground state of multilayer Dirac fermion systems under a magnetic field.

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Fig. 1. The helical edge state in the ν = 0 quantum Hall ferromagnet in a single-layer Dirac fermion system (a), and an electronic state in a multilayer Dirac fermion system (b). This figure is taken from Fig. 1 in Ref. [10].

References

• [1] J. G. Checkelsky, L. Li, and N. P. Ong, Phys. Rev. Lett. 100, 206801 (2008). 10.1103/PhysRevLett.100.206801 Crossref, Google Scholar
• [2] K. Nomura, S. Ryu, and D.-H. Lee, Phys. Rev. Lett. 103, 216801 (2009). 10.1103/PhysRevLett.103.216801 Crossref, Google Scholar
• [3] A. F. Young, C. R. Dean, L. Wang, H. Ren, P. Cadden-Zimansky, K. Watanabe, T. Taniguchi, J. Hone, K. L. Shepard, and P. Kim, Nat. Phys. 8, 550 (2012). 10.1038/nphys2307 Crossref, Google Scholar
• [4] D. A. Abanin, P. A. Lee, and L. S. Levitov, Phys. Rev. Lett. 96, 176803 (2006). 10.1103/PhysRevLett.96.176803 Crossref, Google Scholar
• [5] D. A. Abanin, K. S. Novoselov, U. Zeitler, P. A. Lee, A. K. Geim, and L. S. Levitov, Phys. Rev. Lett. 98, 196806 (2007). 10.1103/PhysRevLett.98.196806 Crossref, Google Scholar
• [6] M. Kharitonov, Phys. Rev. B 85, 155439 (2012) 10.1103/PhysRevB.85.155439; Crossref;, Google ScholarM. Kharitonov, Phys. Rev. B 86, 075450 (2012). 10.1103/PhysRevB.86.075450 Crossref, Google Scholar
• [7] A. F. Young, J. D. Sanchez-Yamagishi, B. Hunt, S. H. Choi, K. Watanabe, T. Taniguchi, R. C. Ashoori, and P. Jarillo-Herrero, Nature 505, 528 (2014). 10.1038/nature12800 Crossref, Google Scholar
• [8] K. Kajita, Y. Nishio, N. Tajima, Y. Suzumura, and A. Kobayashi, J. Phys. Soc. Jpn. 83, 072002 (2014), and references therein. 10.7566/JPSJ.83.072002 Link, Google Scholar
• [9] T. Osada, Phys. Status Solidi B 249, 962 (2012). 10.1002/pssb.201100587 Crossref, Google Scholar
• [10] T. Osada, J. Phys. Soc. Jpn. 84, 053704 (2015). 10.7566/JPSJ.84.053704 Link, Google Scholar

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