Photon Factory Activity Report 2018 #36 (2019)

BL-2A/2018G653

A Dirac nodal line in AlB2 observed by soft-x-ray ARPES
Daichi Takane,1 Seigo Souma,2,3,* Kosuke Nakayama,1 Takechika Nakamura,1 Hikaru Oinuma,1Kentaro Hori,1 Koji Horiba,4 Hiroshi Kumigashira,4,5 Noriaki Kimura,1 Takashi Takahashi,1,2,3 andTakafumi Sato1,2,3
1 Department of Physics, Tohoku University, Sendai 980-8578, Japan
2 Center for Spintronics Research Network, Tohoku University, Sendai 980-8577, Japan
3 WPI-AIMR, Tohoku University, Sendai 980-8577, Japan4 Photon Factory, Institute of Materials Structure Science, High Energy Research Organization,
1-1 Oho, Tsukuba, 305-0801, Japan
5 IMRAM, Tohoku University, Sendai 980-8577, Japan
1 Introduction
Topological semimetals (TSMs) host a novel quantum
state of matter distinct from well-known topologicalinsulators with a finite bulk band gap and metallic Diraccone surface states. Based on the way of band touching in
momentum space, TSMs are categorized into two groups;
point-node type (Dirac or Weyl SM) and line-node type.
Topological nodal line semimetals (TNLSMs) arepredicted to show unique physical properties like a flat
Landau level, long-range Coulomb interaction, andunusual charge polarization and orbital magnetism.
However, many of known materials realizing TNLSMs
include heavy elements with large spin-orbit coupling sothat band crossing points are gapped in momentum space,which would hinder the genuine physical properties
relevant to nodal line.
In this regard, AlB2 is one of most suitable materials for
TNLSM because the energy bands near the Fermi level(EF) are composed of only s and p orbitals of light elements(Al and B). AlB2 is isostructural to well-known hightemperature superconductor MgB2, consisting ofalternatively stacking honeycomb B layers and triangular
Al lattices. A first-principles band calculation suggests thatAlB2 has a linear band crossing (Dirac cone) which arises
from the B sub-lattice at the K point in the bulk BZ [1], asin the case of graphene. A similar prediction is also madefor iso-structural MgB2. It is urgently required toexperimentally establish the DNL in AlB2-type materials
and clarify its possible link to the exotic physical properties.
2 ExperimentHigh-quality single crystals of AlB2 were grown by theAl-flux
method.
Angle-resolved
photoemission
spectroscopy (ARPES) measurements were performed
with a SES2002 electron analyzer at BL2. We used linearlypolarized light of 260-550 eV. The energy and angularresolutions were set to be 150 meV and 0.2˚, respectively.
Crystals were cleaved in situ in an ultrahigh vacuum better
than 1×10-10 Torr along the (0001) crystal plane. Sample
temperature was kept at T = 40 K during ARPES
measurements.
3 Results and Discussion
By utilizing bulk-sensitive soft-x-ray photons fromsynchrotron radiation, we experimentally established thebulk valence band structure in the 3D bulk BZ of AlB2, andfound a highly anisotropic Dirac-cone energy band in thekx−ky plane which disperses along the kz direction [2].
To elucidate the Dirac-cone band dispersion along the kz
direction, we show in Figure 1(a) the ARPES intensity

Fig. 1: (a) and (b) ARPES intensity__and corresponding second-derivative intensity plots of AlB2, respectively,
measured along a cut crossing the K point for selected kz’s. Arrows indicate location of the Dirac points. (c)Schematic of the Dirac-cone dispersion and DNL around the KH line [2].

Photon Factory Activity Report 2018 #36 (2019)__across the K point measured at various kz’s, together withthe corresponding second-derivative intensity plots [Fig.
1(b)]. In Figs. 1(a) and (b), we observe a linearly dispersive
band for all the kz slices. The Dirac point located at ∼ 0.5
eV above EF at kz ∼ 0 gradually moves downward onincreasing kz, and finally reaches 5 eV below EF at kz ∼ π.
Intriguingly,the band always keeps the degeneracy at the__K point irrespective of kz with no indication of energy-gap
opening. This firmly establishes the presence of a DNL
along the whole KH line in AlB2. The DNL has a finite
slope in the E-kz space due to the kz dispersion of π band,as illustrated in Fig. 1(c). It is noted that we surveyed theelectronic states over the entire BZ, and found no evidence
for the existence of other DNLs in AlB2. This__ is reasonable
since the Dirac cone exists only around the K point.
It is inferred that the observed DNL in AlB2 has the same
origin as that recently predicted for MgB2 [1], because bothmaterials have essentially the same crystal structure andconsequently the same band structure except for theposition of the chemical potential (Fermi level) due to thedifference in the number of valence electrons (Al has one
additional electron compared to Mg). It is therefore
suggested that MgB2 also has a DNL and may behave as
topological superconductor with nodal fermionscontributing to the superconducting pairing. It is noted herethat AlB2 is a suitable system to investigate the anomaloustransport properties originating from non-zero Berryphase, because it is theoretically proposed that the Landau
orbit enclosing the KH line gives rise to the non-zero Berryphase [1]. This condition is exactly satisfied in AlB2 [seeFig. 1(a)]. Moreover, by tuning the Al/Mg ratio in(Al,Mg)B2 alloy, we are able to systematically control theelectronic phase between the superconducting phase andthe non-trivial Berry phase without breaking the DNL. The(Al,Mg)B2 system would provide a precious opportunity toinvestigate the relationship between topologicalsuperconductivity and Berry phase.
Acknowledgement
We thank M. Kitamura and R. Yukawa for experimental
support of this work.
References[1] K.-H. Jin et al., npj Comput. Mater. 5, 57 (2019); arXiv
1710.06996 (2017).
[2] D. Takane et al., Phys. Rev. B 98, 041105(R) (2018).
* s.souma@arpes.phys.tohoku.ac.jp