Multiple quantum criticality

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. We have examined the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3 /SrTiO3 interfaces.

Superconductor–insulator transition induced by a magnetic field. a

Sheet resistance RS as a function of temperature for different magnetic fields from 0 to 0.3 T. Inset: Tc and GS = 1/RS as a function of the gate voltage VG . b Zoom on the same data showing the characteristic magnetic field BX, for which RS is constant between 0.12 and 0.22 K. c Zoom on the same data showing the characteristic magnetic field BC, which separates the two regimes at the lowest temperatures.

Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals.

Sketch of the role of mesoscopic disorder on the QPT and phase diagrams. a The dephasing length LΦ diverges with decreasing temperature, and reaches the size of the superconducting puddles Ld at Td. The insets show a piece of material in the two regimes. At high temperature (bottom),
LΦ<Ld and the system is in the clean limit, whereas at low temperature (top), LΦ>Ld, and the system is in the dirty limit. In this drawing, superconducting puddles (blue) are coupled through a 2DEG (yellow). The arrows symbolize the local phase of the superconductor. b Phase diagram in the B–T plane for VG =+80 V. The derivative ∂R/∂T is plotted as a colour scale (blue for negative values, orange for positive ones and white around 0), as a function of the magnetic field B and the temperature T (log scale). The two critical fields BX and BC are reported, together with the different phases: WLM refers to weakly localizing metal, puddle SC to the region where complete superconductivity within the puddles can be observed, array SC where the whole array is superconducting. c Phase diagram in the B–T plane for VG=−15 V. A single critical field BC is observed corresponding to the transition of the whole array.

We have showed that the superconducting 2DEG at the LaTiO3/SrTiO3 interface undergoes a QPT from a superconductor to a weakly localizing metal on applying a perpendicular magnetic field, driven by phase fluctuations and well described by the (2+1)D XY model. By tuning the gate voltage, it is possible to explore the clean and dirty regimes according to the Harris criterion, with a critical exponents product zν=2/3 in the former case, in agreement with previous evaluations in the parent system LaAlO3/SrTiO3, and greater than 1 otherwise. The system is well described by a disordered array of superconducting puddles coupled by a 2DEG, which can exhibit two critical behaviours, one related to regional or local ordering, and another one corresponding to long-range phase coherence, as proposed theoretically. The key parameter, that is, the coupling constant (the 2DEG conductance), can be tuned at will to explore the phase diagram of the system.

References :

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    Nature Materials (2013) doi:10.1038/nmat3624
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