High-pressure superconducting phase diagram of ⁶Li: Isotope effects in dense lithium

Significance

The emergence of exotic quantum states, such as fluid ground state and two-component superconductivity and superfluidity, in a compressed light metallic system has been entertained theoretically for metallic phases of hydrogen. The difficulty of compressing hydrogen to metallization densities has prevented experimental proof of these effects. Studying lithium, which is isovalent to hydrogen and the lightest metal, is considered as a route to studying the lattice quantum effects in a dense light metallic system. Here, by comparing the superconductivity of lithium isotopes under pressure, we present evidence that properties of lithium at low temperature may significantly be dominated by its lattice quantum dynamics. This study is the first experimental report on superconducting properties of ⁶Li, the lightest superconducting material.

Abstract

We measured the superconducting transition temperature of ⁶Li between 16 and 26 GPa, and report the lightest system to exhibit superconductivity to date. The superconducting phase diagram of ⁶Li is compared with that of ⁷Li through simultaneous measurement in a diamond anvil cell (DAC). Below 21 GPa, Li exhibits a direct (the superconducting coefficient, α, $T_c\propto M^{-\alpha },$ is positive), but unusually large isotope effect, whereas between 21 and 26 GPa, lithium shows an inverse superconducting isotope effect. The unusual dependence of the superconducting phase diagram of lithium on its atomic mass opens up the question of whether the lattice quantum dynamic effects dominate the low-temperature properties of dense lithium.

Light elements (low Z) and their compounds have been the subject of many recent studies for their potential as high-temperature superconductors (e.g., refs. 1–5). Due to their low mass, the physical properties of the low-Z compounds can be strongly influenced by zero-point effects (lattice quantum dynamics) (6), and mass-related isotope effects may be present in their thermodynamics of vibrational degrees of freedom. Such effects will influence the superconducting properties of these materials. Dependence of superconductivity on isotopic variations of low-Z compounds can be used to probe and determine the magnitude of mass-related effects. This in turn allows better development of models to determine their superconducting properties.

Under ambient pressure, lithium is the lightest elemental metallic and superconducting system, and it exhibits one of the highest superconducting transition temperatures of any elemental superconductor under compression (7–11). Despite the large mass difference between the stable isotopes of lithium (∼15%), isotope effects in superconductivity of lithium have not been studied before.

In systems with long-range attractive potential, the ratio of lattice zero-point displacements to interatomic distances may increase under compression (increase to the Lindemann ratio at high densities), provided they retain their long-range interactions (12, 13). (This is opposed to systems with short-range interactions, e.g., helium, in which the lattice becomes more classical under compression.) In these systems, more deviations from the static lattice behavior are expected at higher densities. At sufficiently low temperatures, where thermal energy is small, lattice quantum dynamics can play a more dominant role in the bulk properties. Sound velocity measurements on stable isotopes of lithium at 77 K and up to 1.6 GPa show that quantum solid effects in lithium, at least in the pressure range studied, do not decrease as a function of pressure (14). Raman spectroscopy studies between 40 and 123 GPa and at 177 K report a reduced isotope effect in high-frequency vibrational modes of Li, which may be related to quantum solid behavior (15). Up to this point, no experiments have reported a comparison of any physical properties of lithium isotopes at low temperatures and high pressures concurrently. Because the superconducting transition of lithium occurs in a relatively low temperature range (16–18), studying its superconducting isotope effect provides excellent conditions to search for zero-point lattice effects and their evolution as a function of pressure.

In the present study, we have measured the superconducting isotope effects in the stable isotopes of lithium under pressure. Lithium is a simple metallic system that is expected to exhibit conventional phonon-mediated superconductivity and a well-defined superconducting isotope effect with nominal pressure dependence of the relative T_c values (19) [according to the model by Treyeva and Trapezina (19), using theoretical values of Coulomb coupling constant, μ*(P) (20) by Christensen and Novikov and equation of state (EOS) of lithium (21) by Hanfland et al., assuming similar structures for the two isotopes, α should not vary by more than 10% for $15\hspace{0.17em}\text{GPa}<P<25\hspace{0.17em}\text{GPa}$]. Because phonon-mediated superconductivity depends on lattice and electronic properties of a material, any unusual isotopic mass dependence of the superconducting phase diagram can be indicative of the effects of large lattice dynamics on electronic and/or structural properties.

