Quasiparticle Interference of Spin-Triplet Superconductors: Application to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>UTe</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math>

Quasiparticle interference (QPI) obtained from scanning tunneling microscopy (STM) is a powerful method to help extract the pairing symmetry of unconventional superconductors. We examine the general properties of QPI on surfaces of spin-triplet superconductors. It is shown how the multicomponent nature of the spin-triplet $\stackrel{\ensuremath{\rightarrow}}{d}$-vector and the general existence of topological surface states in triplet condensates both offer important differences from QPI on spin-singlet superconductors. We then turn to a microscopic model relevant for the spin-triplet candidate ${\mathrm{UTe}}_{2}$ and compare the computed QPI with recent STM measurements. We conclude that the two candidate pairing instabilities ${B}_{2u}$ and ${B}_{3u}$ exhibit distinct features in the QPI intensity which allows for distinguishing them using the experimental data. Characteristic features of the emergent topological surface states protected by chiral symmetry in general, and by mirror symmetries in the case of ${\mathrm{UTe}}_{2}$, provide further unique signatures to help pinpoint the pairing symmetry channel of this material.