## 1 Introduction  
Spin gapless semiconductor shows a \"zero\" gap at the Fermi level in one of the spin channels, and a semiconductor band gap in the other spin channel from its electronic structure [1]. In Figure 1, several densities of states (DOSs) of the spin gapless semiconductor (SGS) are dramatically described. Both direct (Figure 1c) and indirect (Figure 1d) zero band gap existed in real SGS material. For SGS materials, in the past few years, many novel electronic and thermophysical properties have deeply attracted researchers' attention and are expected to be applied in future spintronic devices [2]. The mobility of carriers, which includes full spin-polarized electrons and holes [3], is higher than that of the classical semiconductors or half-metallic ferromagnetism (HMFs) [4]. Owing to this \"ideal\" spin-polarized electrons and holes, SGS can create a spontaneous transition of electrons from the valence band to the conduction band without any threshold energy [5]. Furthermore, the SGS can also retain high resistance and high Curie temperature simultaneously [6]; moreover, its electrical conductivity is seldom affected by temperature, electric field, electromagnetic radiation, or impurities, and the spin-polarized carriers of n-type and p-type can be switched by applying a gate voltage [7]. In 2008, SGS was first predicted in diluted magnetic semiconductors (DMS) PbPdO\({}_{2}\) by [PERSON]'s group [8]. Thereafter, graphene nanotubes [9], double perovskite La\({}_{2}\)CrFeO\({}_{6}\)[10], and many Heusler alloys with SGS properties were detected. Especially for Heusler alloys, the previous results show that many Heusler alloys are (or nearly) spin gapless semiconductors in their ground states at low temperature. In 2013, five ternary Heusler alloys Ti\({}_{2}\)MnAl, Ti\({}_{2}\)CoSi, Ti\({}_{2}\)VAs, Cr\({}_{2}\)ZnSi, Mn\({}_{2}\)CoAl and one binary Heusler alloy V\({}_{3}\)Al were first detected and predicated as potential SGSs from the first-principle calculations [11]. In the experiment, the polycrystalline Heusler alloy Mn\({}_{2}\)CoAl were also prepared and identified as an SGS [12]. According to Slater-Pauling rule [13; 14; 15], if the magnetic moment per primitive cell is agreeable well with \(Z_{\rm{T}}\)-24 for full-Heusler alloys and few quaternary Heusler alloys or \(Z_{\rm{t}}\)-18 for inverse-Heusler alloys and most of the quaternary Heusler alloys, where \(Z_{\rm{t}}\) is the number of valence electrons in a primitive cell, Heusler alloys will present nonmagnetic states. Among those nonmagnetic Heusler alloys, there are more chances of finding new SGSs. Thus, in the past five years, a lot of SGSs have been found additionally in ternary Hg\({}_{2}\)CuTi-type or LiMgPbSn-type quaternary Heusler alloys, such as Zr-based Heusler alloys including ZrCoVIn, ZrFeVGe, ZrCoFeP, ZrCoCrBe and ZrFeCrZ (\(Z\) = In and Ga), and Zr\({}_{2}\)MnGa [15], Ti-based Heusler alloy Ti\({}_{2}\)CoAs [16], Ti\({}_{2}\)MnAl [17], and Ti\({}_{2}\)CrSi [18], as well as other quaternary Heusler alloy VCoHfGa, CrFeHfGa [19], and CoFeMnSi [1]. In fact, in those SGS candidates by theoretical prediction, it is hard to select an \"ideal\" SGS for promising application experimentally owing to the sensitive and flimsy \"zero\" gap, which can be easily damaged by the crystal structure, surface or interface interaction, and other external factors. A slight adjustment of band gap can sharply decrease the initial spin polarization and weaken the transport properties of the carriers. To solve this problem, the optimal method is to manipulate the band width by means of the external field, controllably. Assuredly, the pressure as a force field is one of the appropriate choices. Thus, the dependence of SGS properties on pressure is focused in our present work. Since Sc\({}_{2}\)FeSi or Sc\({}_{2}\)FeGe is a nonmagnetic inverse-Heusler semiconductor [20] and ZrFeVGe shows typical SGS behavior [16], we, therefore, deduce that quaternary Heusler alloy VFeScZ (\(Z\) = Sb, As, P) is nearly an SGS or a semiconductor.