Open access peer-reviewed chapter

Superconductivity in Materials under Extreme Conditions: An ab-initio Prediction from Density Functional Theory

Written By

Thiti Bovornratanaraks and Prutthipong Tsuppayakorn-aek

Reviewed: 15 July 2021 Published: 09 August 2021

DOI: 10.5772/intechopen.99481

From the Edited Volume

Density Functional Theory - Recent Advances, New Perspectives and Applications

Edited by Daniel Glossman-Mitnik

Chapter metrics overview

302 Chapter Downloads

View Full Metrics

Abstract

The relation between thermodynamically stable and electronic structure preparation is one of the fundamental questions in physics, geophysics and chemistry. Since the discovery of the novel structure, this has remained as one of the main questions regarding the very foundation of elemental metals. Needless to say this has also bearings on extreme conditions physics, where again the relation between structure and performance is of direct interest. Crystal structures have been mainly at ambient conditions, i.e. at room temperature and ambient pressure. Nevertheless it was realized early that there is also a fundamental relation between volume and structure, and that this dependence could be most fruitfully studied by means of high pressure experimental techniques. From a theoretical point of view this is an ideal type of experiment, since only the volume is changed, which is a very clean variation of the external conditions. Therefore, at least in principle, the theoretical approach remains the same irrespective of the high pressure loading of the experimental sample. Theoretical modeling is needed to explain the measured data on the pressure volume relationships in crystal structures. Among those physical properties manifested itself under high pressure, superconductivity has emerged as a prominent property affected by pressure. Several candidate structure of materials are explored by ab initio random structure searching (AIRSS). This has been carried out in combination with density functional theory (DFT). The remarkable solution of AIRSS is possible to expect a superconductivity under high pressure. This chapter provide a systematically review of the structural prediction and superconductivity in elemental metals, i.e. lithium, strontium, scandium, arsenic.

Keywords

  • ab initio random structure searching
  • density functional theory
  • superconductor
  • lithium
  • strontium
  • scandium
  • arsenic

1. Introduction

It is a long time since Kohn and Sham pave the way to the self-consistent equation, based on the exchange and correlation effects in 1965, leading the Kohn–Sham (KS) Equation [1]. This has ignited the success of quantum physics and chemistry, specifically many-body problem, owing to the KS equation can be utilized for the ground state energy. Briefly stated, the KS equation formalism of density functional theory (DFT) described the motion of electron nuclei, which separated to be two part: the energy of electron Eelectron and the Coulomb interactions between the nuclei Enuclei And what is more, the details of Ewald summations have been described extensively in Refs. [2, 3]. Apart from this, Eelectron and Enuclei were performed by using the pseudopotential approximation within the KS equation. It is because of the effects of Coulomb interactions between the nuclei Enuclei, as being in accordance with the the core electrons Ecore, that the terms Eelectron and Ecore used in the static crystal energy of materials relevant to the energies of valence electrons and pseudocores. Subsequently, the KS equation displayed the term Eelectron is from the summation of quasiparticle eigenvalues, corresponding the Kohn–Sham orbital, of occupied states.

Regarding thermodynamic properties, the Gibbs free energy is considered for the static crystal energy of materials; however, the KS equation formalism of DFT carried out at a temperature of 0 K. The Gibbs free energy therefore reduced to the Enthalpy. This, appearing at first glance to be high potential for high-pressure physics, is actually demonstrated the importance of superconductivity. According to the aforementioned theoretical findings by the KS equation formalism of DFT, resulting the exchange and correlation effects Exc. Following this, Perdew et al. [4] presented a simple derivation of a simple of generalized gradient approximations (GGA) with Exc. This methodology appropriated, it is well known to GGA with Perdew-Burke-Ernzerhof (PBE), for description of atoms, molecules, and solids. This is due to the fact that the GGA-PBE method give an accurate with the most energetically important. As a result of this, the role of the GGA-PBE method is key factor in achieving the ground-state energy of the static crystal materials. Herein, we preformed mainly the PBE formalism of GGA for calculations of lithium, strontium, scandium, and arsenic under high pressure.

The extensive studies of electronic structure were initiated chiefly by the KS equation formalism of DFT. In principle, one should note the quasiparticle eigenvalues of occupied states is useful for achieving the electronic band structure, density of sates, phonon dispersion. It is also interesting to note the DFT used mainly strong sides for prediction the metallicity, leading to the prediction of superconducting transition temperature. For considered the superconductivity, the PBE formalism of GGA for exchange-correlation energy is suitable for interpret the metallicity. This implied that the reliable theoretical study has quite a predictive potential, moreover, the GGA-PBE for the exchange-correlation energy give an accurate description of dynamical stability of crystal structure. One of the well-known Bardeen-Cooper-Schrieffer (BCS) theory [5] were already discussed phonon mediated superconductivity, leading to the way to vast both experimental and theoretical studies on high-pressure research. At this stage, using the KS equation formalism of DFT with the GGA-PBE for the exchange-correlation energy were used to have unique features of phonon mediated superconductivity, showing towards the evidence of superconducting materials as well.

There is alternative way to use the KS equation formalism of DFT with the GGA-PBE. It is well known to ab initio random structure searching (AIRSS). The AIRSS method have been described extensively in Refs. [6, 7]. Especially, the AIRSS method is useful in achieving the high-pressure research owing to it can predict novel structure under compressed conditions. The reliable theory for ground-state structure can help to interpret experimental data. In fact, there is also quite some experimental observation cannot identify the atomic position and crystal symmetry. The AIRSS method is powerful tool and it can guide further experimental studies.

High pressure physics is important for structural phase transitions in materials [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Regarding a crystal structure of materials under high pressure, it can enhance electronic properties of materials [19, 20, 21]. Nowadays, superconductivity is one of the most charming in physical properties. Many materials were predicted to be a superconducting transition temperature (Tc), such as SH3 [22, 23, 24, 25], LaH10 [26, 27, 28], YH10 [28, 29, 30], CeH10 [17, 31]. It is worth note that hydrogen (H) is a role important for promoting a Tc. For example, the case of LaH10 was shown that the Tc reached 250 K at 170 GPa [26]. The existence of H displayed that it can support pure element lanthanum (La), one can see that the Tc of pure element lanthanum is 5.88 K [32]. It is interesting to note that the physical property of pure elemental metal should be mentioned.

