Well let me share plot3d code with you which works perfectly, now in the same code lets put another paramter "\Xi" which I shared earlier and change it accordingly and use the command ListDesnityPlot3D it does not work....
Clear["Global`*"]
l = 0; \[Mu] = 1;
\[Eta] = 1;
\[Epsilon] = 0.1 ;
d1 = 1/(4 \[Mu]^2 (1 - 2 \[Tau])) + (1 - 2 \[Tau])/4; d2 =
1/(4 \[Mu]^2 (1 - 2 \[Tau])) - (1 - 2 \[Tau])/4;
c1 = 1/(4 \[Eta]^2 (1 - 2 \[Epsilon])) + (1 - 2 \[Epsilon])/4; c2 =
1/(4 \[Eta]^2 (1 - 2 \[Epsilon])) - (1 - 2 \[Epsilon])/4;
ra = 22; \[Phi] = 0; g = 43; \[Gamma] = 20; \[Lambda] = .3*\[Gamma];
\[Kappa]0 = 20; \[Theta] = 0; tf = 2;
\[CapitalOmega] = 800;
G = 101.7; \[CapitalDelta]1 = 4*\[Lambda] ;
\[CapitalDelta]2 = -4*\[Lambda]; \[Alpha]11 = 0; \[Alpha]22 = 0; \
\[Alpha]11b = 0; \[Alpha]22b = 0;
\[Tau]min = 0.2; wmax = 0.05; wstep = 0.45;
\[Alpha]12 = 2*I*G*\[Gamma]/\[CapitalOmega];
\[Alpha]21 = 2*I*G*\[Gamma]/\[CapitalOmega];
\[Alpha]12b = -2*I*G*\[Gamma]/\[CapitalOmega];
\[Alpha]21b = -2*I*G*\[Gamma]/\[CapitalOmega];
ss1 = (\[Kappa]0*\[Lambda]*\[CapitalDelta]1)/(\[Lambda]^2 + \
\[CapitalDelta]1^2) (1 -
E^(-\[Lambda]*
t) (Cos[\[CapitalDelta]1*t] + \[Lambda]/\[CapitalDelta]1*
Sin[\[CapitalDelta]1*t])) - (\[Kappa]0^2*\[Lambda]^2*
E^(-\[Lambda]*t))/(
2 (\[Lambda]^2 + \[CapitalDelta]1^2)^3) ((1 - (
3*\[Lambda]^2)/\[CapitalDelta]1^2) (E^(\[Lambda]*t) -
E^(-\[Lambda]*t)*Cos[2*\[CapitalDelta]1*t]) -
2 (1 - \[Lambda]^4/\[CapitalDelta]1^4) \[CapitalDelta]1*t*
Sin[\[CapitalDelta]1*t] +
4 (1 + \[Lambda]^2/\[CapitalDelta]1^2)*\[Lambda]*t*
Cos[\[CapitalDelta]1*
t] - \[Lambda]/\[CapitalDelta]1 (3 - \[Lambda]^2/\
\[CapitalDelta]1^2)*E^(-\[Lambda]*t)*Sin[2*\[CapitalDelta]1*t]);
ss2 = (\[Kappa]0*\[Lambda]*\[CapitalDelta]2)/(\[Lambda]^2 + \
\[CapitalDelta]2^2) (1 -
E^(-\[Lambda]*
t) (Cos[\[CapitalDelta]2*t] + \[Lambda]/\[CapitalDelta]2*
Sin[\[CapitalDelta]2*t])) - (\[Kappa]0^2*\[Lambda]^2*
E^(-\[Lambda]*t))/(
2 (\[Lambda]^2 + \[CapitalDelta]2^2)^3) ((1 - (
3*\[Lambda]^2)/\[CapitalDelta]2^2) (E^(\[Lambda]*t) -
E^(-\[Lambda]*t)*Cos[2*\[CapitalDelta]2*t]) -
2 (1 - \[Lambda]^4/\[CapitalDelta]2^4) \[CapitalDelta]2*t*
Sin[\[CapitalDelta]2*t] +
4 (1 + \[Lambda]^2/\[CapitalDelta]2^2)*\[Lambda]*t*
Cos[\[CapitalDelta]2*
t] - \[Lambda]/\[CapitalDelta]2 (3 - \[Lambda]^2/\
\[CapitalDelta]2^2)*E^(-\[Lambda]*t)*Sin[2*\[CapitalDelta]2*t]);
