title: Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators.
abstract: 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.
authors: Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA.
authors: Ilija
authors: I
authors: Zeljkovic
authors: 1] Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA [2] WPI-AIMR, Tohoku University, Sendai 980-8577, Japan.
authors: Yoshinori
authors: Y
authors: Okada
authors: 1] Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA [2] Department of Physics, University of California, Berkeley, California 94720-7300, USA.
authors: Maksym
authors: M
authors: Serbyn
authors: 1] Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan [2] Institute of Physics, Academia Sinica, Taipei 11529, Taiwan.
authors: R
authors: R
authors: Sankar
authors: Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA.
authors: Daniel
authors: D
authors: Walkup
authors: Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA.
authors: Wenwen
authors: W
authors: Zhou
authors: Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors: Junwei
authors: J
authors: Liu
authors: Graphene Research Centre and Department of Physics, National University of Singapore, Singapore 117542, Singapore.
authors: Guoqing
authors: G
authors: Chang
authors: Department of Physics, Northeastern University, Boston, Massachusetts 02115 USA.
authors: Yung Jui
authors: YJ
authors: Wang
authors: Joseph Henry Laboratory, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors: M Zahid
authors: MZ
authors: Hasan
authors: Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan.
authors: Fangcheng
authors: F
authors: Chou
authors: Graphene Research Centre and Department of Physics, National University of Singapore, Singapore 117542, Singapore.
authors: Hsin
authors: H
authors: Lin
authors: Department of Physics, Northeastern University, Boston, Massachusetts 02115 USA.
authors: Arun
authors: A
authors: Bansil
authors: Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors: Liang
authors: L
authors: Fu
authors: 1] Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA [2] Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA.
authors: Vidya
authors: V
authors: Madhavan