Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe2_2

The discovery of unconventional superconductivity in the heavy-fermion material UTe$_2$ has reinvigorated research of spin-triplet superconductivity. We perform a theoretical study of coupled two-component spin-triplet superconducting order parameters and their thermodynamic transitions into the superconducting state. With focus on the behavior of the temperature dependence of the specific heat capacity, we find that two-component time-reversal symmetry breaking superconducting order may feature vanishing or even negative secondary specific heat anomalies. The origin of this unusual specific heat behavior is tied to the non-unitarity of the composite order parameter. Additionally, we supply an analysis of the topological surface states associated with the different possible spin-triplet orders: single-component orders host Dirac Majorana surface states in addition to possible bulk nodes. A second component breaking time-reversal symmetry gaps these surfaces states producing chiral Majorana hinge modes. DFT+$U$ band-structure calculations support that these topological phases are realized in UTe$_2$ when introducing weak superconducting pairing. Our topological analysis suggests measurable signatures for surface-probe experiments to acquire further evidence of the superconducting pairing symmetry.Comment: 20 pages, 8 figure

A microscopic Ginzburg--Landau theory and singlet ordering in Sr2_2RuO4_4

The long-standing quest to determine the superconducting order of Sr$_2$RuO$_4$ (SRO) has received renewed attention after recent nuclear magnetic resonance (NMR) Knight shift experiments have cast doubt on the possibility of spin-triplet pairing in the superconducting state. As a putative solution, encompassing a body of experiments conducted over the years, a $d+ig$-wave order parameter caused by an accidental near-degeneracy has been suggested [S. A. Kivelson et al., npj Quantum Materials $\bf{5}$, 43 (2020)]. Here we develop a general Ginzburg--Landau theory for multiband superconductors. We apply the theory to SRO and predict the relative size of the order parameter components. The heat capacity jump expected at the onset of the second order parameter component is found to be above the current threshold deduced by the experimental absence of a second jump. Our results tightly restrict theories of $d+ig$ order, and other candidates caused by a near-degeneracy, in SRO. We discuss possible solutions to the problem.Comment: 13 pages, 8 figure

Superconducting order of Sr2RuO4\mathrm{Sr}_2\mathrm{RuO}_4 from a three-dimensional microscopic model

We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate ($\mathrm{Sr}_2\mathrm{RuO}_4$) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity $d$-wave order are favored for smaller and larger values of the Hund's coupling parameter $J$, respectively. Both orders are found compatible with specific heat data and the recently-reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al. Nature 574, 72 (2019)]. The chiral $p$-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.Comment: 11 pages, 8 figure

The superconductivity of Sr2RuO4 under c-axis uniaxial stress

Funding: F.J., A.P.M., and C.W.H. acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - TRR 288 - 422213477 (project A10). H.S.R. and S.H.S. acknowledge the financial support of the Engineering and Physical Sciences Research Council (UK). H.S.R. acknowledges support from the Aker Scholarship. T.S. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), in particular the Discovery Grant [RGPIN-2020-05842], the Accelerator Supplement [RGPAS-2020-00060], and the Discovery Launch Supplement [DGECR-2020-00222]. N.K. is supported by a KAKENHI Grants-in-Aids for Scientific Research (Grant Nos.17H06136, 18K04715, and 21H01033), and Core-to-Core Program (No. JPJSCCA20170002) from the Japan Society for the Promotion of Science (JSPS) and by a JST-Mirai Program (Grant No. JPMJMI18A3).Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr2RuO4 can be tuned through a single Van Hove point, resulting in strong enhancement of both Tc and Hc2. Out-of-plane (c axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, by pushing it towards two Van Hove points simultaneously. Here, we achieve a record uniaxial stress of 3.2 GPa along the c axis of Sr2RuO4. Hc2 increases, as expected for increasing density of states, but unexpectedly Tc falls. As a first attempt to explain this result, we present three-dimensional calculations in the weak interaction limit. We find that within the weak-coupling framework there is no single order parameter that can account for the contrasting effects of in-plane versus c-axis uniaxial stress, which makes this new result a strong constraint on theories of the superconductivity of Sr2RuO4.Publisher PDFPeer reviewe