Fanning the flames of quantum criticality

New research at HFML has discovered a previously unknown feature of certain metals which, when cooled close to absolute zero, undergo a quantum-mechanically-driven phase transition. The material in question, the iron-based superconductor FeSe1-xSx, is found to host two different types of electronic excitations, one coherent, the other diffusive. In contrast to previous assumptions, these two excitations are found to coexist over the entire phase diagram studied, like the two “flip sides” of the same electronic states, whose relative weighting depends on the system’s proximity to the quantum phase transition. The research, carried out as part of an international collaboration involving American and Japanese researchers, was published in the new journal Physical Review Research.

Ordinary metals

In ordinary metals, the Coulomb repulsion between electrons is screened simply by the sheer number of electrons present and resistance in the metal is caused only by scattering off the vibrations of the atoms (or ions) that make up the crystalline lattice. As the metal is cooled, these vibrations become weaker, and the resistance duly decreases, but at low enough temperatures, it saturates at a finite value due to scattering off the inevitable imperfections that appear during crystal growth. If the interaction between the electrons and these (quantized) lattice vibrations is sufficiently strong, however, the conduction electrons may form pairs and condense into a superconducting (i.e. zero resistive) state. Only then, it seems, are the electrons aware of each other’s existence.

Correlated metals

There is another class of metals, however, in which the Coulomb interaction is only weakly screened and other phase transitions (not just superconductivity) can ensue. Magnetism, charge order, even a transition into an insulating phase, can occur as the metal is cooled and the interactions that promote these phases overcome the thermal agitation. In these compounds, the principle electron scattering is now off themselves, or in the vicinity of the phase transition, off the fluctuations of the associated order parameter.

Quantum critical metals

An additional form of scattering emerges when the transition temperature to an ordered state is suppressed, e.g. by pressure, high magnetic fields, or by chemical substitution, towards absolute zero. In this case, with no thermal agitation to disturb the ordered state, the phase transition becomes a quantum phase transition, and the fluctuations in its vicinity are now quantum critical fluctuations between the ordered and the disordered phase. One of the (many) remarkable features of this type of metal is that these quantum fluctuations influence their physical properties not just at the quantum critical point (where the order temperature is suppressed to zero Kelvin) but over a wide fan-shaped region in the temperature vs. tuning parameter phase diagram. Moreover, instead of reaching the zero-temperature phase transition, the system more often than not becomes superconducting with the maximum superconducting transition temperature located very often close to the point where the quantum phase transition would have occurred. Thus, quantum criticality and superconductivity appear to be inextricably linked.

Low-temperature phase diagram of FeSe1-xSx

Low-temperature phase diagram of FeSe1-xSx described in terms of the exponent of the T -dependent resistivity that is itself defined in the upper color scale. The size of dots inside the T2 regime indicate the strength of A, the coefficient of the T2 resistivity, normalized to a fixed carrier density (and quantified in the lower color scale in units of μcmK−2).

An example of such behaviour is illustrated in the Figure. The red and blue regions correspond to different forms of the electrical resistivity as a function of temperature and tuning parameter. In the blue regions, the resistivity varies like temperature squared, as expected when the electrons are scattering off each other and as such, they maintain their coherent wave-like motion. In the red fan-shaped region, on the other hand, the resistivity scales linearly with temperature implying that the electrons are being scattered by quantum fluctuations associated with the quantum critical point itself. Under this intense scattering, the electrons lose their coherence and start to move more like particles diffusing through a medium.

Coexistence not crossover

Until now, it has always been assumed that the two phases are distinct, simply merging from one to the other as either temperature or the relevant tuning parameter is varied. In the new study carried out by the HFML team in collaboration with researchers both in the US and in Japan, we have discovered that in reality, both forms of conduction are omnipresent – it is merely their ratio that varies as one moves around the phase diagram. The metal in question is iron selenide doped with sulphur and the quantum critical point is believed to arise from so-called nematic order, though in reality, the details here are not that important since it is likely to be a generic phenomenon. In the end, this discovery may have far-reaching consequences for our understanding of how the electronic properties of metals evolve across a quantum critical point. In effect, the quantum critical and coherent electronic states are found to coexist, like strange bedfellows and as a result, the field of quantum criticality just got hotter.

Related publication

Coexistence of orbital and quantum critical magnetoresistance in FeSe1-xSx Licciardello,  N. Maksimovic, J. Ayres, J. Buhot, M. Čulo, B. Bryant, S. Kasahara, Y. Matsuda, T. Shibauchi, V. Nagarajan, J. G. Analytis and N. E. Hussey, Phys. Rev. Research 1 023011 (2019)


Nigel Hussey