Recently, unconventional superconductivity having a zero-bias conductance peak is reported in doped topological Dirac semimetal (DSM) with lattice distortion. Motivated by the experiments, we theoretically study the possible symmetry-lowering lattice distortions and their effects on the emergence of unconventional superconductivity in doped topological DSM. We find four types of symmetry-lowering lattice distortions that reproduce the crystal symmetries relevant to experiments from the group-theoretical analysis. Considering inter-orbital and intra-orbital electron density-density interactions, we calculate superconducting phase diagrams. We find that the lattice distortions can induce unconventional superconductivity hosting gapless surface Andreev bound states (SABS). Depending on the lattice distortions and superconducting pairing interactions, the unconventional inversion-odd-parity superconductivity can be either topological nodal superconductivity hosting a flat SABS or topological crystalline superconductivity hosting a gapless SABS. Remarkably, the lattice distortions increase the superconducting critical temperature, which is consistent with the experiments. Our work opens a pathway to explore and control pressure-induced topological superconductivity in doped topological semimetals.

最近，在具有晶格畸变的掺杂拓扑狄拉克半金属（DSM）中报道了具有零偏置电导峰的非常规超导性。在实验的推动下，我们从理论上研究了可能降低对称性的晶格畸变及其对掺杂拓扑 DSM 中非常规超导性出现的影响。我们从群论分析中发现了四种类型的对称性降低晶格畸变，它们再现了与实验相关的晶体对称性。考虑到轨道间和轨道内电子密度-密度相互作用，我们计算了超导相图。我们发现晶格畸变可以诱导非常规超导性承载无间隙表面 Andreev 束缚态 (SABS)。取决于晶格畸变和超导配对相互作用，非常规反转奇宇称超导性可以是承载平坦 SABS 的拓扑节点超导性或承载无间隙 SABS 的拓扑晶体超导性。值得注意的是，晶格畸变增加了超导临界温度，这与实验一致。我们的工作为探索和控制掺杂拓扑半金属中压力诱导的拓扑超导性开辟了一条途径。