Experiment and Results

The expected conventional isotopic change in T_c of lithium is $T_c^{\mathrm{6Li}}\approx 1.08T_c^{\mathrm{7Li}}$. This leads to a relatively small temperature shift at low temperatures, where lithium becomes a superconductor [$T_c^{\mathrm{7Li}}\left(\max \right)\le 20\hspace{0.17em}\mathrm{K},$ for which a Bardeen–Cooper–Schrieffer (BCS) isotope shift of <2 K is expected for ⁶Li] (16–18). This small difference in the relative T_c values and lack of in situ thermometry in a diamond anvil cell (DAC) makes designing experiments sensitive enough to resolve the differences challenging. Any inconsistency in the temperature measurement between experimental runs may mask the expected isotope effect. In addition to experimental uncertainties, differences in a sample’s thermal history may change T_c (22). This is especially so for Li, in which the boundary of the martensitic transition (bcc-hR9) is known that can be shifted if the sample is not annealed (23). To achieve the required resolution in evaluating the relative T_c values of the two samples, both isotopes were measured simultaneously inside the same DAC (24, 25). The details of these experiments are given below, and the general principles of the method used have been previously published (24) (Fig. 1). Previous comparative measurements on the low-temperature electrical resistivity on lithium isotopes under ambient pressure also noted the importance of simultaneous measurements (22); however, simultaneous electrical measurements on large samples under ambient pressure are less technically limiting than similar measurements under high pressure. Considerations regarding the thermal history are important for any comparative studies, such as structural or magnetic studies on lithium isotopes.

Fig. 1.

(A) Twin-chamber gasket built on a 500-μm culet diamond, which is used in the present experiments in a DAC for simultaneous measurements of superconductivity. Each pressure chamber has a pair of extra Pt leads and contains several pieces of ruby for accurate determination of pressure gradient within each pressure chamber. The Insets show the gasket and samples under reflected light, at ∼21 GPa, demonstrating the metallic appearance of both samples and map of ruby pieces inside each pressure chamber in the same run. (B) Schematic drawing of the twin-chamber design used in the experiments. Small portions of the platinum leads in the path contribute to the total resistance measured for each sample. The electrodes for measuring the resistance of ⁶Li and ⁷Li are shown in different colors.

In the present work, we have used two isotopically rich samples of lithium: a ⁶Li-rich sample (the ⁶Li samples contained 99.99% lithium with the isotopic composition 95.6% ⁶Li and 4.4% ⁷Li together with the metallic impurities of Na, Mg, Al, and other elements; Sigma-Aldrich) and a ⁷Li-rich sample [the isotopic composition of the 99.9% pure natural lithium (⁷Li) was 92.41% atomic ⁷Li and 7.59% atomic ⁶Li; the metallic impurity composition was the same as in the case of the ⁶Li; Sigma-Aldrich], which we refer to as ⁶Li and ⁷Li samples, respectively, for the remainder of this manuscript.

All measurements were carried out in a DAC using electrical resistance as a means of determining the superconducting transition temperatures. All pressure increases were carried out at room temperature. The return to room temperature after every measurement allowed the samples to be transformed to their equilibrium phase. Lithium reacts readily with many materials including diamond (16, 18, 26), which may cause a DAC to fail. To prevent any such reactions, compressed, dehydrated alumina powder, which was heat treated at 110 °C to remove moisture, was used both as an electrical insulator and a pressure medium (27). This allowed us to keep the samples at room temperature inside the DAC without risking failure of the diamonds. An insulated gasket was made from a 250-μm-thick stainless-steel foil, preindented to a thickness of 40–55 μm. Two pressure chambers with initial diameters of 110 μm were symmetrically drilled 10–20 μm apart from each other on the gasket and several ruby spheres were dispersed evenly in each pressure chamber. The gasket then was insulated with a mixture of epoxy and alumina.

