keeping dynamically allocated memory and vectors post scope in c++11

I am learning c++ and came across an issue that I'm not able to resolve. I have read dozens of articles but still not able to figure out the solution. Here are the details: I have created a simple class with two members

uint8_t* atlas;
std::vector<int> vect;

In the constructor of class, I'm allocating memory and initializing the vector like this:

uint8_t* atlas = new uint8_t[512 * 512]();
std::vector<int> vect{ 10, 20, 30 };

Later in another function when accessing these two variables:

std::cout << vect.size() << std::endl;
if(atlas == nullptr) { 
    std::cout << "null atlas" << std::endl;
    return;
} 

The size of the vector is 0 and the atlas is nullptr. After reading several articles about this issue I came across several things such as heap, stack, scope, and smart pointers. The problem is that locally assigned variables are lost as soon as the function or scope ends. My question is that atlas and vect are the members of the class, not locally assigned variables then why the data is getting lost? As per the documentation, the dynamically allocated memory remains intact, it's the pointer that is lost tracking of it.

Several articles suggested that this problem can be solved using smart pointers but I'm not able to figure out, how it can be done. What I need is to keep the dynamically allocated data and vector safe so that I can access them in another function.