As mentioned above, a structural prediction is a key factor for achieving a Tc. We referred the original predictions regarding superconductivity in strontium (Sr), it is beginning to show that the Tc of the predicted phase increased with a increasing pressure [33]. The case of strontium is interested. At high pressure, Sr. displayed structural phase transition from a simple structure to a complex structure [34, 35, 36, 37]. We can see that Sr. is a normal metal at ambient pressure, with a increasing pressure, Sr. is a metallicity, indicating that it is a superconductivity [33]. Moreover, Sr. is not only superconducting phase at high pressure, but also calcium (Ca) indicating possible increasing of the Tc also at high pressure [38].

A curious aspect of a Tc increased with increasing pressure. We found that Ca is one of a periodic table, indicating the highest Tc among the periodic table [38, 39, 40]. Moreover, it is not always clear whether or not that the increased pressure and Tc are increased. We note that scandium (Sc) [14] and arsenic (As) [12], shown a possible decreasing of Tc with a increasing pressure [12, 14]. Hence, the focus is on pure elemental metals are interesting. This is because that the prediction discovered to novel structure [12, 14], leading to the superconductivity at high pressure.

According to the aforementioned superconductor findings, the characteristic of electronic structure is often attributed to the Tc [14, 17, 41]. It is interesting that Lithium (Li) has the second highest Tc among the elemental metals [42, 43, 44, 45]. The electron localization function (ELF) is one of the tools can determine the Tc [14, 17]. The nature of chemical bonding is directly shown in the ELF, it is considered to be consistent with the highest Tc; this implies that a strong bonding supports the Tc of the metals [46].

Regarding superconductivity in the metals [12, 14, 17, 41], a lattice dynamic is a key factor for consideration a stable structure. In practice, we can achieve the superconducting structure through electron–phonon coupling (EPC) [12, 14, 17, 41]. For example, recent work on LaH10 has shown that the quantum effect is important for the stabilization and destabilization [27]. In fact, both thermodynamically and dynamically structures have to consistent. Generally, the solution of dynamically structure is a harmonic phonon but the case of LaH10 shown that it displayed an anharmonic phonon. This because the EPC exhibited the destabilized structure. Hence, it is worth to note that Sr. is possible to be an anharmonic phonon in the Sr-III structure (the β-tin structure) At this point, we found that there is a discrepancy between a experimental observation and a theoretical study [33, 34, 35, 36, 37, 47]. Herein we review the superconductivity in the elemental metals both the experimental observation and the theoretical study under high pressure. In this review, we provide the success of the metals [12, 14] is BCS-type superconductor [12, 14, 17, 19, 41, 48, 49, 50, 51, 52, 53]. Also, we hope that this review is useful for those interested readers in superconductivity in elemental metal under high pressure.

Advertisement

2. Methodology

In considered in the present work, we performed the first-principles calculations, based on the density functional theory, to examine the thermodynamic stability as a function of pressure. The static crystal energy of materials was considered at a temperature of 0 K. The calculation details of stable structure were determined by neglecting the entropy contributions. This is because the calculations were carried out at 0 K, indicating that the ground-state energy can confirm phase stability. Here, the KS equation formalism of DFT with the GGA-PBE for the exchange-correlation energy were used for Li, Sr., Sc, and As. For further details of the energy cutoff for plane waves and the Monkhorst–Pack k-point mesh as well as the DFT software have been described extensively in Refs. [10, 12, 13, 14]. Our works used the AIRSS technique, based on the density functional theory, to predict the novel structure. Following the AIRSS method, we calculated the enthalpies of the phases at any pressure using the simple linear approximation [7]. For each relaxed structure, the structures were simulated to be a non-symmetry and randomly placed in atomic position. During the calculations of the structures, it started to relax from bias until it reaches unbias. The shape is generating by shaking within a reasonable pressure range. It led to higher-symmetry space groups obtained in a search. The AIRSS technique is the approach in the local minima by giving the lowest enthalpy. We have studied the phonon mediated superconductivity by using isotropic Eliashberg theory, as implemented in the quantum espresso (QE) [54, 55]. Following the result of isotropic Eliashberg theory, the Allen-Dynes modify McMillan Equation [56] was used to estimated the superconducting transition temperature.

Advertisement

3. Result and discussion

3.1 Lithium

According to the aforementioned in the introduction, high pressure physics is useful in achieving a novel structure and superconductivity [12, 13, 14, 17, 33, 57, 58, 59]. Li is one of the challenging to find a novel structure [43, 60, 61, 62, 63]. Since it is interesting that there is complex structures were discovered in alkali metal, i.e. sodium (Na) [64], potassium (K) [65, 66, 67, 68], and rubidium (Rb) [69, 70]. Therefore, Li might be expected to possible to be a complex structure at high pressure. For the transitions sequence of Li, we found that the Im-3 m structure transformed into the Fm-3 m structure at pressure 8 GPa. Next, the Fm-3 m structure transformed into the R-3 m structure at pressure 39 GPa. With increasing pressure, the R-3 m structure transformed into the I-43d structure at pressure 44 GPa, then it transformed into C2mb at pressure 73 GPa. On further compression, the C2mb structure transformed into the C2cb structure at 80 GPa. Finally, it transformed into Cmca 120 GPa. It is interesting that there is no found the incommensurate host-guest structure at any pressure among such sequence [43, 60, 61, 62, 63, 71].

Li was observed by optical spectroscopic through diamond anvil cells (DAC) [72]. The solution of the experimental study revealed that there is unknown phase above 50 GPa. Moreover, the characteristic of the high frequency band, i.e. Li-Li vibration, can interpret to be an incommensurate host-guest structure. The commensurate host-guest structure is defined by the different the number of the guest atoms in channels in along the c axis of the host structure, referring to the commensurate value cH/cG, also known as γ. At this point, it is interested to examine the unknown structure by following the Ref. [72].

As mentioned above, the unknown structure can be identified by a random search techniques. The random search technique is the high performance for the prediction of the materials. For elemental Li, the ab initio random structure searching (AIRSS) technique [6] is employed for determination the unknown structure. The remarkable result shown that Li is predicted to be the incommensurate host-guest structure above 50 GPa. Tsuppayakorn-aek et al. [13] was pointed out that structural phase transitions of Li might be considered to be different origins in two-phase transition sequences (Figure 1). Interestingly, one of two transition sequences can be obtained the incommensurate host-guest structure, indicating that it is energetically stabilized above 50 GPa and Li is likely to crystallize in the incommensurate host-guest structure at high temperature.

Figure 1.

The relative enthalpy of Li as a function of pressure.

The existence of the incommensurate host-guest structure can be considered from the ELF calculation. As a possible cause of this, one might think of there is the s-pμ hybridization between the host–host atoms at 150 GPa (Figure 2) [13]. The study useful to point out that the possibility of the incommensurate host-guest structure is stable. Moreover, the nature of chemical bonding shown that the incommensurate host-guest structure has tend to favor superconductivity at higher pressure. It is worth to note that the nature of the chemical bonding of the host–host atoms, i.e. the μ bonging, might be considered to be a superconducting phase.

Figure 2.

The electron localization function (ELF) of the host-guest structure of Li is calculated in the (001) atomic plane.

3.2 Strontium

Structural phase transitions in alkaline earth metal under high pressure is interested among the periodic table. Nowadays, there are several works reported a transition sequences [33, 37, 40, 47, 58]. It is interesting to consider that a transition sequences of Ca and Sr. are similar. Ca shown that it exhibited stable structure at high temperature and low pressure through compression [58, 73]. The experimental observations [74] and the theoretical study [58, 73] reported that the simple cubic (sc) structure is stable at room temperature. At this point, the solution of theoretical study revealed that the sc structure is stable by performing a molecular dynamics (MD) calculation [73]. This is because the MD calculation can include a temperature via ensemble. However, the sc structure is considered by a lattice dynamics calculation [75], indicating that it is unstable structure. This is due to that fact that the sc structure is not a harmonic phase, but it is anharmonic phase [75]. Here, the sc structure is difficult to estimate the Tc by theoretical study.

In 2009, Ca was reported a novel structure at high pressure that it is the β-tin structure [58]. Here, it is worth to note that the transitions sequence of Ca is similar Sr. (the Fm-3 m structure transformed into the Im-3 m structure, then it transformed into the β-tin structure) Here, the β-tin structure is found that it is stable at high pressure and low temperature [58]. The Tc of the β-tin structure was estimated to be 5 K at 40 GPa. The case of Ca is interesting due to the d electrons are important for the estimated Tc. As a possible cause of this, one might think of the d electron is dominated near the Fermi level.

It is interesting to note that structural phase transitions in Sr. [33, 34, 35, 36, 37, 47]. The remarkable studies revealed that there are discrepancy between the experimental observations [34, 35, 36] and the theoretical studies [33, 37, 47]. The experimental observations were reported that the Fm-3 m structure transformed into the Im-3 m structure, then it transformed into the β-tin structure. Next, the β-tin structure transformed into the Sr-IV, finally, the Sr-IV structure transformed into the Sr-V structure. On the contrary, the theoretical studies were reported that the Fm-3 m structure transformed into the Im-3 m structure, then it transformed into the Sr-IV structure, showing that the the β-tin structure is not energetically favored over the Sr-IV structure.

In 2012, Sr. was predicted that there is a candidate structure [33]. The relative enthalpy of Sr. was reported that the Cmcm structure is thermodynamically favored over the Fm-3 m structure, the Im-3 m structure, and the β-tin structure. In addition, the Cmcm structrue was displayed that it can transform into the hcp structure as well. The Cmcm structure was investigated superconductivity, showing that the Tc of the Cmcm is estimated to be 4 K. The remarkable result manifested that the predicted Tc values are in good agreement with experiment [76, 77].

However, the discrepancy between the experimental observations and the theoretical studies were not solved yet. In 2015, the discrepancies in transition sequence between the experimental and theoretical works was explained by Tsuppayakorn-aek et al. [10]. Regarding transition sequence in Sr., it was investigated by the hybrid exchange-correlation functional, i.e. screened exchange local density approximation (sX-LDA) [78, 79, 80]. The stable structure of the β-tin was corrected by sX-LDA functional. In fact, the sX-LDA functional is important for the d electrons. At this point, it is interesting to compare the experimental observation and the theoretical study [10] by considering the energy levels in each electron configuration of isolate strontium (Figure 3). The solution of the energy levels indicated that the sX-LDA functional is in good agreement with the experiment [81].

Figure 3.

The energy level each electron configuration of isolate Sr.

The remarkable result of the Ref. [10] shown that the β-tin structure is thermodynamically favored over the hcp structure by sX-LDA functional (Figure 4). The Ref. [10] manifested that the Im-3 m structure transformed into the β-tin structure, showing that the theoretical study is in good agreement with experimental observations [34, 35, 36].

Figure 4.

The relative enthalpy of Sr. as a function of pressure by sX-LDA functional.

Regarding the superconductor in the β-tin structure is interesting. Although the β-tin structure is thermodynamically stable by sX-LDA functional, it is not calculated the Tc. This because the sX-LDA functional is not implemented for the Tc calculation. However, other hybrid exchange-correlation functionals, i.e. PBE0 or HSE06, are possible for investigation the stability of the β-tin structure, leading to find the Tc.

3.3 Scandium

Structural prediction at high pressure is suitable for identifying unknown structure. Scandium (Sc) is one of d-transition metal, showing that there is an unknown structure (Sc-III) at high pressure [82]. The transition sequences is found that the hcp structure transformed into the host-guest structure [83, 84]. The host-guest structure is thermodynamically stable up to 70 GPa [85]. It is interesting to note that what is the unknown structure beyond the host-guest structure above 70 GPa. In 2018, Tsuppayakorn-aek et al. [14] was identified the unknown structure by ab initio random structure searching (AIRSS). The predicted structure was manifested that Sc-III is the tetragonal structure with space group P41212. The P41212 structure was shown that it is thermodynamiclly stable favored over the hcp structure and the host-guest structure above 93 GPa (Figure 5) [14]. Also, the P41212 structure was found that it is dynamically structure at 120 GPa, as shown in (Figure 6). Moreover, the solution of the simulated XRD pattern [14] is in good agreement with the observed XRD pattern from the experimental study [82]. Structural phase transitions of Sc was reported that the hcp structure transformed into the host-guest structure, and then, it transformed into the P41212 structure.

Figure 5.

The relative enthalpy of Sc as a fucntion of pressure.

Figure 6.

The phonon dispersion of the P41212 structure.

Regarding superconductor of the P41212 structure, it was found to be the metallicity by considering density of state (DOS), leading to investigate the Tc. The P41212 structure displayed that the estimated Tc is 8.36 K at 110 GPa. While, the experimental study was reported the Tc is 8.31 K and 111 GPa [86]. Moreover, the P41212 structure was explored the Tc above 130 GPa. Also, it was found that the Tc decreased monotonically with increasing pressure (Figure 7). In addition, the EPC strengths decreased with increasing pressure as well.

Figure 7.

The Tc of the P41212 structure compare the Tc of Sc-III phase.

Tsuppayakorn-aek et al. [14] was revealed in that the Tc of the P41212 structure decreased with increasing pressure occurred from the mechanical of the DOS. It can be easily understood by considering the partial-density of state. They were shown that the p-electron decreased with increasing pressure. In contrast, the s electron increased with increasing pressure. In addition, the decreasing of Tc value is supported by the ELF calculation. The ELF is displayed in the (110) atomic plane of the P41212 structure, showing that the characteristic of electron state. One can see that the p-electron is accumulated between Sc atoms, indicating that the nature of the chemical bonding is the weak bonding. On increasing pressure, the p-electron transferred into the s and d electrons. This implied that the decreasing of the p-electron might affect the Tc value.

Sc is one of the group-IIIB element was shown that structural phase transformation displayed the complex to simple transition. Also, it promoted the superconducting temperature transition to be 8.36 K at 110 GPa, which it is in good agreement with the experimental observation.

3.4 Arsenic

The group-V element is one of central interest in superconductor. It is interesting to note that arsenic (As), antimony (Sb), and bismuth (Bi) share the remarkable similarity of structural and property [87, 88]. Structural of the group-V element was reported that As-III, Sb-IV, and Bi-III are the incommensurate host-guest structure [89, 90, 91, 92]. Also, it is worth to note that the Im-3 m structure is thermodynamically stable favored over the incommensurate structure [87, 88].

Tsuppayakorn-aek et al. [12] was explored the high-pressure phase in As. This because it is interesting to find the high-pressure phase, leading to go beyond the Im-3 m structure. The structural prediction was investigated up to 300 GPa. The predicted structure was shown that the body-centered tetragonal (bct) structure with space group I41/acd to be the stable structure at high pressure. The I41/acd structure is energetically and dynamically stable. Also, it is thermodynamically favored over the host-guest structure. The I41/acd structure displayed that it compete with the Im-3 m structure. Moreover, The I41/acd structure and the Im-3 m structure are very closed in enthalpy from 100 to 300 GPa. Also, the I41/acd structure is sub-spacegroup of the the Im-3 m structure. It is possible that the I41/acd structure is coexistence phase with the Im-3 m structure.

Here, the I41/acd structure was discovered to be the metallicity, indicating that it is superconducting phase. As already mentioned, the I41/acd structure and the Im-3 m structure are wonderfully closed in enthalpy. It is interesting to investigate the superconducting phase of both of them. An important and a fundamental of the spectral function led to consider superconductor. In fact, the spectral function is associated with the electron–phonon coupling (EPC). The I41/acd structure was regarded in superconductor, it was found that the estimated Tc is 4.2 K at 150 GPa. On increasing pressure, the Tc of the I41/acd structure decreased with the EPC. Likewise, the Tc of the Im-3 m is likely to decrease, where a pressure increasing. It is worth to note that the I41/acd and Im-3 m structures are very similar in the Tc [12].

The remarkable results of the Tc value were shown that the Tc of the I41/acd structure has higher than the Im-3 m structure at 150 GPa. The reason can be considered by the spectral function (α2F) (Figure 8). The contribution of the α2F shown that the I41/acd structure is higher than those of the Im-3 m structure around middle frequency regime (6–13 THz).

Figure 8.

The spectral function of the I41/acd and Im-3 m structures at 150 GPa.

Now, it is worth to note that the I41/acd structure hold the metallic state at 300 GPa. Tsuppayakorn-aek et al. [12] suggested that the I41/acd structure is not favored superconductor above 300 GPa, indicating that it is likely to transform into a normal metallic state (Figure 9). As a possible cause of this, one might think of phase transformation [19]. Moreover, the EPC of the I41/acd structure is very poor characterized by compression. At this point, it is possible that a novel phase might occur above 300 GPa.

Figure 9.

The Tc of the I41/acd and Im-3 m structures as a function of pressure.

Advertisement

4. Conclusion

Ab initio random structure searching is combined with density functional theory has been use to predict a candidate structure in lithium, strontium, scandium, and arsenic under high pressure. The predicted host-guest structure in lithium is expected to be superconductor, where the electron localization function is considered. The discrepancy between the experimental observations and the theoretical studies in strontium is solved by hybrid exchange-correlation functional. Moreover, the β-tin structure is worth to explore a superconductor by performing hybrid exchange-correlation functional. The role of the electron phonon coupling displays that it is crucial for scandium ans arsenic under compression. The remarkable result of the superconducting transition temperature of scandium and arsenic share to a similar character, indicating that the superconducting transition temperature of both of them is likely to decrease with increasing pressure.

Advertisement

Acknowledgments

This project is funded by National Research Council of Thailand (NRCT): (NRCT5-RSA63001-04). This research is partially funded by Chulalongkorn University; Grant for Research. P.T. acknowledge support from the Second Century Fund (C2F), Chulalongkorn University.

Advertisement

Conflict of interest

The authors declare no conflict of interest.

References

  1. 1. Kohn, W. and Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. DOI: 10.1103/PhysRev.140.A1133
  2. 2. Yin, M. T. and Cohen, Marvin L. Theory of static structural properties, crystal stability, and phase transformations: Application to Si and Ge. DOI: 10.1103/PhysRevB.26.5668
  3. 3. Payne, M. C. and Teter, M. P. and Allan, D. C. and Arias, T. A. and Joannopoulos, J. D, Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. DOI: 10.1103/RevModPhys.64.1045
  4. 4. Perdew, John P. and Burke, Kieron and Ernzerhof, Matthias, Generalized Gradient Approximation Made Simple. DOI: 10.1103/PhysRevLett.77.3865
  5. 5. Bardeen, J. and Cooper, L. N. and Schrieffer, J. R. Theory of Superconductivity. DOI: 10.1103/PhysRev.108.1175
  6. 6. Pickard, Chris J. and Needs, R. J. High-Pressure Phases of Silane. DOI: 10.1103/PhysRevLett.97.045504
  7. 7. Chris J Pickard and R J Needs, Ab initio random structure searching. DOI: 10.1088/0953-8984/23/5/053201
  8. 8. Prutthipong Tsuppayakorn-aek and Piya Phansuke and Pungtip Kaewtubtim and Rajeev Ahuja and Thiti Bovornratanaraks, Enthalpy stabilization of superconductivity in an alloying SPH system: First-principles cluster expansion study under high pressure. https://www.sciencedirect.com/science/article/pii/S0927025621000070
  9. 9. Prayoonsak Pluengphon and Prutthipong Tsuppayakorn-aek and Burapat Inceesungvorn and Udomsilp Pinsook and Thiti Bovornratanaraks, Structural, thermodynamic, electronic, and magnetic properties of superconducting FeSe–CsCl type: Ab initio searching technique with van der Waals corrections. https://www.sciencedirect.com/science/article/pii/S0254058421004910
  10. 10. Tsuppayakorn-aek, P. and Chaimayo, W. and Pinsook, U. and Bovornratanaraks, T. Existence of the β-tin structure in Sr: First evidence from computational approach. DOI: 10.1063/1.4931810
  11. 11. Prayoonsak Pluengphon and Thiti Bovornratanaraks, Phase stability and elastic properties of CuGaSe2 under high pressure. http://www.sciencedirect.com/science/article/pii/S0038109815002082
  12. 12. Tsuppayakorn-aek, Prutthipong and Luo, Wei and Ahuja, Rajeev and Bovornratanaraks, Thiti, The High-Pressure Superconducting Phase of Arsenic. DOI: 10.1038/s41598-018-20088-8
  13. 13. Tsuppayakorn-aek, Prutthipong and Luo, Wei and Watcharatharapong, Teeraphat and Ahuja, Rajeev and Bovornratanaraks, Thiti, Structural prediction of host-guest structure in lithium at high pressure. DOI: 10.1038/s41598-018-23473-5
  14. 14. Tsuppayakorn-aek, Prutthipong and Luo, Wei and Pungtrakoon, Wirunti and Chuenkingkeaw, Kittana and Kaewmaraya, Thanayut and Ahuja, Rajeev and Bovornratanaraks, Thiti, The ideal commensurate value of Sc and the superconducting phase under high pressure. DOI: 10.1063/1.5047251
  15. 15. R. Manotum and R. Klinkla and U. Pinsook and K. Kotmool and P. Tsuppayakorn-aek and R. Ahuja and T. Bovornratanaraks, Effect of pressure on the structure stability, electronic structure and band gap engineering in Zn16O1S15. http://www.sciencedirect.com/science/article/pii/S2352214318302119
  16. 16. Jimlim, Pornmongkol and Tsuppayakorn-aek, Prutthipong and Pakornchote, Teerachote and Ektarawong, Annop and Pinsook, Udomsilp and Bovornratanaraks, Thiti, Theoretical predictions for low-temperature phases, softening of phonons and elastic stiffnesses, and electronic properties of sodium peroxide under high pressure. DOI: 10.1039/C9RA03735G
  17. 17. Prutthipong Tsuppayakorn-aek and Udomsilp Pinsook and Wei Luo and Rajeev Ahuja and Thiti Bovornratanaraks, Superconductivity of superhydride CeH10 under high pressure. DOI: 10.1088%2F2053-1591%2Fababc2
  18. 18. Kotmool, Komsilp and Tsuppayakorn-aek, Prutthipong and Kaewmaraya, Thanayut and Pinsook, Udomsilp and Ahuja, Rajeev and Bovornratanaraks, Thiti, Structural Phase Transitions, Electronic Properties, and Hardness of RuB4 under High Pressure in Comparison with FeB4 and OsB4. DOI: 10.1021/acs.jpcc.0c03959
  19. 19. Bovornratanaraks, Thiti and Tsuppayakorn-aek, Prutthipong and Luo, Wei and Ahuja, Rajeev, Ground-state structure of semiconducting and superconducting phases in xenon carbides at high pressure. DOI: 10.1038/s41598-019-39176-4
  20. 20. Prayoonsak Pluengphon and Thiti Bovornratanaraks and Prutthipong Tsuppayakorn-aek and Udomsilp Pinsook and Burapat Inceesungvorn, High-pressure phases induce H-vacancy diffusion kinetics in TM-doped MgH2: Ab initio study for hydrogen storage improvement. http://www.sciencedirect.com/science/article/pii/S0360319919322773
  21. 21. Prayoonsak Pluengphon and Prutthipong Tsuppayakorn-aek and Burapat Inceesungvorn and Thiti Bovornratanaraks, Pressure-induced structural stability of alkali trihydrides and H2-desorption occurrence: Ab initio study for hydrogen storage improvement. http://www.sciencedirect.com/science/article/pii/S0360319920324587
  22. 22. Drozdov, A. P. and Eremets, M. I. and Troyan, I. A. and Ksenofontov, V. and Shylin, S. I. Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. DOI: 10.1038/nature14964
  23. 23. Papaconstantopoulos, D. A. and Klein, B. M. and Mehl, M. J. and Pickett, W. E. Cubic H3S around 200 GPa: An atomic hydrogen superconductor stabilized by sulfur. DOI: 10.1103/PhysRevB.91.184511
  24. 24. Guigue, Bastien and Marizy, Adrien and Loubeyre, Paul, Direct synthesis of pure H3S from S and H elements: No evidence of the cubic superconducting phase up to 160 GPa. DOI: 10.1103/PhysRevB.95.020104
  25. 25. Goncharov, Alexander F. and Lobanov, Sergey S. and Prakapenka, Vitali B. and Greenberg, Eran, Stable high-pressure phases in the H-S system determined by chemically reacting hydrogen and sulfur. DOI: 10.1103/PhysRevB.95.140101
  26. 26. Drozdov, A. P. and Kong, P. P. and Minkov, V. S. and Besedin, S. P. and Kuzovnikov, M. A. and Mozaffari, S. and Balicas, L. and Balakirev, F. F. and Graf, D. E. and Prakapenka, V. B. and Greenberg, E. and Knyazev, D. A. and Tkacz, M. and Eremets, M. I. Superconductivity at 250 K in lanthanum hydride under high pressures. DOI: 10.1038/s41586-019-1201-8
  27. 27. Errea, Ion and Belli, Francesco and Monacelli, Lorenzo and Sanna, Antonio and Koretsune, Takashi and Tadano, Terumasa and Bianco, Raffaello and Calandra, Matteo and Arita, Ryotaro and Mauri, Francesco and Flores-Livas, José A, Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride. DOI: 10.1038/s41586-020-1955-z
  28. 28. Shipley, Alice M. and Hutcheon, Michael J. and Johnson, Mark S. and Needs, Richard J. and Pickard, Chris J. Stability and superconductivity of lanthanum and yttrium decahydrides. DOI: 10.1103/PhysRevB.101.224511
  29. 29. Liu, Hanyu and Naumov, Ivan I. and Hoffmann, Roald and Ashcroft, N. W. and Hemley, Russell J. Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure. https://www.pnas.org/content/114/27/6990
  30. 30. Heil, Christoph and di Cataldo, Simone and Bachelet, Giovanni B. and Boeri, Lilia, Superconductivity in sodalite-like yttrium hydride clathrates. DOI: 10.1103/PhysRevB.99.220502
  31. 31. Peng, Feng and Sun, Ying and Pickard, Chris J. and Needs, Richard J. and Wu, Qiang and Ma, Yanming, Hydrogen Clathrate Structures in Rare Earth Hydrides at High Pressures: Possible Route to Room-Temperature Superconductivity. DOI: 10.1103/PhysRevLett.119.107001
  32. 32. Baǧcı, S. and Tütüncü, H. M. and Duman, S. and Srivastava, G. P. Phonons and superconductivity in fcc and dhcp lanthanum. DOI: 10.1103/PhysRevB.81.144507
  33. 33. Young Kim, Duck and Srepusharawoot, Pornjuk and Pickard, Chris J. and Needs, Richard J. and Bovornratanaraks, Thiti and Ahuja, Rajeev and Pinsook, Udomsilp, Phase stability and superconductivity of strontium under pressure. DOI: 10.1063/1.4742323
  34. 34. D. R. Allan and R. J. Nelmes and M. I. McMahon and S. A. Belmonte and T. Bovornratanaraks, Structures and Transitions in Strontium
  35. 35. McMahon, M. I. and Bovornratanaraks, T. and Allan, D. R. and Belmonte, S. A. and Nelmes, R. J. Observation of the incommensurate barium-IV structure in strontium phase V. DOI: 10.1103/PhysRevB.61.3135
  36. 36. Bovornratanaraks, T. and Allan, D. R. and Belmonte, S. A. and McMahon, M. I. and Nelmes, R. J. Complex monoclinic superstructure in Sr-IV. DOI: 10.1103/PhysRevB.73.144112
  37. 37. Phusittrakool, A. and Bovornratanaraks, T. and Ahuja, R. and Pinsook, U. High pressure structural phase transitions in Sr from ab initio calculations. DOI: 10.1103/PhysRevB.77.174118
  38. 38. Sakata, Masafumi and Nakamoto, Yuki and Shimizu, Katsuya and Matsuoka, Takahiro and Ohishi, Yasuo, Superconducting state of Ca-VII below a critical temperature of 29 K at a pressure of 216 GPa. DOI: 10.1103/PhysRevB.83.220512
  39. 39. Lei, Shi and Papaconstantopoulos, D. A. and Mehl, Michael J. Calculations of superconducting properties in yttrium and calcium under high pressure. DOI: 10.1103/PhysRevB.75.024512
  40. 40. Yao, Yansun and Tse, John S. and Song, Zhe and Klug, Dennis D. and Sun, Jian and Le Page, Yvon, Structures and superconducting properties of the high-pressure IV and V phases of calcium from first principles. DOI: 10.1103/PhysRevB.78.054506
  41. 41. Wiwittawin Sukmas and Prutthipong Tsuppayakorn-aek and Udomsilp Pinsook and Thiti Bovornratanaraks, Near-room-temperature superconductivity of Mg/Ca substituted metal hexahydride under pressure.
  42. 42. Shimizu, Katsuya and Ishikawa, Hiroto and Takao, Daigoroh and Yagi, Takehiko and Amaya, Kiichi, Superconductivity in compressed lithium at 20 K. DOI: 10.1038/nature01098
  43. 43. Yao, Yansun and Tse, J. S. and Tanaka, K. and Marsiglio, F. and Ma, Y. Superconductivity in lithium under high pressure investigated with density functional and Eliashberg theory. DOI: 10.1103/PhysRevB.79.054524
  44. 44. Struzhkin, Viktor V. and Eremets, Mikhail I. and Gan, Wei and Mao, Ho-kwang and Hemley, Russell J. Superconductivity in Dense Lithium. https://science.sciencemag.org/content/298/5596/1213
  45. 45. Deemyad, Shanti and Schilling, James S. Superconducting Phase Diagram of Li Metal in Nearly Hydrostatic Pressures up to 67 GPa. DOI: 10.1103/PhysRevLett.91.167001
  46. 46. Heil, Christoph and Boeri, Lilia, Influence of bonding on superconductivity in high-pressure hydrides. DOI: 10.1103/PhysRevB.92.060508
  47. 47. P. Srepusharawoot and W. Luo and T. Bovornratanaraks and R. Ahuja and U. Pinsook, Evidence of a medium-range ordered phase and mechanical instabilities in strontium under high pressure. http://www.sciencedirect.com/science/article/pii/S0038109812001743
  48. 48. Cui, Wenwen and Bi, Tiange and Shi, Jingming and Li, Yinwei and Liu, Hanyu and Zurek, Eva and Hemley, Russell J. Route to high-Tc superconductivity via CH4-intercalated H3S hydride perovskites. DOI: 10.1103/PhysRevB.101.134504
  49. 49. Ye, Xiaoqiu and Zarifi, Niloofar and Zurek, Eva and Hoffmann, Roald and Ashcroft, N. W. High Hydrides of Scandium under Pressure: Potential Superconductors. DOI: 10.1021/acs.jpcc.7b12124
  50. 50. Bi, Tiange and Miller, Daniel P. and Shamp, Andrew and Zurek, Eva, Superconducting Phases of Phosphorus Hydride Under Pressure: Stabilization by Mobile Molecular Hydrogen. https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201701660
  51. 51. D. A. Papaconstantopoulos, Possible High-Temperature Superconductivity in Hygrogenated Fluorine. https://www.degruyter.com/view/journals/nsm/3/1/article-p29.xml
  52. 52. Majumdar, Arnab and Tse, John S. and Yao, Yansun, Modulated Structure Calculated for Superconducting Hydrogen Sulfide. https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201704364
  53. 53. Li, Yinwei and Hao, Jian and Liu, Hanyu and Li, Yanling and Ma, Yanming, The metallization and superconductivity of dense hydrogen sulfide. DOI: 10.1063/1.4874158
  54. 54. Baroni, Stefano and de Gironcoli, Stefano and Dal Corso, Andrea and Giannozzi, Paolo, Phonons and related crystal properties from density-functional perturbation theory. DOI: 10.1103/RevModPhys.73.515
  55. 55. Paolo Giannozzi and Stefano Baroni and Nicola Bonini and Matteo Calandra and Roberto Car and Carlo Cavazzoni and Davide Ceresoli and Guido L Chiarotti and Matteo Cococcioni and Ismaila Dabo and Andrea Dal Corso and Stefano de Gironcoli and Stefano Fabris and Guido Fratesi and Ralph Gebauer and Uwe Gerstmann and Christos Gougoussis and Anton Kokalj and Michele Lazzeri and Layla Martin-Samos and Nicola Marzari and Francesco Mauri and Riccardo Mazzarello and Stefano Paolini and Alfredo Pasquarello and Lorenzo Paulatto and Carlo Sbraccia and Sandro Scandolo and Gabriele Sclauzero and Ari P Seitsonen and Alexander Smogunov and Paolo Umari and Renata M Wentzcovitch, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. DOI: 10.1088/0953-8984/21/39/395502
  56. 56. Allen, P. B. and Dynes, R. C. Transition temperature of strong-coupled superconductors reanalyzed. DOI: 10.1103/PhysRevB.12.905
  57. 57. Yao, Yansun and Tse, John S. Electron-phonon coupling in the high-pressure hcp phase of xenon: A first-principles study. DOI: 10.1103/PhysRevB.75.134104
  58. 58. Yao, Yansun and Klug, Dennis D. and Sun, Jian and Martoňák, Roman, Structural Prediction and Phase Transformation Mechanisms in Calcium at High Pressure. DOI: 10.1103/PhysRevLett.103.055503
  59. 59. Yao, Yansun and Klug, Dennis D. Stable structures of tantalum at high temperature and high pressure. DOI: 10.1103/PhysRevB.88.054102
  60. 60. Ma, Yanming and Oganov, Artem R. and Xie, Yu, High-pressure structures of lithium, potassium, and rubidium predicted by an ab initio evolutionary algorithm. DOI: 10.1103/PhysRevB.78.014102
  61. 61. Pickard, Chris J. and Needs, R. J. Dense Low-Coordination Phases of Lithium. DOI: 10.1103/PhysRevLett.102.146401
  62. 62. Marqués, M. and McMahon, M. I. and Gregoryanz, E. and Hanfland, M. and Guillaume, C. L. and Pickard, C. J. and Ackland, G. J. and Nelmes, R. J. Crystal Structures of Dense Lithium: A Metal-Semiconductor-Metal Transition. DOI: 10.1103/PhysRevLett.106.095502
  63. 63. Lv, Jian and Wang, Yanchao and Zhu, Li and Ma, Yanming, Predicted Novel High-Pressure Phases of Lithium. DOI: 10.1103/PhysRevLett.106.015503
  64. 64. Lundegaard, L. F. and Gregoryanz, E. and McMahon, M. I. and Guillaume, C. and Loa, I. and Nelmes, R. J. Single-crystal studies of incommensurate Na to 1.5 Mbar. DOI: 10.1103/PhysRevB.79.064105
  65. 65. McMahon, M. I. and Nelmes, R. J. and Schwarz, U. and Syassen, K. Composite incommensurate K-III and a commensurate form: Study of a high-pressure phase of potassium. DOI: 10.1103/PhysRevB.74.140102
  66. 66. Lundegaard, L. F. and Stinton, G. W. and Zelazny, M. and Guillaume, C. L. and Proctor, J. E. and Loa, I. and Gregoryanz, E. and Nelmes, R. J. and McMahon, M. I. Observation of a reentrant phase transition in incommensurate potassium. DOI: 10.1103/PhysRevB.88.054106
  67. 67. McBride, E. E. and Munro, K. A. and Stinton, G. W. and Husband, R. J. and Briggs, R. and Liermann, H.-P. and McMahon, M. I. One-dimensional chain melting in incommensurate potassium. DOI: 10.1103/PhysRevB.91.144111
  68. 68. Zhao, Long and Zong, Hongxiang and Ding, Xiangdong and Sun, Jun and Ackland, Graeme J. Commensurate-incommensurate phase transition of dense potassium simulated by machine-learned interatomic potential. DOI: 10.1103/PhysRevB.100.220101
  69. 69. Falconi, S. and McMahon, M. I. and Lundegaard, L. F. and Hejny, C. and Nelmes, R. J. and Hanfland, M. X-ray diffraction study of diffuse scattering in incommensurate rubidium-IV. DOI: 10.1103/PhysRevB.73.214102
  70. 70. Loa, I. and Lundegaard, L. F. and McMahon, M. I. and Evans, S. R. and Bossak, A. and Krisch, M. Lattice Dynamics of Incommensurate Composite Rb-IV and a Realization of the Monatomic Linear Chain Model. DOI: 10.1103/PhysRevLett.99.035501
  71. 71. Matsuoka, T. and Sakata, M. and Nakamoto, Y. and Takahama, K. and Ichimaru, K. and Mukai, K. and Ohta, K. and Hirao, N. and Ohishi, Y. and Shimizu, K. Pressure-induced reentrant metallic phase in lithium. DOI: 10.1103/PhysRevB.89.144103
  72. 72. Goncharov, Alexander F. and Struzhkin, Viktor V. and Mao, Ho-kwang and Hemley, Russell J. title = Spectroscopic evidence for broken-symmetry transitions in dense lithium up to megabar pressures. DOI: 10.1103/PhysRevB.71.184114
  73. 73. Yao, Yansun and Martoňák, Roman and Patchkovskii, Serguei and Klug, Dennis D. Stability of simple cubic calcium at high pressure: A first-principles study. DOI: 10.1103/PhysRevB.82.094107
  74. 74. Li, Bing and Ding, Yang and Yang, Wenge and Wang, Lin and Zou, Bo and Shu, Jinfu and Sinogeikin, Stas and Park, Changyong and Zou, Guangtian and Mao, Ho-kwang, Calcium with the β-tin structure at high pressure and low temperature. https://www.pnas.org/content/109/41/16459
  75. 75. Liu, Hanyu and Cui, Wenwen and Ma, Yanming, Hybrid functional study rationalizes the simple cubic phase of calcium at high pressures. DOI: 10.1063/1.4765326
  76. 76. Dunn, K. J. and Bundy, F. P. Pressure-induced superconductivity in strontium and barium. DOI: 10.1103/PhysRevB.25.194
  77. 77. Mizobata, Shigeki and Matsuoka, Takahiro and Shimizu, Katsuya, title = Pressure Dependence of the Superconductivity in Strontium. DOI: 10.1143/JPSJS.76SA.23
  78. 78. Clark, Stewart J. and Robertson, John, Screened exchange density functional applied to solids. DOI: 10.1103/PhysRevB.82.085208
  79. 79. Gillen, Roland and Robertson, John, Density functional theory screened-exchange approach for investigating electronical properties of graphene-related materials. DOI: 10.1103/PhysRevB.82.125406
  80. 80. Gillen, Roland and Clark, Stewart J. and Robertson, John, Nature of the electronic band gap in lanthanide oxides. DOI: 10.1103/PhysRevB.87.125116
  81. 81. Moore, Charlotte E, Atomic Energy Levels as Derived from the Analyses of Optical Spectra. Volume III. 42Mo to 57La; 72Hf to 89Ac
  82. 82. Akahama, Yuichi and Fujihisa, Hiroshi and Kawamura, Haruki, New Helical Chain Structure for Scandium at 240 GPa. DOI: 10.1103/PhysRevLett.94.195503
  83. 83. Fujihisa, Hiroshi and Akahama, Yuichi and Kawamura, Haruki and Gotoh, Yoshito and Yamawaki, Hiroshi and Sakashita, Mami and Takeya, Satoshi and Honda, Kazumasa, Incommensurate composite crystal structure of scandium-II. DOI: 10.1103/PhysRevB.72.132103
  84. 84. McMahon, M. I. and Lundegaard, L. F. and Hejny, C. and Falconi, S. and Nelmes, R. J. Different incommensurate composite crystal structure for Sc-II. DOI: 10.1103/PhysRevB.73.134102
  85. 85. Determination of the Structural Parameters of an Incommensurate Phase from First Principles: The Case of Sc-II, Arapan, Sergiu and Skorodumova, Natalia V. and Ahuja, Rajeev. DOI: 10.1103/PhysRevLett.102.085701
  86. 86. Debessai, M. and Hamlin, J. J. and Schilling, J. S. Comparison of the pressure dependences of Tc in the trivalent d-electron superconductors Sc, Y, La, and Lu up to megabar pressures. DOI: 10.1103/PhysRevB.78.064519
  87. 87. Häussermann, Ulrich and Söderberg, Karin and Norrestam, Rolf, Comparative Study of the High-Pressure Behavior of As, Sb, and Bi. DOI: 10.1021/ja020832s
  88. 88. Katzke, Hannelore and Tolédano, Pierre, Displacive mechanisms and order-parameter symmetries for the A7-incommensurate-bcc sequences of high-pressure reconstructive phase transitions in Group Va elements. DOI: 10.1103/PhysRevB.77.024109
  89. 89. McMahon, M. I. and Degtyareva, O. and Nelmes, R. J. and van Smaalen, S. And Palatinus, L. Incommensurate modulations of Bi-III and Sb-II. DOI: 10.1103/PhysRevB.75.184114
  90. 90. Coleman, A. L. and Stevenson, M. and McMahon, M. I. and Macleod, S. G. Phase diagram of antimony up to 31 GPa and 835 K. DOI: 10.1103/PhysRevB.97.144107
  91. 91. Khasanov, Rustem and Luetkens, Hubertus and Morenzoni, Elvezio and Simutis, Gediminas and Schönecker, Stephan and Östlin, Andreas and Chioncel, Liviu and Amato, Alex, Superconductivity of Bi-III phase of elemental bismuth: Insights from muon-spin rotation and density functional theory. DOI: 10.1103/PhysRevB.98.140504
  92. 92. Kartoon, D. and Makov, G. Structural and electronic properties of the incommensurate host-guest Bi-III phase. DOI: 10.1103/PhysRevB.100.014104

Written By

Thiti Bovornratanaraks and Prutthipong Tsuppayakorn-aek

Reviewed: 15 July 2021 Published: 09 August 2021