Publications

preprints:

o  Takashi Oka
Photo-control of collective excitations in a Mott insulator --- Landau-Dykhne method applied to an integrable model
[arXiv:1105.3145]
A theoretical scheme to calculate excitations in strongly correlated systems beyond the Kubo formula regime is proposed. This is done by combining the Landau-Dykhne method with the Bethe ansatz solution and is applied to DC, AC and pulse electric fields. We show that the distribution of holon-antiholon pairs in a one-dimensional Mott insulator created by a strong laser can be controlled by changing the laser's photon energy. Relevance to controlling photo-induced phase transitions in strongly correlated systems in pump-probe experiments is discussed. A comparison with time dependent density matrix renormalization group is also done.

o  Takuya Kitagawa, Takashi Oka, Arne Brataas, Liang Fu, Eugene Demler
Photo-induced quantum Hall insulators without Landau levels
[arXiv1104.4636]
In recent years, there is a tremendous interest and effort to control novel materials such as graphene to have desirable electric and magnetic properties via chemical, mechanical, and electrical manipulations. A particularly appealing approach is a {\it dynamical} engineering of materials, which offers a fascinating possibility to switch on and off properties at will. Here we propose a mechanism to dynamically control quantum transport in a class of semi-metals, such as graphene and topological insulators, via the application of light. In contrast to a conventional effect of light where photons induce current carriers by exciting electrons, we consider off-resonant, circularly polarized light which induces an effective gap in semi-metals. We analyze the transport properties of the resulting photo-induced non-equilibrium systems and show that graphene and surfaces of topological insulators exhibit insulating behaviors. Remarkably, these systems also exhibit quantum Hall effects in the absence of a magnetic field with a near quantization of the Hall conductance, realizing so-called quantum Hall systems without Landau levels. Our work opens new avenues for the study of quantum Hall effects in semi-metals and dynamical control of topological transport properties.

o  Takashi Oka
Strong field physics in condensed matter
[arXiv:1102.2482]
There are deep similarities between non-linear QFT studied in high-energy and non-equilibrium physics in condensed matter. Ideas such as the Schwinger mechanism and the Volkov state are deeply related to non-linear transport and photovoltaic Hall effect in condensed matter. Here, we give a review on these relations.

o  Koji Hashimoto, Norihiro Iizuka, Takashi Oka
Rapid Thermalization by Baryon Injection in Gauge/Gravity Duality
[arXiv:1012.4463]
Using the AdS/CFT correspondence for strongly coupled gauge theories, we calculate thermalization of mesons caused by a time-dependent change of a baryon number chemical potential. On the gravity side, the thermalization corresponds to a horizon formation on the probe flavor brane in the AdS throat. Since heavy ion collisions are locally approximated by a sudden change of the baryon number chemical potential, we discuss implication of our results to RHIC and LHC experiments, to find a rough estimate of rather rapid thermalization time-scale t_{th} < 1 [fm/c]. We also discuss universality of our analysis against varying gauge theories.

o  Naoto Tsuji, Takashi Oka, Philipp Werner, Hideo Aoki,
Dynamical band flipping in fermionic lattice systems: an ac-field driven change of the interaction from repulsive to attractive
[arXiv:1008.2594]
We show theoretically that sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive. The nonadiabatically driven system is characterized by a negative temperature with a population inversion. We numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method. Based on this, we propose the possibility that an ac field can dynamically induce superconductivity if it is turned on in a suitable manner.

o  Takashi Oka, and Hideo Aoki,
Charge Confinement in Carbon-Nanotubes as a Realization of Extended Massive Schwinger Model
[arXiv:1007.5393]
 Carbon nanotube with electric fluxes confined in one dimension is studied with an effective massive Schwinger model with multi-species fermions labeled by the band and valley indices. A peculiar ($\propto |x|$) Coulomb interaction leads to charge confinement, which we characterize in terms of the exciton spectrum calculated via the 't Hooft-Berknoff equation with the light-front field theory. In electric fields, nonlinear transport with a power-law $J$-$E$-characteristics is predicted to emerge, which is related to Coleman's "half-asymptotic" state.

o  Takashi Oka, and Hideo Aoki,
All Optical Measurement Proposed for the Photovoltaic Hall Effect
[arXiv:1007.5399]
 We propose an all optical way to measure the recently proposed "photovoltaic Hall effect", i.e., a DC Hall effect induced by a circularly polarized light in the absence of static magnetic fields. For this, we have calculated the Faraday rotation angle induced by the photovoltaic Hall effect with the Kubo formula extended for photovoltaic optical response in the presence of strong AC electric fields treated with the Floquet formalism. We also point out the possibility of observing the effect in three-dimensional graphite, and more generally in multi-band systems such as materials described by the dp-model.