\[Kappa]\[Kappa]1 = (\[Kappa]0*\[Lambda]^2)/(\[Lambda]^2 + \
\[CapitalDelta]1^2) (1 -
E^(-\[Lambda]*
t) (Cos[\[CapitalDelta]1*t] - \[CapitalDelta]1/\[Lambda]*
Sin[\[CapitalDelta]1*t])) + (\[Kappa]0^2*\[Lambda]^5*
E^(-\[Lambda]*t))/(
2 (\[Lambda]^2 + \[CapitalDelta]1^2)^3) ((1 - (
3*\[CapitalDelta]1^2)/\[Lambda]^2) (E^(\[Lambda]*t) -
E^(-\[Lambda]*t)*Cos[2*\[CapitalDelta]1*t]) -
2 (1 - \[CapitalDelta]1^4/\[Lambda]^4) \[Lambda]*t*
Cos[\[CapitalDelta]1*t] +
4 (1 + \[Lambda]^2/\[CapitalDelta]1^2)*\[CapitalDelta]1*t*
Sin[\[CapitalDelta]1*
t] + \[CapitalDelta]1/\[Lambda] (3 - \[CapitalDelta]1^2/\
\[Lambda]^2)*E^(-\[Lambda]*t)*Sin[2*\[CapitalDelta]1*t]);
\[Kappa]\[Kappa]2 = (\[Kappa]0*\[Lambda]^2)/(\[Lambda]^2 + \
\[CapitalDelta]2^2) (1 -
E^(-\[Lambda]*
t) (Cos[\[CapitalDelta]2*t] - \[CapitalDelta]2/\[Lambda]*
Sin[\[CapitalDelta]2*t])) + (\[Kappa]0^2*\[Lambda]^5*
E^(-\[Lambda]*t))/(
2 (\[Lambda]^2 + \[CapitalDelta]2^2)^3) ((1 - (
3*\[CapitalDelta]2^2)/\[Lambda]^2) (E^(\[Lambda]*t) -
E^(-\[Lambda]*t)*Cos[2*\[CapitalDelta]2*t]) -
2 (1 - \[CapitalDelta]2^4/\[Lambda]^4) \[Lambda]*t*
Cos[\[CapitalDelta]2*t] +
4 (1 + \[Lambda]^2/\[CapitalDelta]2^2)*\[CapitalDelta]2*t*
Sin[\[CapitalDelta]2*
t] + \[CapitalDelta]2/\[Lambda] (3 - \[CapitalDelta]2^2/\
\[Lambda]^2)*E^(-\[Lambda]*t)*Sin[2*\[CapitalDelta]2*t]);
s1 = Simplify[ss1]; s2 = Simplify[ss2]; \[Kappa]1 =
Simplify[\[Kappa]\[Kappa]1]; \[Kappa]2 = Simplify[\[Kappa]\[Kappa]2];
solA = ParametricNDSolve[{n1'[
t] == (1/2) (\[Alpha]11 + \[Alpha]11b - 4 \[Kappa]1)*
n1[t] + (1/2) E^(I \[Phi]) \[Alpha]12b*
ms[t] + (1/2) E^(-I \[Phi]) \[Alpha]12*mss[t] +
1/2*(\[Alpha]11 + \[Alpha]11b),
n2'[t] == (1/2) (\[Alpha]22 + \[Alpha]22b - (4 \[Kappa]2)) n2[
t] + (1/2) E^(I \[Phi]) \[Alpha]21*
ms[t] + (1/2) E^(-I \[Phi]) \[Alpha]21b*mss[t] +
1/2*(\[Alpha]22 + \[Alpha]22b),
ms'[t] == (1/2) E^(-I \[Phi]) \[Alpha]21b*
n1[t] + (1/2) E^(-I \[Phi]) \[Alpha]12*
n2[t] + (1/
2) (\[Alpha]11 + \[Alpha]22b - (2 (\[Kappa]1 + \[Kappa]2)) -
I (s1 - s2))*
ms[t] + (1/2) (\[Alpha]12 + \[Alpha]21b) E^(-I \[Phi]),
mss'[t] == (1/2) E^(I \[Phi]) \[Alpha]21*n1[t] + (1/2) E^(
I \[Phi]) \[Alpha]12b*
n2[t] + (1/
2) (\[Alpha]11b + \[Alpha]22 - (2 (\[Kappa]1 + \[Kappa]2)) +
I (s1 - s2))*mss[t] + (1/2) (\[Alpha]12b + \[Alpha]21) E^(
I \[Phi]), n1[0] == d1 - 0.5, n2[0] == c1 - 0.5 , ms[0] == 0,
