Origin of Quantum Criticality in Yb–Al–Au Approximant Crystal and Quasicrystal

Abstract

To get insight into the mechanism of emergence of unconventional quantum criticality observed in quasicrystal Yb 15 Al 34 Au 51 , the approximant crystal Yb 14 Al 35 Au 51 is analyzed theoretically. By constructing a minimal model for the approximant crystal, the heavy quasiparticle band is shown to emerge near the Fermi level because of strong correlation of 4f electrons at Yb. We find that charge-transfer mode between 4f electron at Yb on the 3rd shell and 3p electron at Al on the 4th shell in Tsai-type cluster is considerably enhanced with almost flat momentum dependence.The mode-coupling theory shows that magnetic as well as valence susceptibility exhibits χ ∼ T −0.5 for zero-field limit and is expressed as a single scaling function of the ratio of temperature to magnetic field T/B over four decades even in the approximant crystal when some condition is satisfied by varying parameters, e.g., by applying pressure. The key origin is clarified to be due to the strong locality of the critical Yb-valence fluctuation and small Brillouin zone reflecting the large unit cell, giving rise to the extremely-small characteristic energy scale. This also gives a natural explanation for the quantum criticality in the quasicrystal corresponding to the infinite limit of the unit-cell size.Recent discovery of unconventional quantum critical phenomena in quasicrystal Yb 15 Al 34 Au 51 has attracted much attention.1, 2) The measured criticality such as magnetic susceptibility χ ∼ T −0.5 , NMR relaxation rate (T 1 T ) −1 ∼ T −0.5 , specific heat C e /T ∼ − log T , and resistivity ρ ∼ T is unconventional and quite similar to those observed in periodic crystals such as heavy-electron metals YbRh 2 Si 2 3) and β-YbAlB 4 , 4,5) which are well explained by quantum critical phenomena of Yb-valence fluctuations.6)The quasicrystal Yb 15 Al 34 Au 51 is constituted of concentric shell structures of Tsai-type cluster shown in Fig. 1. 1, 7) There also exists approximant crystal Yb 14 Al 35 Au 51 .7) The approximant crystal has periodic arrangement of the body-centered cubic (bcc) structure whose unit cell contains shell structures shown in Figs. 1(a)-1(e). Theoretical analysis of the Yb-AlAu cluster taking account of critical Yb-valence fluctuations has provided a natural explanation for robustness of quantum criticality in the quasicrystal measured under pressure and has pointed out a possibility that the same criticality appears even in the approximant crystal when pressure is applied. 8,9) On the other hand, a new theoretical framework for critical Yb-valence fluctuation under magnetic field has been developed recently.10) The theory has succeeded in explaining novel scaling discovered in β-YbAlB 4 where the magnetic susceptibility χ is expressed as a single scaling function of the ratio of temperature to magnetic field T/B over four decades. 5)Surprisingly, recent measurement of magnetic susceptibility in the quasicrystal Yb 15 Al 34 Au 51 has revealed that the same T/B-scaling behavior appears over six decades of T/B.11) This strongly s...

Non-divergent Grüneisen parameter in quantum critical quasicrystal Yb15Al34Au51: Reflection of robustness of quantum criticality under pressure

“…3 are exactly the same as those used in Ref. [18], our results give a unified explanation for the measured magnetic susceptibility as χ(T ) ∼ T −0.5 for the zero-field 11…”

“…and the T/B scaling, where χ(T, B) is expressed as a single scaling function of the ratio of temperature T and magnetic field B, appear at the pressure-tuned valence QCP [18]. This theoretical prediction [18] has actually been confirmed in the AC at P = 1.96 GPa [ Fig.…”

“…The CVF theory is consistent with the criticality in the magnetic susceptibility and its robustness under pressure in the QC [8] as well as emergence of the same criticality in the pressure-tuned AC [ Fig. 1(b)] [18]. First, we will construct a general formalism for calculating C V , α, and Γ in the thermodynamically consistent way near the valence QCP in the periodic lattice systems in Sect.…”

“…2(c)] and 3p electron at Al on just the outer icosidodecahedron (4th shell) [see Fig. 2(d)] is considerably enhanced [18]. The mode-mode coupling theory applied to the most dominant CT fluctuation, i.e., CVF, has shown that the magnetic susceptibility…”

Quantum Valence Criticality in Heavy Fermions on Periodic and Aperiodic Crystals

“…We note here that the renormalization factor for this state is z = 1.9 × 10 −3 , which is obtained directly from the solutionb i of the slave-boson mean-field equations as z ≡b 2 i (see Ref. [36] for detail). Since this small z implies that the Kondo temperature, which is three decades smaller than the conduction-electron band width, is realized in the present lattice system, this state is in the heavyfermion regime.…”