The use of alumina as pressure medium exposes the sample to nonhydrostatic conditions that may in principle affect the superconductivity. However, in the case of lithium, studies up to 50 GPa, in which no pressure medium was used, show very sharp Bragg peaks. This provides evidence that lithium itself remains a very soft solid that does not support large shear stresses (21, 28). [The superconducting phase diagram of ⁷Li measured using helium as hydrostatic pressure medium by Deemyad and Schilling and nonhydrostatic measurements by Struzhkin et al. without any pressure medium, are very similar below 30 GPa (see Fig. 3C).] In the current work, the presence of quasi-hydrostatic conditions is supported by the sharpness of ruby peaks.

Fig. 3.

(A) Superconducting phase diagram of lithium isotopes. Open shapes represent ⁶Li, and solid shapes represent ⁷Li. The different shapes designate separate loadings (open stars are representing data from ⁶Li measured in a conventional single-chamber gasket design for comparison). A sample transition, which is shown as Inset of graph A, shows the temperature error analysis. Shaded areas are just a guide to the eye (an actual fit to different regions is presented in SI Text). The pink shaded region from 18 to 21.5 GPa shows the direct isotope effect with a large difference in the T_c values for ⁶Li and ⁷Li. The gray shaded region shows the inverse isotope effect from 21.5 to 26 GPa. The pressure error bars represent the maximum pressure difference between all of the rubies shown in Fig. 1 in the two chambers. (The value is generally equal to the difference between the pressure from the ruby in the smallest radii of one chamber and the ruby in the largest radii of the opposite chamber.) (B) Sample data analysis used to determine T_c. (C) Comparison of the various superconducting phase diagram of natural lithium measured by various techniques (open triangles: Deemyad and Schilling; open squares: Struzhkin et al.; diamonds: Shimizu et al.; and circles: this study). The solid lines are a guide to the eye. The dashed line is the speculated boundary between hR9 and fcc at low temperature. (D) The isotope coefficient, α, as a function of pressure. The dashed line at α = 0.5 shows the expected value for a conventional isotope effect.

We have used high-precision spectroscopy to measure the pressure distribution of each chamber from several ruby spheres. The maximum pressure gradient remained below ±0.8 GPa up to the highest pressure measured (see Fig. 1 and SI Text for further discussion). In a twin-chamber gasket, not only the absolute pressure difference between the chambers and the pressure gradient across each sample is measured but also each chamber on its own acts as an independent indicator of the pressure dependence of the properties of its sample.

An isolated quasi–four-probe arrangement was built on each sample chamber using platinum electrodes. To eliminate the interference between the two circuits, each circuit was connected to a separate lock-in amplifier and run on a different frequency (∼5 and 13 Hz). To prevent any possible chemical reactions, the samples were loaded and pressurized inside a high-purity dry argon glove box. An AC current of I_rms ∼ 100 μA was applied across each sample. Because the arrangement used here was a quasi-four probe, a small portion of the signal always came from the piece of Pt electrode in the path (Fig. 1). The onset of superconductivity was defined by the temperature at which the resistance of sample drops to zero (Fig. 2C). As an additional test of superconductivity, we used a small magnetic field (∼100 Oe) to suppress T_c (Fig. 2 B and C). The experiments were completed with six separate loadings of the lithium isotopes, all of which overlapped in pressure range and showed complete internal consistency.

Fig. 2.

(A) Superconducting transitions as determined by electrical resistivity. All black lines show transitions for ⁷Li, and red lines are the transitions for ⁶Li. Each pair shows the simultaneous measurement. The double step in 18.1-GPa transition of ⁶Li may be related to presence of mixed phases with different T_c values at a structural phase boundary. The samples’ resistances in a normal state above their superconducting transitions is ∼0.5–10 mΩ varying by the sample size and geometry. These values would give an estimate of ρ ≈ 0.5–1 μΩ⋅cm, at room temperature, for a typical sample size of 50 × 50 × 10 μm³. A residual resistivity ratio (RRR) value of ∼75 is estimated from ambient pressure measurements on the samples used here (29). The transitions above are scaled for ease of comparison. (B and C) The shift of T_c with an applied external magnetic field of B ∼ 100 Oe for ⁶Li at 23.3 and 26.6 GPa. B ∼ 100 Oe for green lines and B = 0 for red lines.

