Momentum-resolved superconducting energy gaps of Sr <sub>2</sub> RuO <sub>4</sub> from quasiparticle interference imaging
Rahul Sharma, Stephen Edkins, Zhenyu Wang, Andrey Kostin, Chanchal Sow, Y. Maeno, A. P. Mackenzie, J. C. Davis, Vidya Madhavan
Abstract
Sr 2 RuO 4 has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space ( k -space) structure of the superconducting energy gap <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="bold">Δ</mml:mi> <mml:mi mathvariant="bold-italic">i</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi mathvariant="bold-italic">k</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="bold">Δ</mml:mi> <mml:mi mathvariant="bold-italic">i</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi mathvariant="bold-italic">k</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> of Sr 2 RuO 4 . Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="bold">Δ</mml:mi> <mml:mi mathvariant="bold-italic">i</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi mathvariant="bold-italic">k</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="bold">q</mml:mi> <mml:mi mathvariant="bold-italic">j</mml:mi> </mml:msub> <mml:mo>:</mml:mo> <mml:mi mathvariant="bold-italic">j</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> consistent with eight gap nodes/minima that are all closely aligned to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al. , Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al. , Nature 574, 72–75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al. , Phys. Rev B , 100, 094530 (2019)], and theory [A. T. Rømer et al. , Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr 2 RuO 4 appears most consistent with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="bold">Δ</mml:mi> <mml:mi mathvariant="bold-italic">i</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi mathvariant="bold-italic">k</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> having <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="bold-italic">d</mml:mi> <mml:mrow> <mml:msup> <mml:mi mathvariant="bold-italic">x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mi mathvariant="bold-italic">y</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:msub> <mml:mi mathvariant="bold-italic">B</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi mathvariant="bold-italic">g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> symmetry.