Books:

oT. Oka and H. Aoki,
Nonequilibrium Quantum Breakdown in a Strongly Correlated Electron System.  
[arXiv:0803.0422]
The nonlinear transport properties of the Mott insulator are discussed with focus on the many-body Landau-Zener mechanism. After reviewing basic concepts such as the non-adiabatic geometric phase and the Schwinger mechanism, we study the decay of the insulating groundstate in strong electric fields using the time-dependent density matrix renormalization group. A short comment on the proposed mapping to the quantum walk model is added before discussing the relevance of the theory to experimental results.
in `` Quantum and Semi-classical Percolation and Breakdown in Disordered Solids"
edited by A.K. Sen, K.K. Bardhan, B.K. Chakrabarti, (Lecture Note in Physics Vol. 762, Springer-Verlag), (2008).
to Amazon page.

papers:

o  Martin Eckstein, Takashi Oka, Philipp Werner,
Dielectric breakdown of Mott insulators in dynamical mean-field theory
[arXiv:1006.3516]
Phys. Rev. Lett. 105, 146404 (2010)
 Using nonequilibrium dynamical mean-field theory, we compute the time evolution of the current in a Mott insulator after a strong electric field is turned on. We observe the formation of a quasistationary state in which the current is almost time-independent although the system is constantly excited. At moderately strong fields this state is stable for quite long times. The stationary current exhibits a threshold behavior as a function of the field, in which the threshold increases with the Coulomb interaction and vanishes as the metal-insulator transition is approached.

oT. Oka and H. Aoki,
Nonequilibrium magnetic and superconducting phases in the two-dimensional Hubbard model coupled to electrodes
[arXiv:0905.3955]
Phys. Rev. B 82, 0645160-1-064516-5 (2010)
A theory is presented for nonequilibrium magnetic and superconducting phases in the two-dimensional Hubbard model coupled to electrodes, for which we extend the fluctuation exchange approximation to systems out of equilibrium with the Keldysh formalism. The effect of the nonequilibrium distribution of carriers is studied, and presented as a phase diagram against the band filling, temperature, and the bias voltage between the electrodes. The nonequilibrium distribution function in the presence of electron correlation is evoked to capture a general feature in the phase diagram.

oT. Oka and H. Aoki,
Dielectric Breakdown in a Mott Insulator: Many-body Schwinger-Landau-Zener Mechanism studied with a Generalized Bethe Ansatz.
Phys. Rev. B 81, 033103 (2010)
[arXiv:0903.2707]
The nonadiabatic quantum tunneling picture, which may be called the many-bodySchwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a metod due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density matrix renormalization group result is obtained.

o    S. Endo, T. Oka; H. Aoki
Realization of tight-binding photonic bands in metallophotonic waveguide networks with application to a flat band in kagome lattice
Phys. Rev. B 81, 113104-1-4 (2010)
[arXiv:0905.4826]
 We propose that we can realize "tight-binding photonic bands" in metallophotonic waveguide networks, where the photonic bound states localized around the crossings of a network form a tight-binding band. Model calculations show that the low-lying photon dispersions are indeed described accurately by the tight-binding model. The formation of bound states at the crossings is distinct from the conventional bound states at defects in photonic crystals, but comes from a photonic counterpart of the zero-point states in wave mechanics. To exemplify how we can exploit the tight-binding analogy for a novel way of "designing" photonic bands, we propose a concept of ``flat photonic bands" in the kagome network, and have shown that we have photonic flat bands with group velocities that can be as small as 1/1000 times the velocity of light in vacuum.

