Home >  About ISSP >  Publications > Activity Report 2018 > Xxxx Group

Discovery of Zero-Field Quantum Critical Point in the Heavy Fermion Superconductor β-YbAlB4

Nakatsuji and Sakakibara Groups

Singularities where the smoothness of physical laws breaks down and is replaced by mathematical infinities are studied extensively in physics as sources of fascinating new forms of behavior. For instance, lightning bolts, tornadoes and black holes are show-cases of singularities in physics. In the past few decades, it has been recognized that similar singularities also develop inside "ordinary" materials at low temperatures, and when they do, a new kind of emergent phenomena appears. In particular, the electron fluid that carries electricity in metals becomes unstable. For the past 80 years, Fermi liquid theory, which is the idealized picture of electron liquid, has provided a mainstay of our understanding of metals. However, in β-YbAlB4, a new ytterbium-based material, this picture breaks down, revealing an underlying singularity at zero temperature i.e. quantum critical point (QCP) [1,2].


Fig.1. A) Crystal structures of β-YbAlB4. B) A picture of single crystals of β-YbAlB4.

Fig.2. Scaling observed for the magnetization at T ≲ 3 K and B ≲ 2 T. Here, the magnetization M satisfies a scaling equation -dM/dT = B-1/2f(T/B) over a wide range of temperature and field shown in the inset. This means that the physical properties around QCP are determined only by the ratio T/B. In addition this proves that the QCP is located just at zero-magnetic field. Inset shows the B-T phase diagram of β-YbAlB4 in the low T and B region. The filled circles are determined from the peak temperatures of −dM/dT, below which the FL ground state is stabilized. At low field, the thermodynamic boundary between the FL and NFL regions is on a kBT ~ BB line (broken line). The open circles are the temperature scale TFL, below which the T2 dependence of the resistivity is observed [1].

In order to study a singularity in a material (QCP), a tuning of a physical parameter such as temperature, magnetic field, pressure, and doping is necessary to make the material approaches to QCP in the phase space. This can be compared to traveling around space and time searching black holes. However, like the black hole forms around a singularity masking the mathematical singularity at its center in the fabric of space and time, the breakdown of the Fermi liquid picture in β-YbAlB4 is masked by superconductivity which prohibits any direct measurement of the underlying metallic state [2,3]. Moreover, the singularities have often been obscured by disorder. For all these difficulties, we have succeeded in probing deep inside the singularity using the ultrapure form of the crystals and high fidelity magnetization measurements [2]. As a result, we have found that the magnetization M satisfies a scaling equation -dM/dT = B-1/2f(T/B) over a wide range of temperature and field at T ≲ 3 K and B ≲ 2 T. In other words, this means that the singularity lets its presence be known by affecting the material properties at elevated temperatures and magnetic fields, several orders of magnitude larger than the boundaries of the superconducting domain. It bears resemblance to a black hole, which cannot be probed directly, but whose gravitational pull is felt by the surrounding stars, long distances away. The T/B scaling proves not only unconventional quantum criticality but, furthermore, that the singularity in β-YbAlB4 occurs just at zero magnetic field with an experimental error comparable to Earth’s magnetic field at ambient pressure.

This is quite surprising compared to canonical QCP materials which require a tuning of a control parameter to approach QCP. This raises an intriguing possibility that this metal may be part of a new, quantum critical, phase of matter i.e. the spontaneous quantum criticality in β-YbAlB4 would persist in a finite region of the phase-space, as a function of pressure or doping [2]. This strange state, which displays an intriguing correspondence of self-similarity under applied magnetic field and temperature, can be viewed as the third state of the matter in addition to the Fermi liquid and a superconductor. It is expected that this observation opens new horizons in our understanding of quantum criticality and provides us with important information which can help shed light on the strange metal state and superconductivity not only in this material, but also in other families of unconventional superconductors.


References
  • S. Nakatsuji, K. Kuga, Y. Machida, T. Tayama, T. Sakakibara, Y. Karaki, H. Ishimoto, S. Yonezawa, Y. Maeno, E. Pearson, G. G. Lonzarich, L. Balicas, H. Lee, and Z. Fisk, Nature Physics 4, 603 (2008).
  • Yosuke Matsumoto, Satoru Nakatsuji, Kentaro Kuga, Yoshitomo Karaki, Naoki Horie, Yasuyuki Shimura, Toshiro Sakakibara, Andriy H. Nevidomskyy, Piers Coleman, Science 331, 316 (2011).
  • K. Kuga, Y. Karaki, Y. Matsumoto, Y. Machida, and S. Nakatsuji, Physical Review Letters 101, 137004 (2008).
Authors
  • cRoyal Holloway, University of London,   
  • bRice University,
  • aRutgers University,
  • Y. Matsumoto, S. Nakatsuji, K. Kuga, Y. Karaki, N. Horie, Y. Shimura, T. Sakakibara, A. H. Nevidomskyyaa, b, and P. Colemana, c