Fig. 3A shows the superconducting phase diagram of ⁶Li and ⁷Li for pressures between 16 and 26 GPa. The correlation between the superconducting transition temperatures of the two isotopes is anomalous, and in the range of this study three distinct regions can be identified. The sign of $\left(d{T}_c/dP\right)$ in the pressure range $16\hspace{0.17em}\text{GPa}<P<26\hspace{0.17em}\text{GPa}$ changes two times for ⁶Li. In this region, the slope is always positive, although not constant, for ⁷Li. A change in slope may be indicative of the presence of a structural phase boundary (such as hR9 to fcc for ⁷Li). Between 16 and 21.5 GPa, the superconducting T_c of ⁶Li is higher than that of ⁷Li. Fig. 3C shows the calculated values of the superconducting isotopic coefficient, α ($T_c\propto M^{-\alpha }$), as a function of pressure. The lowest pressure points at 16 and 18 GPa for ⁶Li display an initial positive slope $\left(d{T}_c/dP\right)$; however, the paucity of data in this region does not allow to properly assign a slope of α vs. P. For 18 GPa < P < 21.5 GPa, the value of the isotopic coefficient decreases monotonically with pressure, and the value of α is always higher than expected for BCS-type superconductors, $1\lesssim \alpha \lesssim 4$. For P > 21.5 GPa, the value of the isotopic coefficient, α, changes sign and remains constant within error ($\alpha \approx -1.5\pm 0.5$) (SI Text).

Fig. 3B shows the superconducting phase diagram of ⁷Li, which has been plotted here together with all of the previous measurements. The current result only overlaps with the studies of Deemyad and Schilling for 22 GPa < P < 26 GPa. As shown in Fig. 3C, the measurements of the superconductivity of natural lithium in the present work display the same trend as Deemyad and Schilling (with the shallow slope at the beginning followed by rapid increase in the slope). The present measurements consistently show slightly lower transition temperatures than those of Deemyad and Schilling, which can be caused by differences in thermometry and/or thermal histories of the samples and other differences between the methods that have been used. For example, Deemyad and Schilling never annealed their samples above 100 K, which, according to the phase diagram suggested by Guillame et al., may not allow the sample to relax to fcc or bcc phase between pressure applications below 20 GPa (26). In the present experiments, we applied the pressures at room temperature. For the comparison of the transition temperatures of the two isotopes, however, the samples compared need to have experienced the exact same thermal history and their relative transition temperature must be known precisely. All previous measurements of the high-pressure phase diagram of lithium done in past (excluding the measurements of the superconducting phase diagram of natural lithium by Deemyad and Schilling) used no pressure medium (15, 16, 18, 21, 26, 28, 29). The experiments done by Deemyad and Schilling used helium as pressure medium and found very reproducible results. The results, however, may have been influenced by diffusion of helium into the lithium lattice. Moreover, Deemyad and Schilling as well as Struzhkin et al. used magnetic susceptibility to detect the superconducting transition. Magnetic susceptibility measurements currently cannot be used for simultaneous measurements, critical for an experiment designed to characterize the slight differences between isotopes.

Discussion

For a BCS-type superconductor composed of one atomic species with a harmonic lattice, the superconducting transition temperature (T_c) and the ionic mass follow the simplified relationship, $T_c\propto M^{-\alpha },$ in which α = 0.5. This relation is mainly attributable to differences in the Debye temperature for different ionic masses of different isotopes. In the current experiment, we observe an anomalous isotope effect in the superconducting phase diagram of lithium that cannot be explained for a material with very harmonic lattice and absence of substantial mass-related dynamic effects.

In the presence of large-amplitude zero-point motion and related large anharmonicity, electrons do not see the lattice as a perfect crystal (this is the case even if the ionic displacements do not affect the structures of the isotopes); thus, in total, drastic deviations from conventional isotope effects in a superconducting quantum solid can be expected (30, 31).