mss[0] == 0}, {n1, n2, ms, mss}, {t, 0, tf}, {\[Tau]}];
solB = ParametricNDSolve[{m1'[
t] == (\[Alpha]11 - I s1 - 2 \[Kappa]1)*m1[t] +
E^(-I \[Phi]) \[Alpha]12*mc[t],
m2'[t] == (\[Alpha]22 - I s2 - 2 \[Kappa]2) m2[t] +
E^(I \[Phi]) \[Alpha]21*mc[t],
mc'[t] ==
1/2 E^(I \[Phi]) \[Alpha]21*m1[t] +
1/2 E^(-I \[Phi]) \[Alpha]12*m2[t] +
1/2 (\[Alpha]11 + \[Alpha]22 - 2 (\[Kappa]1 + \[Kappa]2) -
I (s1 - s2))*mc[t], m1[0] == -d2 , m2[0] == -c2 ,
mc[0] == 0}, {m1, m2, mc}, {t, 0, tf}, {\[Tau]}];
n1sol[\[Tau]_, t_] := n1[\[Tau]][t] /. solA[[1]];
n2sol[\[Tau]_, t_] := n2[\[Tau]][t] /. solA[[2]];
mssol[\[Tau]_, t_] := ms[\[Tau]][t] /. solA[[3]];
msssol[\[Tau]_, t_] := mss[\[Tau]][t] /. solA[[4]];
m1sol[\[Tau]_, t_] := m1[\[Tau]][t] /. solB[[1]];
m2sol[\[Tau]_, t_] := m2[\[Tau]][t] /. solB[[2]];
mcsol[\[Tau]_, t_] := mc[\[Tau]][t] /. solB[[3]];
tr4 = ( {
{1, 1, 0, 0},
{-I, I, 0, 0},
{0, 0, 1, 1},
{0, 0, I, -I}
} );(*Vtq=Chop[(Vt+Vt\[Transpose])/2];*)
Vt = ( {
{n1sol[\[Tau], t] + 0.5, -m1sol[\[Tau], t],
mssol[\[Tau], t], -mcsol[\[Tau], t]},
{-Conjugate[m1sol[\[Tau], t]],
n1sol[\[Tau], t] + 0.5, -Conjugate[mcsol[\[Tau], t]],
Conjugate[mssol[\[Tau], t]]},
{Conjugate[mssol[\[Tau], t]], -mcsol[\[Tau], t],
n2sol[\[Tau], t] + 0.5, -m2sol[\[Tau], t]},
{-Conjugate[mcsol[\[Tau], t]],
mssol[\[Tau], t], -Conjugate[m2sol[\[Tau], t]],
n2sol[\[Tau], t] + 0.5}
} );
Vtq = Chop[(Vt + Vt\[Transpose])/2];
Aq = Evaluate[Vtq[[1 ;; 2, 1 ;; 2]]];
Bq = Vtq[[3 ;; 4, 3 ;; 4]];
Cq = Vtq[[1 ;; 2, 3 ;; 4]];
sigma = Det[Aq] + Det[Bq] - 2 Det[Cq];
\[Xi] = Evaluate[
Sqrt[(sigma - Sqrt[sigma^2 - 4*Det[Vtq]])/
2] /. {\[Tau] -> \[Tau]\[Tau], t -> tt}];
Eme[\[Tau]\[Tau]_, tt_] = Max[0, -Log2[2 \[Xi]]];
Plot3D[{Eme[\[Tau], t]}, {t, 0, tf}, {\[Tau], 0.45, 0},
PlotRange -> Full, AxesLabel -> {Gt, \[Tau], EN},
AxesStyle -> Directive[Black, 17],
ColorFunction -> ColorData["Aquamarine"], Background -> White,
AxesStyle -> Black, TicksStyle -> Black, Boxed -> False,
AxesEdge -> {{0, 0}, {1, 0}, {0, 0}}, ViewPoint -> {3, -2, 1.5} ,
Mesh -> None, LabelStyle -> {FontSize -> 18, Black, Bold},
PlotLegends -> Automatic, PlotPoints -> {200, 50},
TicksStyle -> Directive["Label", 30], Boxed -> True,
Ticks -> {{{0.5, 50}, {1, 100}, {1.5, 150}, {2, 200}}, {0.1, 0.2,
0.3, 0.4, 0.5 }, Automatic},
FaceGrids -> {{-1, 0, 0}, {0, 0, -1}, {0, 1, 0}},
FaceGridsStyle -> Directive[Dashed, Black]]