Arrested Kondo effect and hidden order in URu2Si2

Complex electronic matter shows subtle forms of selforganization, which are almost invisible to the available experimental tools. One prominent example is provided by the heavy-fermion material URu2Si2. At high temperature, the 5f electrons of uranium carry a very large entropy. This entropy is released at 17.5 K by means of a second-order phase transition1 to a state that remains shrouded in mystery, termed a ‘hidden order’ state2. Here, we develop a first-principles theoretical method to analyse the electronic spectrum of correlated materials as a function of the position inside the unit cell of the crystal and use it to identify the low-energy excitations of URu2Si2. We identify the order parameter of the hidden-order state and show that it is intimately connected to magnetism. Below 70 K, the 5f electrons undergo a multichannel Kondo effect, which is ‘arrested’ at low temperature by the crystalfield splitting. At lower temperatures, two broken-symmetry states emerge, characterized by a complex order parameter ψ. A real ψ describes the hidden-order phase and an imaginary ψ corresponds to the large-moment antiferromagnetic phase. Together, they provide a unified picture of the two brokensymmetry phases in this material. URu2Si2 crystallizes in the body-centred tetragonal structure shown in Fig. 1a. Starting from a localized point of view for U-5f electrons, that is, treating them as core states in density functional theory (DFT) calculations, one obtains a set of wide bands, entirely of spd character, as shown in Fig. 1b. In an itinerant picture, there are f states close to the Fermi level, which hybridize with the spd bands to form itinerant states of predominantly f character, with a bandwidth of the order of 1 eV. This is shown in Fig. 1c. This situation is realized in Ceand Yr-based heavy-fermion materials, the electronic states of which are well described by narrowing the bands of the DFT by a factor of 10–1,000, to account for the heavy mass3. For URu2Si2, we propose a new scenario for the transfer of atomic f weight to the itinerant carriers, which we name the ‘arrested Kondo effect’. At high temperatures, above the characteristic coherence temperature T ∗ ∼ 70K, the U-5f electrons are localized and do not participate in forming the low-energy bands. The U atoms settle in the 5f 2 configuration, for which the crystal environment chooses the non-degenerate atomic ground state. However, the first excited state, which is also non-degenerate, is only∆= 35K above the ground state, as first observed in polarized neutron scattering experiments4. Hence, in the temperature range ∆<T <T , the ground state seems doubly degenerate, and hence the Kondo effect develops, leading to the formation of very narrow states near the Fermi energy and a narrow peak in the density of states. The Kondo effect is partially arrested below T <∆, because the crystal-field splitting between the two singlet states induces a partial gapping at the Fermi level. The situation is shown in Fig. 1c. A non-dispersing slab of f spectral weight is pushed to roughly 8meV away from the Fermi energy. Although only a small fraction