Following an earlier proposal that the observed temperature dependence of the normal-state c-axis resistivity of oxide superconductors can be understood as arising from the inhibition of electron transport along the c axis due to in-plane incoherent inelastic scatterings suffered by the tagged electron, we consider a specific form for the interaction Hamiltonian. In this, the tagged electron is coupled to bosonic baths at adjacent planes (the baths at any two planes being uncorrelated) and is coupled also to the intraplane momentum-flip degree of freedom via the bath degrees of freedom. Thus our model Hamiltonian incorporates the earlier proposed picture that each in-plane inelastic scattering event is like a measurement of which plane the electron is in, and this, as in the quantum Zeno effect, leads to the suppression of interplane tunneling. In the present scenario it is the baths which bring about a coupling between the intraplane and interplane degrees of freedom. For simplicity we confine ourselves to dynamics in two adjacent planes and allow for two states only, as far as momentum flips due to scattering are concerned. In the case when the intraplane dynamics is absent, our model reduces effectively to the usual spin-boson model. We solve for the reduced tunneling dynamics of the electron using a non-Markovian master equation approach. Our numerical results on the survival probability of the electron in the initial plane show that the intraplane momentum flips lead to further inhibition of the interplane tunneling over and above the inhibition effected by pure spin-boson dynamics.
In recent years the notion of intrinsic decoherence and dephasing of a particle interacting with its environment is being investigated intensively. This has an important bearing on a plausible causal connection between incoherent c-axis resistivity and high-temperature superconductivity. In our work we study the tunnel supression and incoherent motion of a particle tunneling between two sites. The bosonic excitations of the environment are coupled to only one site inducing on-site spin flips. We show that this on-site spin flip scattering makes the tunnel motion incoherent. In the high-temperature limit incoherent rate or hopping rate has been calculated. We also briefly discuss the renormalization of the effective tunneling by environmental coupling at zero temperature following Wegner's renormalization group procedure.
We study the Hubbard model on a bilayer with repulsive on-site interactions U in which fermions undergo both intraplane (t) and interplane (
tz) hopping. This situation is what one would expect in high-temperature superconductors such as
YBa2Cu3${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$, with two adjacent
CuO2 planes. Magnetic and pairing properties of the system are investigated through quantum Monte Carlo simulations for both half- and quarter-filled bands. We find that in all cases interplanar pairing with
dx2-
z2 symmetry is dominant over planar pairing with
dx2-
y2 symmetry, and that for a large enough
tz pair formation is possible through antiferromagnetic correlations. However, another mechanism is needed to make these pairs condense into a superconducting state at lower temperatures. We identify the temperature for pair formation with the spin-gap crossover temperature.
Quantum Zeno Effect (QZE) is the suppression of the inter-subspace transition by a relatively fast intra-subspace decoherence. Earlier, we had proposed a QZE-based mechanism for the temperature-dependent normal-state c-axis resistivity of the layered high-T
c cuprate superconductors in which the single-particle inter-layer tunneling is blocked by the strong intra-layer decoherence (entanglement). We now argue that while the single-particle inter-layer tunneling is thus blocked, the tunneling of the bosonic BCS-like pairs must remain unblocked inasmuch as a BCS pairing condensate is an eigenstate of the pair annihilation operator. This pair tunneling stabilizes
The field of twistronics, recently extended to twisted bilayer cuprate systems, has generated considerable interest due to the prediction of
d+id′ states close to a
45∘ twist, as suggested by multiple experimental probes. Theoretical studies of these systems using a variety of models and many-body theoretical techniques have revealed multiple competing order parameters. The large variability in experimental results and theoretical predictions demands an accurate microscopic model for these systems, in particular a more realistic description of the interlayer tunneling. In this study, we fit the in-plane hopping and compute the interlayer tunneling amplitudes by calculating the orbital overlap between
dx2−y2 wave functions at each site of the twisted square-lattice model. We observe sign-changing tunneling amplitudes, a strong twist-angle dependence of the direct tunneling term, and long-range tunneling amplitudes that often dominate over direct tunneling. We investigate the band structure, Fermi surfaces, and spectral functions in comparison with those obtained from the phenomenological model and find a substantial redistribution of spectral weight that modifies the competition between different superconducting ground states. We determine the phase diagram as a function of twist angle, filling, and direct tunneling strength, which is controlled by the
c-axis distance between the monolayers, and observe a reduction in the region of time-reversal-symmetry-breaking (TRSB)
d+id′ states compared with the phenomenological model. Finally, we investigate the Josephson critical current across the phase diagram and find strongly suppressed critical currents close to a
45∘ twist, consistent with experimental observations.
Resonant tunneling of electrons through a dissipative barrier is studied within a generalized spin–boson model. The model accounts for a nonlinear inelastic coupling between the electron and harmonic (bath) nuclear modes inside the barrier. In particular, we study the case in which the nuclear frequencies are similar to the decay rate of the electronic resonance states, as may appear in electron transport through narrow molecular barriers. Two cases are considered. In the case of a single responsive mode numerically exact wave-packet dynamics shows that the inelastic coupling increases the time delay of the tunneling electron in the barrier and the decay process out of the barrier is characterized by nonexponential steps. In the case of a multimode (Ohmic) bath an approximate treatment of the dynamics, based on temperature dependent nonlinear Langevin–Schrödinger equations, implies that the trapped electron wavepacket is fully solvated in the barrier due to irreversible dissipation at low temperatures. An interpretation of the solvation process in terms of the mean-field approximation is given and discussed.
We consider a model consisting of a finite number of quantum dots each of which confines a spinless electron. We zoom in on a single quantum dot containing an electron of interest treating it as being strongly coupled to the surrounding finite bath of electrons. The fermionic bath is embedded in a bosonic Markovian bath. The master equation for the fermion of interest interacting with the fermionic bath is derived. Based on the master equation for this system, the reduced dynamics and thermalization of the spinless electron is studied. We start with a description of the Hamiltonian of the entire system which we call total Hamiltonian. Because the electron of interest is strongly coupled to the surrounding fermionic bath, we treat the Hamiltonian consisting of the electron of interest, the fermionic bath and the interaction between them as the system Hamiltonian. Then using techniques of linear algebra, we diagolize the system Hamiltonian making it appear in what we are calling quasi-fermionic picture. After this, we take the diagonalized system Hamiltonian back to the total Hamiltonian. We then use this total Hamiltonian to switch to the interaction picture. Since the general expression of the Markovian quantum master equation is in terms of the interaction Hamiltonian, we now substitute our interaction Hamiltonian into it and begin from there to derive the quantum master equation of our system. In the next step, we solve the derived quantum master equation casting the solution in Kraus representation. Using the explicit form of the Kraus operators and initial conditions, the density matrix of the reduced system is obtained in the quasifermionic picture. We then transform to the original fermionic picture and trace out the fermionic bath coming out with the density matrix of the electron of interest. We then check the normalization of the density matrix of the electron of interest by calculating the trace and then use it to calculate the mean number of fermions. The mean number of fermions is then plotted against time for different coupling strengths and varying numbers of fermions in the fermionic bath to visually check the dynamics and thermalization of the fermion of interest.