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Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators


The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb1−xSnxSe for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons—a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Finally, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.

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Figure 1: Bulk cubic crystal structure of Pb1−xSnxSe.
Figure 2: Symmetry-breaking distortion on the surface of Pb1−xSnxSe.
Figure 3: Landau level spectroscopy.
Figure 4: Evolution of the Dirac gap with alloy composition.
Figure 5: Evolution of band structure with alloy composition.
Figure 6: Evolution of SS across the topological quantum phase transition.


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We thank R. Buczko, C. Chamon, J. C. Seamus Davis, M. El-Batanouny, A. Mesaros, Y. Ran and A. Soumyanarayanan for useful conversations and G. McMahon for help with EDS measurements. V.M. gratefully acknowledges funding from the US Department of Energy, Scanned Probe Division under Award Number DE-FG02-12ER46880 for the support of I.Z., Y.O., W.Z. and D.W. for this project. Work at Massachusetts Institute of Technology is supported by US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010526 (L.F.), and NSF-DMR-1104498 (M.S.). H.L. acknowledges the Singapore National Research Foundation for support under NRF Award No. NRF-NRFF2013-03. Y.O. was partly supported by JSPS KAKENHI Grant Numbers 26707016 and 00707656. The work at Northeastern University is supported by the US Department of Energy grant number DE-FG02-07ER46352, and benefited from Northeastern University’s Advanced Scientific Computation Center (ASCC), theory support at the Advanced Light Source, Berkeley and the allocation of supercomputer time at the NERSC through DOE grant number DE-AC02-05CH11231. Work at Princeton University is supported by the US National Science Foundation Grant, NSF-DMR-1006492. F.C. acknowledges the support provided by MOST-Taiwan under project number NSC-102-2119-M-002-004.

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Authors and Affiliations



Y.O. and I.Z. contributed equally to this work. Y.O., I.Z. and V.M. designed the experiments. STM experiments were carried out by Y.O., I.Z., D.W. and W.Z. I.Z., Y.O., L.F. and V.M. analysed the data and wrote the paper. Samples were obtained from R.S., F.C. and M.Z.H. F.C. and R.S. contributed to the single-crystal growth and structural analysis. L.F. conceived the theoretical explanation for this work. M.S. performed analytical model calculations. H.L. and A.B. supervised the first-principles part of the work, which was performed by G.C., Y.J.W., J.L. and H.L.

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Correspondence to Ilija Zeljkovic, Yoshinori Okada or Vidya Madhavan.

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Zeljkovic, I., Okada, Y., Serbyn, M. et al. Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators. Nature Mater 14, 318–324 (2015).

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