The outstanding structural, electrical and optical changes at the insulator-metal-transition (IMT) of VO₂, just above room temperature (T_IMT=340 K) turned this material into a candidate for many potential applications.  Although most investigations focus on thin films, the less robust single crystals exhibit unique features that deserve attention. Under an applied current at ambient temperature, the resistance drops due to Joule heating, the voltage reaches a maximum and a current controlled negative differential resistivity (CC-NDR) regime sets on. The mixed M-I phase appears within the NDR regime. The stability of I(V) of a sample in this regime is governed by the load resistance (R_L) in series with the sample. For small enough R_L the sample switches from the last steady state with maximal Joule heating power (P_max) to a state with minimal Joule heating power (P_min) [1].  In thin films this is achieved by the formation of hot filaments (metallic in the case of VO₂), in the presence of thermal gradients. A tetragonal metallic filament cannot be accommodated along a monoclinic insulating bar-shaped single crystal oriented along the tetragonal c-axis, due to huge stress.  Consequently, the mixed state of single crystals consists of dynamic or static domain patterns with metal-insulator boundaries that cross the width of the crystal at favorable inclinations [2]; these imply isothermal conditions (T=T_IMT).  Sliding domains are typical of voltage-controlled NDR and not of CC-NDR [1].  The recently discovered large contrast between the emissivity in the infrared of the insulator and that of the metal at T_IMT (e_I/e_M>2) [3] and the anomalously low thermal conductivity of metallic VO₂ [4] seem to corroborate domain formation in single crystals of VO_2.  In the simplest case narrow insulating domains slide within metallic background in the sense of the electric current, their drift being driven by exchange of latent heat with Peltier heat at the M-I boundaries [2]. In our investigation we traced I-V characteristics of high quality mm-size VO₂ single crystals for various load resistances and recorded on video the domain patterns of the samples using the camera of an I-phone 5 attached to the ocular of the microscope. Here we report on P(V) and P(I) derived from I-V characteristics of several VO₂ single crystals and show images of domain patterns snipped from the corresponding videos. The results [5] show that: 1. The ratio P_max / P_min may exceed by far e_I/e_M measured in thin films and 2. Beyond the minimum, P increases with increasing current due to sliding domains but this increase as well as sliding are suppressed by damage caused by repeated switching.

[1] B. K. Ridley,  Proc. Phys. Soc.  82, 954 (1963).

[2] B. Fisher, J. Phys. C:Solid State 8, 2072 (1975), ibid 9, 1201 (1976), B. Fisher and L. Patlagan, Materials, 10, 554 (2017).

[3] M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, Phys. Rev. X 3, 041004 (2013).

[4] S. Lee, K. Hippalgaonkar,  F. Yang, J. Hong, C. Ko,  J. Suh, K. Liu,  K. Wang,  J.J. Urban, X. Zhang, C. Dames, S. A. Hartnoll, O. Delaire, J. Wu, Science 355, 371 (2017).

[5] B. Fisher and L. Patlagan, submitted to Phys. Rev. Applied.