o  P. Werner, T. Oka, M. Eckstein, A. J. Millis,
Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model
Phys. Rev. B 81, 035108 (2010)
[arXiv:0911.0587 ]
 We present optimized implementations of the weak-coupling continuous-time Monte Carlo method defined for nonequilibrium problems on the Keldysh contour. We describe and compare two methods of preparing the system before beginning the real-time calculation: the "interaction quench" and the "voltage quench", which are found to be suitable for large and small voltage biasses, respectively. We also discuss technical optimizations which increase the efficiency of the real-time measurements. The methods allow the accurate simulation of transport through quantum dots over wider interaction ranges and longer times than have heretofore been possible. The current-voltage characteristics of the particle-hole symmetric Anderson impurity model is presented for interactions U up to 10 times the intrinsic level width Gamma. We compare the Monte Carlo results to fourth order perturbation theory, finding that perturbation theory begins to fail at U/Gamma>4. Within the parameter range studied we find no evidence for a splitting of the Kondo resonance due to the applied voltage. The interplay of voltage and temperature and the Coulomb blockade conductance regime are studied.

oNaoto Tsuji, T. Oka and H. Aoki,
Nonequilibrium steady state in photoexcited correlated electrons with dissipation.  
Phys. Rev. Lett. 103, 047403 (2009)
[arXiv:0903.2332]
We present a framework to determine nonequilibrium steady states in strongly correlated electron systems in the presence of dissipation. This is demonstrated for a correlated electron (Falicov-Kimball) model attached to a heat bath and irradiated by an intense pump light, for which an exact solution is obtained with the Floquet method combined with the nonequilibrium dynamical mean-field theory. On top of a Drude-like peak indicative of photo-metallization as observed in recent pump-probe experiments, new nonequilibrium phenomena are predicted to emerge, where the optical conductivity exhibits dip and kink structures around the frequency of the pump light, a midgap absorption arising from photoinduced Floquet subbands, and a negative attenuation (=gain) due to a population inversion.

oT. Oka and H. Aoki,
Photovoltaic Hall effect in graphene.  
Phys. Rev. B 79, 081406 (R) (2009), selected in Virtual Journal of Nanoscale Science & Technology
Erratum Phys. Rev. B 79, 169901 (2009)
[arXiv:0807.4767]
Response of electronic systems in intense lights (AC electric fields) to DC source-drain fields is formulated with the Floquet method. We have then applied the formalism to graphene, for which we show that a non-linear effect of a circularly polarized light can open a gap in the Dirac cone, which leads to a photo-induced dc Hall current. This is numerically confirmed for a graphene ribbon attached to electrodes with the Keldysh Green's function.

oP. Werner, T. Oka, A. J. Millis, 
Phys. Rev. B 79, 035320 (2009)
Diagrammatic Monte Carlo simulation of non-equilibrium systems. 
[arXiv:0810.2345]
We generalize the recently developed diagrammatic Monte Carlo techniques for quantum impurity models from an imaginary time to a Keldysh formalism suitable for real-time and nonequilibrium calculations. Both weak-coupling and strong-coupling based methods are introduced, analysed and applied to the study of transport and relaxation dynamics in interacting quantum dots.

oT. Oka and H. Aoki,
Photo-induced Tomonaga-Luttinger-like liquid in a Mott insulator.  
Phys. Rev. B 78, 241104 (R) (2008)
[arXiv:0808.1475]
Photo-induced metallic states in a Mott insulator are studied for the half-filled, one-dimensional Hubbard model with the time-dependent density matrix renormalization group. An irradiation of strong AC field is found to create a linear dispersion in the optical spectrum (current-current correlation) in the nonequilibrium steady state reminiscent of the Tomonaga-Luttinger liquid for the doped Mott insulator in equilibrium. The spin spectrum in nonequilibrium retains the des Cloizeaux-Pearson mode with the spin velocity differing from the charge velocity. The mechanism of the photocarrier-doping, along with the renormalization in the charge velocity, is analyzed in terms of an effective Dirac model.

oN. Tsuji, T. Oka and H. Aoki,
Correlated electron systems periodically driven out of equilibrium -- Floquet + DMFT formalism.  
Phys. Rev. B 78, 235124 (2008)
[arXiv:0808.0379]

We propose to combine the Floquet formalism for systems in AC fields with the dynamical mean-field theory to study correlated electron systems periodically driven out of equilibrium by external fields such as intense laser light. This approach has a virtue that we can nonperturbatively incorporate both the correlation effects and nonlinear effects due to the driving field, which is imperative in analysing recent experiments for photoinduced phase transitions. In solving the problem, we exploit a general theorem, found in the present paper, that the Hamiltonian in a Floquet matrix form can be exactly diagonalized for single band noninteracting systems. As a demonstration, we have applied the method to the Falicov-Kimball model in intense AC fields to calculate the spectral function. The result shows that photoinduced midgap states emerge from strong AC fields, triggering an insulator-metal transition.

