Electric-field-driven resistive switching in dissipative Hubbard model Jiajun Lil,Camille Aron23,Gabriel Kotliar2 and Jong E.Han! Department of Physics,Sta University of New ersity,New Jersey 08455,USA We study how st correlated electrons on a dissipative lattice evolve from equilibrium under actions,by means of a non-ed dyna n than th -Da Fo arge b st but experi 8 metal into Mott insu lator. We pre non-monotoni field due to an interpla neous metal-insulator mixed state PACS numbers:7127 4a 71.30.+h.7220.Ht anding of 1d driven out equilib ium by lated system.The derived en for the are within the feasible tal ro We study the Hubbard model in a constant and homo sistive transitions. Multiple studies of this phenomenor 10.m ew- toa dramatic drop of resistivity up to5orders of mag anced by coupling the system to a thermostat which The relatively accessible threshold fields E cess of onergy transfer [14,15,21- 包keth ide TB)erm ries.A Landau-Zener hanism [11]see the Coulomb ga ulikely as it predicts a threshold field on the order trostatic pote ential -E imposed on the (-th TB site of 10 V/m. (E= 6 倒wa ated fermion bath [15 Yet The ng Hath ant mod In organic charge -transfer Ho=->(dfladto +H.c.)- ∑daCtaz+Ho ple a the electro-c emica ch nary oxides such as Nio 7]and VO28-10:the electric +god-2+h0 driven current locally heats up the sample which whered are the tight-binding electron creation opera- ng. tors at the -th site with spin o-↑or↓， and the electro ope rators attach librium under an external field,and how we describe the rsion relatiot defined with res ect to the electro quilibrium steadys tates that onsequently emerge static potential-E.g is the overlap between the TB we velope ded ba microscopic theory o cha and the rese ervoirs of length which will be sent to in ty, ical efforts [11-271 we tify in a canonical model of strongly interacting elec will extend this chain into higer dimensional lattice.The resistive switch electric field does not act within each res voirs whos ng ta emonstrat Jo ne ho ating e role is to cha eom th the line me loul vidth)for the e the di ing parameter asr)We work with Electric-field-driven resistive switching in dissipative Hubbard model Jiajun Li1 , Camille Aron2,3 , Gabriel Kotliar2 and Jong E. Han1 1 Department of Physics, State University of New York at Buffalo, Buffalo, New York 14260, USA 2 Department of Physics, Rutgers University, New Jersey 08854, USA 3 Department of Electrical Engineering, Princeton University, New Jersey 08455, USA. (Dated: May 18, 2015) We study how strongly correlated electrons on a dissipative lattice evolve from equilibrium under a constant electric field, focusing on the extent of the linear regime and hysteretic non-linear effects at higher fields. We access the non-equilibrium steady states, non-perturbatively in both the field and the electronic interactions, by means of a non-equilibrium dynamical mean-field theory in the Coulomb gauge. The linear response regime, limited by Joule heating, breaks down at fields much smaller than the quasi-particle energy scale. For large electronic interactions, strong but experi￾mentally accessible electric fields can induce a resistive switching by driving the strongly correlated metal into a Mott insulator. We predict a non-monotonic upper switching field due to an interplay of particle renormalization and the field-driven temperature. Hysteretic I-V curves suggest that the non-equilibrium current is carried through a spatially inhomogeneous metal-insulator mixed state. PACS numbers: 71.27.+a, 71.30.+h, 72.20.Ht Understanding of solids driven out of equilibrium by external fields [1, 2] has been one of the central goals in condensed matter physics for the past century and is very relevant to nanotechnology applications such as re￾sistive transitions. Multiple studies of this phenomenon have been performed in semiconductors and oxides [3– 10]. In oxides, the application of an electric field can lead to a dramatic drop of resistivity up to 5 orders of mag￾nitude. The relatively accessible threshold fields Eth ∼ 104−6 V/m and the hysteretic I-V curves make them good candidates for the fabrication of novel electronic memories. A Landau-Zener type of mechanism [11] seems unlikely as it predicts a threshold field on the order of 108−9 V/m. In narrow gap chalcogenide Mott in￾sulators, an avalanche breakdown was suggested with Eth ∼ E2.5 gap [3]. Yet, the resistive switchings in other classes of correlated materials do not seem to involve solely electronic mechanisms. In organic charge-transfer complexes, it is believed to occur via the electro-chemical migration of ions [4, 5]. Finally, there are strong indica￾tions that a Joule heating mechanism occurs in some bi￾nary oxides such as NiO [7] and VO2 [8–10]: the electric- field-driven current locally heats up the sample which experiences a temperature-driven resistive switching. These experiments raise basic questions of how a strongly correlated state continuously evolves out of equi￾librium under an external field, and how we describe the non-equilibrium steady states that consequently emerge. We develope a much needed basic microscopic theory of the driven metal-insulator transition. Building on earlier theoretical efforts [11–27] we iden￾tify in a canonical model of strongly interacting elec￾trons a region where electric-field-driven resistive switch￾ing takes place. We demonstrate how Joule heating ef￾fects modify the linear response regime and how, away from the linear regime, the same Joule physics leads to the hysteretic resistive transitions of the strongly corre￾lated system. The derived energy scales for resistive tran￾sitions are orders of magnitude smaller than bare model parameters, within the feasible experimental range. We study the Hubbard model in a constant and homo￾geneous electric field E which induces electric current J. After a transient regime, a non-equilibrium steady state establishes if the power injected in the system, J·E, is bal￾anced by coupling the system to a thermostat which can absorb the excess of energy via heat transfer [14, 15, 21– 24]. The thermostat is modeled by identical fermion reservoirs attached to each tight-binding (TB) sites. In the Coulomb gauge, the electric field amounts in an elec￾trostatic potential −`E imposed on the `-th TB site (` = −∞, · · · , ∞) and on its associated fermion bath [15]. The model is fully consistent with gauge-covariant mod￾els [23]. The non-interacting Hamiltonian reads, Hˆ 0 = −γ X `σ (d † `+1,σd`σ + H.c.) − g √ V X `ασ (d † `σc`ασ + H.c) + X `ασ αc † `ασc`ασ− X `σ `E(d † `σd`σ+ X α c † `ασc`ασ), (1) where d † `σ are the tight-binding electron creation opera￾tors at the `-th site with spin σ =↑ or ↓, and c † `ασ are the corresponding reservoir electron operators attached. α is a continuum index corresponding to the reservoir dispersion relation α defined with respect to the electro￾static potential −`E. g is the overlap between the TB chain and the reservoirs of length V which will be sent to infinity, assuming furthermore that the reservoirs re￾main in equilibrium at bath temperature Tb. Later we will extend this chain into higer dimensional lattice. The electric field does not act within each reservoirs whose role is to extract energy but not electric charge from the system [15]. We use a flat density of states (infinite band￾width) for the reservoir spectra α, and define the damp￾ing parameter as Γ = V −1πg2 P α δ(α). We work with arXiv:1410.0626v2 [cond-mat.str-el] 15 May 2015