Hi davout,
By default the DateTimePicker in the dropdown(pop-up) will highlight the todays date in the dropdown even if the nullable property is set to true.
However there is a way to achieve this and you can check the solution in the code snippet below :
//In your HTML file:

    <smart-date-time-picker
                          calendar-button
                          enable-mouse-wheel-action
                          spin-buttons
                          spin-buttons-position="left"
                          nullable
                          value = 'null'
                          hide-tooltip-arrow
                        >
                        </smart-date-time-picker> 

Note that I have set the nullable property to true and set the DAteTimePicker value to null
And in your CSS:
/* Necessery styles for the initial selected date */

.smart-calendar .smart-calendar-week .smart-calendar-cell[today]{
    background-color: white;
    color: black;
    border-color: transparent;
}

Please, do not hesitate to contact us if you have any additional questions.
Best regards,
Yavor Dashev
Smart UI Team
https://www.htmlelements.com/