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

We analyze and overview several different unconventional quantum criticalities. One origin of the unconventionality is the proximity to first-order transitions. The border between the first-order and continuous transitions is described by a quantum tricritical point (QTCP) for symmetry-breaking transitions. One of the characteristic features is the concomitant divergence of order-parameter and uniform fluctuations in contrast to the conventional quantum critical point (QCP). Several puzzling non-Fermi-liquid properties are referred to be accounted for as in the cases of YbRh2Si2, CeRu2Si2 and beta-YbAlB4. Another more dramatic unconventionality appears in this case for topological transitions such as metal-insulator and Lifshitz transitions. This border, the marginal quantum critical point (MQCP), belongs to an unprecedented universality class with diverging uniform fluctuations at zero temperature. The MQCP has a unique feature by a combined character of symmetry-breaking and topological transitions. The theoretical results are supported by experimental indications for V2-xCrxO3 and an organic conductor kappa-(ET)2Cu[N(CN)2]Cl. Identifying topological transitions also reveals how non-Fermi liquid appears as a phase in metals. The theory also accounts for the criticality of a metamagnetic transition in ZrZn2, by interpreting it as an interplay of Lifshitz transition and correlation effects. We discuss common underlying physics in these examples.