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Type-II Symmetry-Protected Topological Dirac Semimetals Tay-Rong Chang_,1 Su-Yang Xu_y,2 Daniel S. Sanchez,2 Wei-Feng Tsai,3, 4 Shin-Ming Huang,5 Guoqing Chang,3, 4 Chuang-Han Hsu,3, 4 Guang Bian,2 Ilya Belopolski,2 Zhi-Ming Yu,6, 7 Shengyuan A. Yang,7 Titus Neupert,8 Horng-Tay Jeng,1, 9 Hsin Liny,3, 4 and M. Zahid Hasany2 1Department 2Laboratory of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan for Topological Quantum Matter and Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA 3Centre for Advanced 2D Materials and Graphene Research Centre National University of Singapore, 6 Science Drive 2, Singapore 117546 4Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 5Department of Physics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan 6School of Physics, Beijing Institute of Technology, Beijing 100081, China 7Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore 8Department 9Institute of Physics, University of Zurich, 190, CH-8052, Switzerland, Winterthurerstrass of Physics, Academia Sinica, Taipei 11529, Taiwan The discoveries of Dirac and Weyl semimetal states in spin-orbit compounds led to the realizations of elementary particle analogs in table-top experiments. Recently, a new type of emergent Weyl fermion attracted interest because it strongly violates Lorentz symmetry whose analog does not exist in the Standard Model. While this state has been dubbed the type-II Weyl semimetal and predicted in a number of materials, its Dirac counterpart has remained elusive. In this paper, we propose the concept of the three-dimensional type-II Dirac fermion and theoretically identify this new symmetry-protected topological state in the large family of transition-metal icosagenides, MA3 (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl3 family features a pair of strongly Lorentz violating type-II Dirac nodes and that each Dirac node consists of four type-II Weyl nodes with chiral charge ±1 via symmetry breaking. Furthermore, we predict the Landau level spectrum arising from the type-II Dirac fermions in VAl3 that is distinct from that of known Dirac/Weyl semimetals. We also show a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions.