Large negative magnetoresistance and pseudogap phase in superconducting A15-type La 4 H 23

High pressure plays a crucial role in the field of superconductivity. Compressed hydride superconductors are leaders in the race for a material that can conduct electricity without resistance at high or even room temperature. In the present work, we have discovered new lanthanum superhydride, cubic A15-type La 4 H 23 , with lower stabilization pressure compared to the reported fcc -LaH 10 . Superconducting La 4 H 23 was obtained by laser heating of LaH 3 with ammonia borane at about 120 GPa. Transport measurements reveal the maximum critical temperature T c (onset) = 105 K and the critical field μ 0 H C2 (0) ≈ 32 T at 118 GPa, as evidenced by the sharp drop of electrical resistance and the displacement of superconducting transitions in magnetic fields. Moreover, we provide evidence for unconventional transport associated with a pseudogap phase in La 4 H 23 using pulsed magnetic fields up to 68 T. A large negative magnetoresistance in the non-superconducting state below 40 K, quasi T -linear electrical resistance, and a sign-change of its temperature dependence mark the emergence of pseudogap in this hydride. Discovered lanthanum hydride is a new member of the A15 family of superconductors with T C exceeding the boiling point of liquid nitrogen.


Introduction
The search for high-temperature superconductors has been an important goal pursued tirelessly by researchers since the discovery of the superconductivity in mercury [1].However, until 2014, the critical temperature (Tc) of conventional superconductors had never exceeded the McMillan limit (~ 40 K) [2].As one of the most effective methods of changing the structure of matter, pressure can lead to appearance of unusual properties of materials that are unlikely to occur in ambient conditions, such as conventional high-temperature superconductivity (HTSC).The increase of Tc in Hg-containing cuprates to 164 K under high pressure motivated extensive further research in this field [3].On the basis of the chemical pre-compression idea, first proposed by Ashcroft [4], the breakthrough discovery of conventional HTSC in compressed sulfur hydride All twisted pairs were fixed using the GE7031 varnish.A bath helium cryostat was used, which made it possible excellent control of the DAC temperature between 4.5 K and 78 K.A 100 cm long NiCr wire with a resistance of about 150 Ohms wrapped around the diamond chamber was used as a heater.Cernox thermometers were attached to the DAC's body (60 mm long and 12 mm in diameter) for measurements of the temperature.A high-frequency (33.33 and 16.666 kHz) lock-in amplifier technique was employed to measure the sample resistance.For the measurements in high magnetic fields, we used a four-probe AC method with the excitation current of 1-2 mA (10 mA already significantly suppresses superconductivity in La4H23).The voltage drop across the sample was amplified by an instrumentation amplifier and detected by a lock-in amplifier.In general, we used the same methodology as in the previous studies of (La, Nd)H10 [24], SnH4 [25], and CeH9-10 [26].
To investigate the La-H system, we performed both fixed-and variable-composition searches at 100, 120, 150 and 200 GPa.The number of generations was 100.We calculated the convex hulls in the temperature range from 0 K to 2000 K, using free energies computed by Phonopy [30].Metastable structures with the energy ≤ 30 meV/atom above the hull are also presented on the convex hulls.
Structure relaxations and energy calculations were performed using the VASP code [31][32][33] within density functional theory (DFT) [34,35], implementing the Perdew-Burke-Ernzerhof (PBE) exchangecorrelation functional [36] and the projector-augmented wave (PAW) method [37,38].The kinetic energy cutoff was set at 600 eV.Γ-centered k-point meshes with a resolution of 2π×0.05Å -1 were used for sampling the Brillouin zone.The phonon band structure and density of states were computed using Phonopy [30] package implementing the finite displacement method, 2 × 2 × 2 supercells were generated.The energy cutoff and kspacing parameters for the VASP calculations were set at 500 eV and 2π×0.1 Å -1 , respectively.Sumo package [39] was used to visualize the phonon density of states and band structure.The k-points for phonon band structures were chosen using Hinuma's recommendation [40].The Phonopy package was also used to calculate zero-point energy (ZPE) corrections and thermal properties, such as entropy and free energy.To calculate phonon frequencies and electron-phonon coupling (EPC) coefficients, we used Quantum Espresso (QE) package [41] utilizing density functional perturbation theory (DFPT) [42], plane-wave PZ HGH pseudopotentials and the tetrahedron method [43,44].In general, we used the same methodology as in the study of La-Mg-H system [45].

Superconducting properties of La4H23
The scheme of the electrical DAC H1 prepared for the transport measurements is shown in Figures 1b,   c.Laser heating of the LaH3/AB sample to temperature above 1500 K was performed at 123 GPa, then the pressure reduced to 120 GPa.Cryogenic measurements of the sample immediately showed the appearance of a drop in electrical resistance from 0.12 Ω to 10 -4 Ω at 93 K (onset) corresponding to the manifestation of superconductivity in the sample (Figure 1a).After the second laser heating, a sharp superconducting transition was observed at 90 K at 114 GPa.The third laser heating led to an increase in pressure to 118 GPa and the critical temperature Tc also rose to 105 K.This value is very close to the critical temperatures of cerium superhydrides CeH9 and CeH10 in the same pressure range [11], but the advantage of the studied La4H23 is the much smaller amount of hydrogen (< 6 atoms per La) required to obtain this result.To further investigate the dependence of Tc on pressure, we decompressed the DAC to 91 GPa (Figure 1a).We found that Tc (P) decreases monotonically during the decompression runs reaching the maximum of 105 K at 118 GPa (Figure 1c).
Remarkably, a change in the sign of the quasi-linear temperature dependence of the electrical resistance (dR/dT) is observed during decompression (Figure 1a) of the DAC H1.This phenomenon was previously observed during decompression in sulfur hydrides H2S and H3S [6], in phosphorus hydride PH3 [46], in CeH10 [26] and in ternary superhydride (La,Ce)H9 [47].As we have shown earlier for SnH4 [48], the change in the sign of dR/dT is incompatible with the view of La4H23 as a normal Fermi-liquid metal whose resistance is due to the scattering of electrons on phonons.Indeed, the influence of electron-phonon interaction on the transport properties of metals can be described using the Eliashberg transport spectral function α 2 Ftr(ω), which, as a rule, differs little from the Eliashberg function for electron-phonon interaction α 2 F(ω) [49].In the first approximation of the variational solution of the Boltzmann equations for electron transport [50], the dependence of electrical resistivity (ρ) on temperature (T) is linear where x = ℏ/  , Vcell -is the unit cell volume, NF -is the electron density of states at the Fermi level and the 〈  2 〉 -is the band-averaged Fermi speed of electrons.All of the above parameters are positive in all known three-dimensional materials, which leads to positive dR/dT for the vast majority of metals and alloys.
Very rare exceptions are complex alloys with disorder effects at low temperatures, such as manganin and constantan [51][52][53].At high temperatures the term → 1, and we come to simple formula ( 2) where λtr -is the transport electron-phonon coupling (EPC) parameter [49].From this equation it is absolutely clear that if dR/dT < 0, then the transport EPC parameter must also be negative (λtr < 0), and the usual electron-phonon coupling strength (λ) will also be negative or about zero, which is incompatible with the concept of conventional superconductivity in La4H23.The negative sign of dR/dT and the narrowing of superconducting transitions in a magnetic field were independently confirmed by Cross et al. [54] and, therefore, are reproducible phenomena.
Instead, the properties of polyhydrides in the non-superconducting state on the verge of their dynamic stability [55] should be described in the framework of a non-Fermi liquid model close to the models developed for describing the pseudogap phase and metal-to-insulator transitions in cuprates [56].As we will see in the next paragraph, A15 La4H23 exhibits the strong negative magnetoresistance characteristic of superconductors with a pseudogap phase.As can be seen from Figure 1с, a further decrease in pressure of DAC H1 leads to broadening of superconducting transitions up to complete disappearance of the superconducting state and decomposition of La4H23 (Figures 1c, d).To further confirm the superconductivity, we measured the electrical resistance of the sample in DAC H1 in steady magnetic fields ranging from 0 to 8 T. Figure 1e shows the temperature dependence of electrical resistance of A15 La4H23 in steady magnetic fields at 114 GPa.The sample demonstrates the absence (and even negative value) of broadening of superconducting transitions in a magnetic field, as previously observed for yttrium (YH6) [60] and lanthanum-yttrium ((La,Y)H10) hydrides [61].Tc shifts linearly to lower temperatures as the magnetic field increases from 0 to 8 T, as it should for superconductors.To estimate the upper critical magnetic field μ0HC2(0), we applied the GL model [57], and the WHH model [58], simplified by Baumgartner [59].As Figure 1f shows, these two models yield the μ0HC2(0) as 24 T and 33 T, respectively.
Interestingly, the superconducting properties of La4H23 are found to be more pronounced than those of the recently studied A15 Lu4H23 (max Tc = 71 K, [63]).This indicates that isostructural lutetium compounds, such as proposed LuH10, LuH9, and LuH6, will have lower critical temperatures than the corresponding lanthanum polyhydrides in contradiction with earlier theoretical predictions [64].Moreover, due to the smaller atomic radius of Lu, we would have to apply much higher pressures to stabilize the corresponding lutetium hydrides (e.g., LuH10), making them less convenient to study than LaHx.

Pulsed magnetic field experiments and crystal structure of La4H23
Unusual transport properties of La4H23 were the reason for further studies of this compound in DAC H2 at 121 GPa in stronger pulsed magnetic fields up to 68 T (Figure 2).Before the experiment, the DAC H2 was tested in steady fields up to 8T (Supporting Figure S8).The sample exhibited a superconducting transition at 84 K (onset), the extrapolated μ0HC2(0) is 32-45 T. Thus, the reproducibility of the synthesis results was demonstrated, although in this particular sample the derivative dR/dT was positive.
Pulse measurements allowed us to establish the presence of a region of pronounced negative magnetoresistance at temperatures below 40 K and at the field H > 25 T, and obtain inflection points where MR changes sign back to positive (Figure 2a, b).These points limit a separate region of the magnetic phase diagram (MR < 0, Figure 2b), which corresponds to the pseudogap phase of A15 La4H23.The amplitude of the jump in electrical resistance (Re Z) Rmax/Rn = 1.55 at 4.5 K in the pseudogap region exceeds that in cerium superhydride CeH10, for which we previously found similar phenomena [26].As in the case of cerium polyhydrides, a sign reversal of dRmax/dT is observed in the pseudogap region: Rmax reaches maximum of 0.185 Ω at 4.5 K and decreases along with temperature to Rn = 0.115 Ω at 50.9 K.It is interesting to note that above the superconducting transition, at 102 K, the phenomenon of zero magnetoresistance is observed: MR ∝ dR(H)/dH = 0 (Supporting Figure S10).
We also were able to completely suppress superconductivity at μ0HC2(0) ≈ 32 T in the La4H23 and complete the magnetic phase diagram for this compound (Figure 2b).In general, the behavior of μ0HC2(T), is in satisfactory agreement with the WHH model traditionally used for Bardeen-Cooper-Schrieffer superconductors.For the first time among polyhydrides, structural type A15 (Pm3 ̅ n ) was found when studying the formation of europium hydrides [65] above 100 GPa.Then, polyhydrides with the same structure were found in Ba-H system [66], among lanthanum [18] and lutetium [63] polyhydrides and in the Y-H system [67], forming a fairly large family of superhydrides.As we found out in the previous section, A15 La4H23 has the highest Tc among all superconductors with A15 structure.Below we discuss the results of X-ray diffraction analysis of this compound.
Considering the large number of superconducting phases in the La-H system at megabar pressures, we combined the experimental powder XRD data and the computational crystal structure search [18].The in-situ synchrotron X-ray diffraction patterns, shown in Figure 2c, indicate that the lanthanum sublattice of DAC H1 sample possessing cubic Pm3 ̅ n symmetry at 118 GPa.The volume of the unit cell is 28.9 Å 3 /La and the unit cell parameter a = 6.14 Å (Z = 8).This is in close agreement with the theoretical results in 118 GPa (≈ 28 Å 3 /La, see Supporting Figure S12).We also compared obtained unit cell volume of Pm n-La4H23 with the reported one [18], which is 27.98 Å 3 /La at 150 GPa.This is slightly different due to higher pressure in the Laniel et al. experiment.The hydrogen content can be estimated by the difference between atomic volumes of La atoms and the hydrogen [68,69].According to Ref. [70] the volume of a hydrogen atom in pure compressed hydrogen at 118 GPa is 2.20 Å 3 /H, whereas La atom has a volume of 15.7 Å 3 /La [68].Combining these data, we conclude that the La:H composition in our compound is close to 1:6.respectively.We used a k-mesh of 8×8×8 and a q-mesh of 2×2×2.The results were also verified on k-mesh 12×12×12 and q-mesh 3×3×3.Pictures were prepared using python script available on GitHub Superconducting properties of Pm n -La4H23 have been investigated theoretically using the normconserving Goedecker-Hartwigsen-Hutter (HGH) pseudopotential with the Perdew-Zunger (LDA) functional and k, q-grids of low density.These pseudopotentials give results that are in close agreement with the experimental data, so it is this computational approach that we will discuss below (Table 1 and Figure 3 a, c).
We found that La4H23 exhibits moderate superconducting properties at 100 GPa, and the electron-phonon interaction strength reaches λ ≈ 1.5.Critical temperature of superconductivity decreases with increasing pressure due to a decrease in the λ.The calculated Tc of La4H23 reaches 92-95 K at 100 GPa in the harmonic approximation in agreement with the experiment.The relatively low Tc of this superhydride correlates with the low contribution of the hydrogen sublattice to the density of electronic states (Figure 3d), which is equal to about 30% of the total density of electronic states at the Fermi level (NF = 0.79 states/eV/La).The expected [72] upper critical magnetic field μ0HC2(0) = 29-51 T is also in reasonable agreement with the experiment (Figure 2b).Thus, as can be clearly seen, theoretical calculations show excellent agreement with experimental data for La4H23.However, this situation should be considered as unique!To demonstrate it, we carried out a primary analysis of the superconducting properties of two other polyhydrides of the A15 family: Lu4H23 and Y4H23.
To date, there are several publications that are in qualitative agreement with the results of our calculations for Lu4H23.First of all, it's prediction of the room-temperature superconductivity in LuH6 [64] at 100 GPa.Considering the similar hydrogen content in Lu4H23 and LuH6, as well as the high symmetry of these hydrides, it is not difficult to guess that in the experiment LuH6 will have a much lower Tc than predicted by theory.Secondly, one cannot fail to mention predictions of the room-temperature superconductivity in the Lu-Y-H system at a pressure of 100-200 GPa [75].In both of these cases, we are dealing with a clear deviation of theoretical predictions from the experiment, due to strong correlation effects in f-shell of Lu, the inclusion of which has an extremely strong effect on superconductivity, but cannot be carried out within the framework of DFT.
A very similar situation is observed for Pm n-Y4H23 at 150 GPa: calculations with different q-point meshes lead to the fact that Tc(Y4H23) must exceed 250 К (Supporting Figures S15-S16).This is hard to believe, given that previously studied Im m-YH6 also demonstrated an abnormally low critical temperature: being a predicted room-temperature superconductor with Tc > 270 K [76], it exhibits superconductivity only below 224 K [9].Thus, here we encounter the problem of discrepancy between DFT calculations and experimental results that currently has no solution and should be addressed to future research.

Conclusions
We have synthesized novel lanthanum superhydride La4H23 with the A15 structure via laser heating of LaH3 and NH3BH3 at 118-123 GPa.Powder X-ray diffraction revealed a Pm3 ̅ n-La4H23 phase as the main reaction product, which has a clathrate hydrogen sublattice.Transport measurements confirm pronounced superconducting properties of La4H23 with a maximum transition temperature of 105 K at 118 GPa in agreement with theoretical calculations.The calculated electron-phonon interaction strength λ is around 1.5.
During decompression, Tc of La4H23 decreases along with the pressure below 118 GPa, and at 91 GPa the superconducting transition completely disappears.In the non-superconducting state between 98 and 120 GPa, La4H23 demonstrates a change in the sign of the quasi-linear temperature dependence of the electrical resistance corresponding to the non-Fermi liquid (strange metal) behavior.
Experimental magnetic phase diagrams down to 4.5 K was constructed and the upper critical field of La4H23 μ0HC2(0) = 32 T were established.The experimental behavior of μ0HC2(T) in this compound, in general, can be described in terms of the WHH model.Discovered La4H23 exhibits pronounced properties of a strange metal below Tc: large H-linear negative magnetoresistance, the reversal of the sign of temperature coefficient of electrical resistance (dR/dT) below 40 K, and quasi-linear R(T) in non-superconducting state, which corresponds to the properties of the pseudogap phase of cuprate superconductors.The experiment shows that the physics of high-TC superhydrides is rather close to this of cuprates.

S5
Table S1.Enthalpies of formation of various lanthanum hydrides (in eV/atom) at 100 GPa and 0 K (Figure S1).ZPE stands for the zero-point energy.X, Y are coordinates of lanthanum hydrides on the two-dimensional convex hull diagram.Fitness is the distance from the convex hull line.The compound has a small number of imaginary phonon modes, which are likely to disappear when anharmonic effects are considered.[2] a2f -Superconducting properties calculation, https://github.com/GitGreg228/a2f,2023.

Figure 1 .
Figure 1.Electrical DAC construction and transport properties of La4H23 under pressure.(a) Dependence of the electrical resistance of the sample on temperature during decompression of DAC H1 from 120 GPa to 91 GPa.Tc corresponds to the onset transition point.(b) Dependence of electrical resistance of the sample on applied magnetic field at 114 GPa.Inset: photograph of the sample loaded in the DAC's chamber and four Mo electrodes after the laser heating at 114 GPa.The hydrogen source (NH3BH3) and the LaH3 are indicated by red and blue curves, respectively.(c) Pressure dependence of the critical temperature of La4H23.Inset: schematic diagram of the electrical DAC with the four-electrode van der Pauw scheme.(d) Upper critical magnetic field BС2(T) of La4H23 at 114 GPa obtained by extrapolation of the experimental data (steady fields) using the Ginzburg-Landau (GL), [57] the Werthamer-Helfand-Hohenberg (WHH) [58, 59] and linear models.Inset: residual resistance of the sample after SC transition.

Figure 2 .
Figure 2. Transport properties in pulsed magnetic field and X-ray diffraction analysis of La4H23.(a) Dependence of the electrical resistance of the sample in DAC H2 on the external magnetic field R(H) measured in the AC mode at frequencies of 16.66 kHz (4.5 K) and 33.33 kHz (most cases).For ease of analysis, the original data were smoothed using a Fourier filter (Origin lab).Raw data can be found in the Supporting Information.Inset: photo of the DAC H2.(b) Magnetic phase diagram of La4H23 at 121 GPa."SC" marks superconducting region, the pseudogap phase ("PG") is marked by red and blue color where MR < 0, "FL" denotes the Fermi liquid metal behavior of the sample with MR > 0 and positive dR/dT > 0. (c) X-ray diffraction pattern and Le Bail refinement of the unit cell parameters of La4H23 phase at 118 GPa.Experimental XRD data and the Le Bail fit are represented by red hollow circles and black lines, respectively.XRD pattern contains spurious signals from molybdenum (Mo) electrodes.(d) XRD patterns measured across the sample with a step of 5 μm.The sample is very homogeneous.

Figure 2d shows a
Figure 2d shows a series of XRD patterns measured at several positions across the sample in steps of 5 μm.All XRD images are almost identical at all locations containing the signals from the Mo electrodes andPm n-La4H23.This confirms the uniform distribution of hydrogen and selective formation of only one phase in the process of synthesis.Computer modeling of this structure shows that in the hydrogen cage of La4H23, the shortest H-H distance is about 1.3 Å at 118 GPa, which is in the range of 1.0 -1.5 Å, typical for hydride superconductors.This bond length is much longer than in pure H2: dHH ≈ 1.1 Å at 115 GPa[22].

Figure 3 .
Figure 3. Results of theoretical calculations of electronic, phonon and superconducting properties of La4H23 at 100, 120 and 150 GPa.(a, c) Eliashberg functions of La4H23 calculated without considering symmetry at 150 and 100 GPa, [71].(b) Phonon band structure and density of states of La4H23 at 120 GPa calculated in the harmonic approximation.The compound was found to be dynamically stable at this pressure.(d) Electron band structure and density of states projected on H and La atoms at 120 GPa.The contribution of hydrogen is ≈ 30 % of the total density of states.

Figure S1 .
Figure S1.Convex hull of the La-H system calculated at 100 GPa and 0 K in harmonic approximation.Only those phases that lie less than 30 meV/atom from the convex hull are shown.Zero-point energy (ZPE) was included in the calculations.

Figure S2 .Figure S3 .
Figure S2.Convex hull of the La-H system calculated at 120 GPa and 0 K in harmonic approximation.Only those phases that lie less than 30 meV/atom from the convex hull are shown.Zero-point energy (ZPE) was included in the calculations.

Figure S4 .
Figure S4.Convex hull of the La-H system calculated at 150 GPa and 1000 K in harmonic approximation.Only those phases that lie less than 30 meV/atom from the convex hull are shown.Zero-point energy (ZPE) was included in the calculations.The numbers in parentheses correspond to the distance of the connections from the convex hull in eV/atom.

Figure S5 .
Figure S5.Convex hull of the La-H system calculated at 150 GPa and 1500 K in harmonic approximation.Only those phases that lie less than 30 meV/atom from the convex hull are shown.Zero-point energy (ZPE) was included in the calculations.The numbers in parentheses correspond to the distance of the connections from the convex hull in eV/atom.

Figure S6 .
Figure S6.Convex hull of the La-H system calculated at 150 GPa and 2000 K in harmonic approximation.Only those phases that lie less than 30 meV/atom from the convex hull are shown.Zero-point energy (ZPE) was included in the calculations.The numbers in parentheses correspond to the distance of the connections from the convex hull in eV/atom.

Figure S7 .Figure S9 .
Figure S7.Experimental transport properties of La4H23 in DAC H1.(a) Decompression of the DAC H1 and temperature dependence of the electrical resistivity of the sample in real scale.Pronounced increase in electrical resistance in 10-100 times at T > TC is observed during decompression due to the beginning of the metal-insulator transition.The anomaly at 114 GPa is an exception.(b) Residual resistance of the sample detected in the SC state in magnetic fields of 0-4 T.

Figure S10 .
Figure S10.Dependence of the electrical resistance of the sample in DAC H2 on the external magnetic field R(H) measured in the AC mode at frequencies of 16.66 kHz (4.5 K) and 33.33 kHz (most cases).Raw data.Such loud periodic noise is caused by large open loops in the contact wires of the DAC H2.(a) Magnetic field sweeps up and down together; (b) only sweeps down are shown and used to determine μ0HC2(T) according to R50% criteria.

Figure S11 .
Figure S11.Phonon band structure and corresponding density of states of La4H23 at 100 GPa in harmonic approximation.

Figure S12 .Figure S13 .Figure S14 .Figure S15 .
Figure S12.Equation of state, bulk modulus (B) and its derivative (dB/dP) of La4H23 at pressures from 80 to 155 GPa.Calculations were done using VASP code with the PAW PBE pseudopotentials for La and H.

Table S2 .
Enthalpies of formation of various lanthanum hydrides (in eV/atom) at 120 GPa and 0 K (FigureS2).ZPE stands for the zero-point energy.X, Y are coordinates of lanthanum hydrides on the two-dimensional convex hull diagram.Fitness is the distance from the convex hull line.

Table S3 .
Enthalpies of formation of various lanthanum hydrides (in eV/atom) at 150 GPa and 0 K (FigureS3).ZPE stands for the zero-point energy.X, Y are coordinates of lanthanum hydrides on the two-dimensional convex hull diagram.Fitness is the distance from the convex hull line.