oT. Oka, and N. Nagaosa,
Interfaces of correlated electron systems: Proposed mechanism for colossal electroresistance,  
Phys. Rev. Lett. 95, 266403- 266407 (2005)
[arXiv:cond-mat/0509050]

Mott's metal-insulator transition at an interface due to band bending is studied by the density matrix renormalization group (DMRG). We show that the result can be recovered by a simple modification of the conventional Poisson's equation approach used in semi-conductor heterojunctions. A novel mechanism of colossal electroresistance is proposed, which incorporates the hysteretic behavior of the transition in higher dimensions.

oT. Oka, and H. Aoki,
Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators,  
Phys. Rev. Lett. 95, 137601- 137605 (2005)
[arXiv:cond-mat/0503503]

Non-linear transport of electrons in strong electric fields, as typified by dielectric breakdown, is re-formulated in terms of the ground-state decay rate originally studied by Schwinger in non-linear QED. We discuss the effect of electron interaction on Zener tunneling by comparing the dielectric breakdown of the band insulator and the Mott insulator, where the latter is studied by the time-dependent density-matrix renormalization group (DMRG). The relation with the Berry's phase theory of polarization is also established.

oT. Oka, N. Konno, R. Arita and H. Aoki,
Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk,  
Phys. Rev. Lett.94, 100602-100606 (2005), selected in virtual journal of quantum information.
[arXiv:quant-ph/0407013]

Quantum transport properties of electron systems driven by strong electric fields are studied by mapping the Landau-Zener transition dynamics to a quantum walk on a semi-infinite one-dimensional lattice with a reflecting boundary, where the sites correspond to energy levels and the boundary the ground state. Quantum interference induces a distribution localized around the ground state, and when the electric field is strengthened, a delocalization transition occurs describing breakdown of the original electron system.

oR. Arita, T. Miyake, T. Kotani, M. van Schilfgaarde, T. Oka, K. Kuroki, Y. Nozue, and H. Aoki,
Electronic properties of alkali-metal loaded zeolites -- a "supercrystal" Mott insulator,  
Phys. Rev. B 69, 195106-195110 (2004).
[arXiv:cond-mat/0304322]

oT. Oka, R. Arita and H. Aoki,
Breakdown of a Mott Insulator: A Nonadiabatic Tunneling Mechanism,  
Phys. Rev. Lett.91, 066406-066409 (2003).
[arXiv:cond-mat/0304036]

Time-dependent nonequilibrium properties of a strongly correlated electron system driven by large electric fields is obtained by means of solving the time-dependent Schroedinger equation for the many-body wave function numerically in one dimension. While the insulator-to-metal transition depends on the electric field and the interaction, the metallization is found to be described in terms of an universal Landau-Zener quantum tunneling among the many-body levels. These processes induces current oscillation for small systems, while give rise to finite resistivity through dissipation for larger systems/on longer time scales. 

proceedings:

o  T. Oka; H. Aoki,
Photovoltaic Berry curvature in the honeycomb lattice
J. Phys.: Conf. Ser. 200 062017, (2010)
[arXiv:0905.4191]

oT. Oka, and H. Aoki,
Photo-induced metallic liquid in a one-dimensional Mott insulator in AC fields,
Journal of Physics: Conference Series 150 (2009) 042152.
[pdf]

oN. Horiguchi, T. Oka, and H. Aoki,
Non-equilibrium dynamics in Mott-to-superfluid transition in Bose-Einstein condensation in optical lattices,
Journal of Physics: Conference Series 150 (2009) 032007.
[pdf]

oT. Oka, and H. Aoki,
Photo-induced Hall Effect in Graphene ---Effect of Boundary Types,
Journal of Physics: Conference Series 148 (2009) 012061.
[arXiv/0903.4220]

oT. Oka, and H. Aoki,
Nonlinear Transport in One-Dimensional Mott Insulator in Strong Electric Fields,
Physica B, Vol 359-361C, pp 759-761, (2005)
[arXiv:0505028]