Unconventional quantum criticality emerging as a new common languageof transition-metal compounds, heavy-fermion systems, and organic conductors

Abstract

We analyze and overview some of the different types of unconventional quantumcriticalities by focusing on two origins. One origin of the unconventionality is the proximityto first-order transitions. The border between the first-order and continuous transitions isdescribed by a quantum tricritical point (QTCP) for symmetry breaking transitions. Oneof the characteristic features of the quantum tricriticality is the concomitant divergence ofan order parameter and uniform fluctuations, in contrast to the conventionalquantum critical point (QCP). The interplay of these two fluctuations generatesunconventionality. Several puzzling non-Fermi-liquid properties in experimentsare taken to be accounted for by the resultant universality, as in the cases ofY bRh2Si2,CeRu2Si2 andβ-Y bAlB4. Another more dramatic unconventionality appears again at the border of the first-order andcontinuous transitions, but in this case for topological transitions such as metal–insulatorand Lifshitz transitions. This border, the marginal quantum critical point (MQCP),belongs to an unprecedented universality class with diverging uniform fluctuations at zerotemperature. The Ising universality at the critical end point of the first-order transition atnonzero temperatures transforms to the marginal quantum criticality when the criticaltemperature is suppressed to zero. The MQCP has a unique feature with a combinedcharacter of symmetry breaking and topological transitions. In the metal–insulatortransitions, the theoretical results are supported by experimental indications forV2 − xCrxO3 and an organicconductor κ-(ET)2Cu[N(CN)2]Cl. Identifying topological transitions also reveals how non-Fermi liquid appears as a phase inmetals. The theory also accounts for the criticality of a metamagnetic transition inZrZn2, by interpreting it as an interplay of Lifshitz transition and correlation effects. We discussthe common underlying physics in these examples.