Another possible mechanism that may be responsible for the isotope effects observed here can be due to the differences in the structures of the two isotopes under pressure. For a solid with static lattice and in the absence of large zero-point energy, the equilibrium distance between the lattice particles is determined by the minimum of the potential energy of the lattice and, to first approximation, is independent of the particles’ mass (32, 33), and isotope effects in the structures are not expected. On the other hand, in a solid with large lattice quantum dynamics, the large zero-point energy of the lattice will significantly contribute to the vibrational and rotational energies, which can have an impact on the equilibrium structures (32, 33). Because BCS assumes identical structures for isotopes, the BCS superconducting isotope relation is not applicable in systems with a structural isotope effect. In the case of lithium, it has been theoretically shown that, without inclusion of zero-point energy, some of the known structures of natural lithium (oC88) will not be stable. Therefore, it is not unexpected if the differences in the zero-point energies of lithium isotopes lead to different structural phase diagram for them (34). It should be emphasized here that, given the known differences between the phonon free energies of the two lithium isotopes (these measurements are not overlapping in pressure and temperature range with the present work) (35), one can see that large differences in structures of two isotopes is unlikely and the conditions for such differences would be thermodynamically rather stringent.

The structures of Li as a function of pressure [for pressures above 0.65 GPa (36)] are not known for T < 77 K, which contains the boundaries of the hR9 phase (with bcc and fcc phases) (26). This phase is thought to play an important role in superconductivity. Moreover, the isotopic dependence of the structures of lithium is not known in this pressure regime. Between 16 and 22 GPa, ⁶Li exhibits a change from a positive to a negative slope in T_c. In contrast, ⁷Li shows a positive slope in the entire range where superconductivity was observed. It is possible that the large difference in T_c values, the initial change in slope for ⁶Li, and the opposite slopes observed between 18 and 22 GPa are caused by a low-temperature structure in ⁶Li not present in ⁷Li. Low-temperature structural studies are required to characterize this region. Above ∼21 GPa, the superconducting T_c of ⁶Li falls below that of ⁷Li, and this effect remains until the highest pressure studied here, ∼26 GPa. The inverse isotope effect in conventional superconducting systems is noted in some transition metal hydrides (MH), such as PdH, and in the element α-U (37–40). The inverse isotope effect in MH has been attributed to the existence of large quantum effects in hydrogen, which cause anharmonicity in phonon spectra (41, 42), an explanation that cannot account for the behavior of α-U. If the unusual isotope effect in Li is solely a consequence of its zero-point displacements and a consequent anharmonicity in its lattice, Li is the only elemental solid known to exhibit such behavior (dominant anharmonic effects may also be responsible for large positive isotope coefficient in pressures below 21 GPa). Another possible condition for inverse isotope effect is when the magnitude of the Coulomb coupling constant (μ*) becomes comparable to the electron–phonon coupling constant (λ). However, in this case, a small T_c (<1 K) is expected for realistic values of the parameters (43). For fcc lithium, this condition is theoretically not present (44) and cannot explain the sudden change in the sign of isotopic shift above 21 GPa. However, in the present case, electronic and structural effects may be entangled. Comparative structural studies for lithium isotopes at low temperature are very challenging, but they are currently possible in third-generation synchrotron sources. The results of this study would justify the investment on such works. The detailed comparative studies on additional low-temperature properties of lithium isotopes may also shed light on the predicted properties of metallic hydrogen.

It should be emphasized that, based on current experimental results and without complementary structural studies, one cannot conclude a departure from isotope effects expected within BCS. Hypothetically, if the sequence of structural phase transitions in ⁶Li were different from that of ⁷Li, which on its own is an interesting mass-related effect, the present observations could still be consistent with a BCS model. Under such conditions, emphasis then would be on explaining isotope effects on the phase stability and the origin of such mass-related phase instabilities. However, should it turn out in follow-up structural studies that there is no significant difference in the PT phase diagrams of the two isotopes, it would imply that the present observations point to superconductivity-related physics, possibly the strength of the electron–phonon coupling. This could, for instance, be an effect of zero-point vibrations on the ground state (i.e., T = 0) electronic structure.

It is notable that isotopes of Li possess different quantum statistics, and natural lithium has been shown to exhibit nuclear order at 1 atm (45). The magnetic order in lithium isotopes may contribute to their superconducting isotope effects at ambient pressure where natural lithium superconducts below 0.4 mK. Studying the isotope effects in ambient pressure superconductivity of lithium would be also enlightening.