arXiv subjects

Bhaskar Mukherjee

Publications and source records attributed to Bhaskar Mukherjee.

23 records · Page 2Linked to original sources

arXiv2018

Floquet topological transition by unpolarized light

We study Floquet topological transition in irradiated graphene when the polarization of incident light changes randomly with time. We numerically confirm that the noise averaged time evolution operator approaches a steady value in the limit of exact Trotter decomposition of the whole period where incident light has different polarization at each interval of the decomposition. This steady limit is found to coincide with time-evolution operator calculated from the noise-averaged Hamiltonian. We observe that at the six corners (Dirac($K$) point) of the hexagonal Brillouin zone of graphene random Gaussian noise strongly modifies the phaseband structure induced by circularly polarized light whereas in zone-center ($Γ$ point) even a strong noise isn't able to do the same. This can be understood by analyzing the deterministic noise averaged Hamiltonian which has a different Fourier structure as well as lesser no of symmetries compared to the noise-free one. In 1D systems noise is found to renormalize the drive amplitude only.

cond-mat.other↗

arXiv2017

Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain

We study the Floquet phase diagram of two-dimensional Dirac materials such as graphene and the one-dimensional (1D) spin-1/2 $XY$ model in a transverse field in the presence of periodic time-varying terms in their Hamiltonians in the low drive frequency ($ω$) regime where standard $1/ω$ perturbative expansions fail. For graphene, such periodic time dependent terms are generated via the application of external radiation of amplitude $A_0$ and time period $T = 2π/ω$, while for the 1D $XY$ model, they result from a two-rate drive protocol with time-dependent magnetic field and nearest-neighbor couplings between the spins. Using the adiabatic-impulse method, we provide several semi-analytic criteria for the occurrence of changes in the topology of the phase bands of such systems. For irradiated graphene, we point out the role of the symmetries of $H(t)$ and $U$ behind such topology changes. Our analysis reveals that at low frequencies, phase band topology changes may also happen at $t= T/3, 2T/3$ (apart from $t=T$). We chart out the phase diagrams at $t=T/3, 2T/3,\, {\rm and }\, T$ as a function of $A_0$ and $T$ using exact numerics, and compare them with the prediction of the adiabatic-impulse method. We show that several characteristics of these phase diagrams can be analytically understood from results obtained using the adiabatic-impulse method and point out the crucial contribution of the high-symmetry points in the graphene Brillouin zone to these diagrams. Finally we study the 1D $XY$ model with a two-rate driving protocol using the adiabatic-impulse method and exact numerics revealing a phase band crossing at $t=T/2$ and $k=π/2$. We also study the anomalous end modes generated by such a drive. We suggest experiments to test our theory.

cond-mat.mes-hall↗

arXiv2017

Bosons with incommensurate potential and spin-orbit coupling

We chart out the phase diagram of ultracold `spin-half' bosons in a one-dimensional optical lattice in the presence of Aubry-André (AA) potential and with spin-orbit (SO) and Raman couplings investigating the transition from superfluid (SF) to localized phases and the existence of density wave phase for nearest-neighbor interaction (NNI). We show that the presence of SO coupling and AA potential leads to a novel spin-split momentum distribution of the bosons in the localized phase near the boundary with the SF phase, which can act as a signature of such a transition. We also obtain the level statistics of the bosons in the superfluid phase with finite NNI and demonstrate its change from Gaussian Unitary Ensemble (GUE) to Gaussian Orthogonal Ensemble (GOE) as a function of the Raman coupling. We discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2016

Signatures and conditions for phase band crossings in periodically driven integrable systems

We present generic conditions for phase band crossings for a class of periodically driven integrable systems represented by free fermionic models subjected to arbitrary periodic drive protocols characterized by a frequency $ω_D$. These models provide a representation for the Ising and $XY$ models in $d=1$, the Kitaev model in $d=2$, several kinds of superconductors, and Dirac fermions in graphene and atop topological insulator surfaces. Our results demonstrate that the presence of a critical point/region in the system Hamiltonian (which is traversed at a finite rate during the dynamics) may change the conditions for phase band crossings that occur at the critical modes. We also show that for $d>1$, phase band crossings leave their imprint on the equal-time off-diagonal fermionic correlation functions of these models; the Fourier transforms of such correlation functions, $F_{\vec k_0}( ω_0)$, have maxima and minima at specific frequencies which can be directly related to $ω_D$ and the time at which the phase bands cross at $\vec k = \vec k_0$. We discuss the significance of our results in the contexts of generic Hamiltonians with $N>2$ phase bands and the underlying symmetry of the driven Hamiltonian.

cond-mat.str-el↗

arXiv2016

Tuning towards dynamic freezing using a two-rate protocol

We study periodically driven closed quantum systems where two parameters of the system Hamiltonian are driven with frequencies $ω_1$ and $ω_2=r ω_1$. We show that such drives may be used to tune towards dynamics induced freezing where the wavefunction of the state of the system after a drive cycle at time $T= 2π/ω_1$ has almost perfect overlap with the initial state. We locate regions in the $(ω_1 ,r)$ plane where the freezing is near exact for a class of integrable and a specific non-integrable model. The integrable models that we study encompass Ising and XY models in $d=1$, Kitaev model in $d=2$, and Dirac fermions in graphene and atop a topological insulator surface whereas the non-integrable model studied involves the experimentally realized one-dimensional (1D) tilted Bose-Hubbard model in an optical lattice. In addition, we compute the relevant correlation functions of such driven systems and describe their characteristics in the region of $(ω_1,r)$ plane where the freezing is near-exact. We supplement our numerical analysis with semi-analytic results for integrable driven systems within adiabatic-impulse approximation and discuss experiments which may test our theory.

cond-mat.str-el↗