Resistive asymmetry due to spatial confinement in first-order phase transitions

We report an asymmetry in the $R$ vs $T$ characteristics across the first-order metal-insulator transition (MIT) of ${\mathrm{V}}₂{\mathrm{O}}₃$ nanowires. The resistance changes in a few, large jumps during cooling through the MIT, while it does it in a smoother way during warming. The asymmetry is greatly enhanced as the width of the nanowire approaches a characteristic domain size. Our results, together with previous reports on ${\mathrm{VO}}₂$ [W. Fan et al., Phys. Rev. B 83, 235102 (2011)] and FeRh [V. Uhl\'{\i}\ifmmode \check{r}\else \v{r}\fi{} et al., Nat. Commun. 7, 13113 (2016)] imply that asymmetry is a generic feature of first-order phase transitions in one-dimensional systems. We show that this behavior is a simple, elegant consequence of the combined effects of the transition hysteresis and the temperature dependence of the insulating gap in this case (and generically, the order parameter relevant for the physical observable). We conclude that our proposed asymmetry mechanism is universally applicable to many electronic first-order phase transitions.