The Quantum Garden of UTe2: How a Magnetic Field Cultivates Three Superconducting Phases ✛ ✎ ✦

Superconductivity and magnetic field are age-old foes: the field barges in like a whirlwind, tearing apart the delicate pairing of Cooper pairs, destroying order. But in materials with strong electronic correlations, where particles seem to dance an intricate minuet of attraction and repulsion, this enmity sometimes transforms into alliance. That’s exactly what happens in the crystal uranium ditelluride UTe2. Here, the magnetic field isn’t a destructive hurricane but a patient gardener, cultivating three rare flowers of superconductivity in a seemingly barren quantum wasteland. The phases SC1, SC2, and SC3 succeed each other, obeying the slightest changes in the field’s strength and angle, as if an invisible conductor sets the rhythm of a symphony.

A single crystal of record purity (residual resistivity 576) with a critical temperature of 2.05 K was placed in a static field up to 42 T, and the picture of quantum states revealed subtle shades. Along the b-axis, the low-field phase SC1 is replaced by SC2 already at 20 T. But tilt the field more than 20 degrees toward the c-axis, and the mysterious SC3 enters the stage. Its true zero resistance appears only after the metamagnetic transition at 34 T, as if a secret gate opens to a world where spins are aligned, and entangled pairs, against all odds, gain stability. Measurements of the temperature dependence at various angles found that SC2 and SC3 can coexist in a narrow parameter corridor, and the critical temperature of SC3 skyrockets with angle, just like a flower reaching for the sun.

These findings challenge the classical Jaccarino–Peter model, where superconductivity was saved only by precise compensation of the external field by internal exchange interaction. Instead, critical magnetic fluctuations take center stage, flaring up near the metamagnetic transition, like a storm that doesn't destroy but creates. This picture echoes the great works of John Bardeen (BCS theory) and Lev Landau (Fermi liquid theory) but requires their extension into the uncharted territory of strong correlations. UTe2 becomes an ideal laboratory where, in a single flask, superposition of spin states and a condensate of electron pairs obeying Bose-Einstein statistics are mixed. Here, quantum fluctuations are not a nuisance but a tool of creation.

Unraveling this field-driven evolution of entropy and the restructuring of energy bands promises the creation of superconducting magnets of unprecedented strength — from fusion reactors to next-generation accelerators. We stand on the threshold of understanding how strongly correlated electrons and the topology of the Fermi surface give birth to new states of matter near quantum critical points. Uranium ditelluride, with its three superconducting faces, reminds us: sometimes destruction is not the end, but the beginning.