AUTHOR=Ngampruetikorn Vudtiwat , Sauls J. A. 

TITLE=Anomalous Hall effects in chiral superconductors

JOURNAL=Frontiers in Physics

VOLUME=12

YEAR=2024

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1384275

DOI=10.3389/fphy.2024.1384275

ISSN=2296-424X

ABSTRACT=<p>We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E<sub>1</sub> and E<sub>2</sub> representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and—as we highlight—the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi></mml:mrow></mml:math></inline-formula>, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mo>±</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></inline-formula>, but vanishes for <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>|</mml:mo><mml:mi>ν</mml:mi><mml:mo>|</mml:mo><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi><mml:mo>≥</mml:mo><mml:mi>ℏ</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, the thermal Hall conductivity is finite for chiral order with <inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo stretchy="false">|</mml:mo><mml:mi>ν</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math></inline-formula>, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.</p>