Understanding of the emergent electronic phases and competing interactions through Re and Rh co-substitution in the correlated f-electron superconductor URu₂Si₂.

URu₂Si₂ is heavy fermion Pauli limited singlet, chiral d wave superconductor T_c~1.5K, with line & point nodes. It crystallizes in ThCr₂Si₂ type, I_4/mmm str. Origin of Hidden Order (HO) phase transition at T_HO~17.5 K & its order parameter never unveiled. HO is characterized by large BCS λ-type specific heat anomaly, hump in resistivity, kink in susceptibility, enhanced thermal conductivity, field trainable polar Kerr effect, giant Nernst effect etc. Neutron shows ordered moment ~0.03 μB. Partial gapping of FS is involved in HO. URu₂Si₂ has interplay of competing interactions & correlated electron phases & phenomena, e.g., HO, SC, FM, AFM, SDW, QC, NFL & high field phases. Competing interactions tuned via composition (x), pressure (P) & field (H). Transition metal doping at Ru site manifest competing interactions, hole doping by Re suppresses HO & emerges itinerant FM phase, electron doping by Rh suppresses HO & forms LMAFM phases. I will review effects of co-substitution of equal amounts of Re & Rh, isoelectronic on average, to form URu_2-2xRe_xRh_xSi₂, pseudo ternary alloys based on lattice parameters, electrical resistivity, magnetic susceptibility, & specific heat. Features in physical properties characterizing energy gap associated with HO phase (e.g., exponential T-dependence of specific heat) are suppressed rapidly with Re & Rh co-substitution level so that by x ~ 0.11, HO phase transition is no longer discernible. T_HO & gap decrease monotonically with “x”.