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Mott–Hubbard transition in a 2D 3He fluid monolayer
Physica B 280 (2000) 100}101
Mott}Hubbard transition in a 2D He #uid monolayer J. Saunders*, A. Casey, H. Patel, J. NyeH ki, B. Cowan Millikelvin Laboratory, Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK
Abstract We discuss recent observations of the heat capacity and magnetization of a #uid He monolayer adsorbed on graphite plated with a bilayer of HD. Approaching the density at which the monolayer solidi"es into a (7;(7 commensurate solid, we observe an apparent divergence of the e!ective mass. However, the inferred values of F tend to a constant. We interpret this in terms of a Mott}Hubbard transition between a 2D Fermi liquid and a magnetically disordered solid occurring via the Brinkman}Rice}Anderson}Vollhardt scenario. 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: 2D helium; Fermi liquid; He 2D; Mott transition
1. Mott transition The description of the solidi"cation of bulk He as a Mott}Hubbard metal}insulator transition has been widely discussed [1}5]. Bulk liquid He is described in terms of versions of a lattice gas model, which must deal with the fact that there is no real lattice! In its simplest version, the Hubbard model is solved in the Gutzwiller approximation with the lattice at half-"lling. Tuning the density of the liquid varies the on-site repulsive potential energy ;. As ;P; , the e!ective mass ratio mH/mP R and F P!. The theory accounts for the weak pressure dependence of F observed in liquid He [1}3]. Experimentally, mH/m varies from 2.8 at zero pressure to 5.85 at 34 bar, at which pressure solidi"cation occurs via a "rst-order phase transition. In this paper we discuss the solidi"cation of 2D He adsorbed on graphite as a classic example of a Mott transition [6,7]. The key distinction from bulk, apart from dimensionality, is the fact that the He is exposed to a crystalline substrate potential. This is important since the &insulating' phase "rst forms a triangular lattice in commensuration with it. The exchange coupling of the S" nuclear spin &local moments' in this solid arises * Corresponding author. E-mail address: [email protected] (J. Saunders) Permanent address: Institute of Experimental Physics, Slovak Academy of Sciences, Kos\ ice, Slovak Republic.
from cyclic atomic permutations and there is mounting evidence that the ground state is a quantum spin liquid. Thus by varying the 2D density at ¹"0, we explore the Mott metal}insulator transition between a 2D Fermi liquid and a disordered spin system. This He system has the advantage of being truly two dimensional (no interlayer coupling), having simple short range van der Waals interactions, and no spin}orbit coupling (since exchange is between nuclear spins). 2. (7 ⴛ (7 commensurate solid The second layer of He adsorbed on bare graphite solidi"es at 6.4 nm\ [8]. This is consistent with the formation of a triangular lattice in (7;(7 commensuration with the He "rst layer, whose density from neutron scattering is 11.2 nm\. The ratio of these densities is close to the value expected. This structure is also found in PIMC calculations [9]. Experimentally, plating the graphite surface with a bilayer of HD (for which the density of each layer is 9.1 nm\) is found to reduce the density at which a He layer solidi"es to close to 5.2 nm\, further supporting the proposed structure. It is clear therefore that the periodic potential is crucial to the stability of this low-density 2D solid. 3. Strongly correlated 2D 6uid 3He The "rst heat capacity and magnetization studies of the second layer of He on graphite, as a function of
0921-4526/00/$ - see front matter 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 4 8 3 - 0
J. Saunders et al. / Physica B 280 (2000) 100}101
surface density [8,10], found values of mH/m up to 4.5 and an apparent saturation of F close to !. (The enhance ment of the low-temperature nuclear magnetization relative to that of an ideal Fermi gas is given by M/M " (mH/m)/(1#F ).) Later work explored more closely the density region near solidi"cation, where somewhat larger magnetization enhancements were observed, leading to the proposal of a highly correlated regime [11]. Recently, we have measured both heat capacity and magnetization of the #uid He on graphite preplated with an HD bilayer [12]. We "nd an apparent divergence of mH/m as n P5.1 nm\, a density close to that of the commensur ate solid phase. At 5.0 nm\, mH/m"13.1. The dramatic increase in magnetization as solidi"cation is approached is associated with this diverging e!ective mass, and consistent with F P!. These results indicate that localisation into the commensurate phase should be viewed as a Mott}Hubbard transition occurring via the Brinkman}Rice}Anderson} Vollhardt scenario [1}3]. In the present case we study the "lling controlled transition, as the density is tuned towards that of the (spin liquid) insulating phase, and "nd that the e!ective mass and magnetization diverge in the same way. Similar behaviour is observed in the titanate Sr La TiO as xP1 [13]. In this system e!ective \V V magnetic frustration reduces the antiferromagnetic ordering temperature in the insulating phase [14]. Associated with the mass diverging transition we "nd here a collapse of the Fermi-liquid regime, observed for ¹:0.05¹H, as the critical density is approached. $
101
Acknowledgements We thank A. Millis, M. Imada, G. Kotliar, P. Coleman for valuable discussions and correspondence. This work was supported by EPSRC (UK).
References [1] P.W. Anderson, W.F. Brinkman, in: K.H. Bennemann, J.B. Ketterson (Eds.), The Physics of Liquid and Solid Helium, Part II, Wiley, New York, 1978. [2] D. Vollhardt, Rev. Mod. Phys. 56 (1984) 99. [3] D. Vollhardt, P. WoK l#e, P.W. Anderson, Phys. Rev. B 35 (1987) 6703. [4] R.B. Laughlin, Adv. Phys. 47 (1998) 943. [5] P.W. Anderson, G. Baskaran, cond-mat/9711197. [6] M. Imada, J. Phys. Soc. Japan 64 (1995) 2954. [7] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70 (1998) 1039. [8] D.S. Greywall, Phys. Rev. B 47 (1990) 309. [9] M. Pierce, E. Manousakis, Phys. Rev. Lett. 81 (1998) 156. [10] C.P. Lusher, B.P. Cowan, J. Saunders, Phys. Rev. Lett. 67 (1991) 2497. [11] K.D. Morhard, C. BaK uerle, J. Bossy, Yu.M. Bunkov, S.N. Fisher, H. Godfrin, Phys. Rev. B 53 (1996) 2658. [12] A. Casey, H. Patel, J. NyeH ki, B.P. Cowan, J. Saunders, J. Low Temp. Phys. 113 (1998) 293. [13] Y. Tokura, Y. Taguchi, Y. Okada, Y. Fujishima, T. Arima, K. Kumagai, Y. Iye, Phys. Rev. Lett. 70 (1993) 2126. [14] H. Kajueter, G. Kotliar, G. Moeller, Phys. Rev. B 53 (1996) 16214.
Mott}Hubbard transition in a 2D He #uid monolayer J. Saunders*, A. Casey, H. Patel, J. NyeH ki, B. Cowan Millikelvin Laboratory, Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK
Abstract We discuss recent observations of the heat capacity and magnetization of a #uid He monolayer adsorbed on graphite plated with a bilayer of HD. Approaching the density at which the monolayer solidi"es into a (7;(7 commensurate solid, we observe an apparent divergence of the e!ective mass. However, the inferred values of F tend to a constant. We interpret this in terms of a Mott}Hubbard transition between a 2D Fermi liquid and a magnetically disordered solid occurring via the Brinkman}Rice}Anderson}Vollhardt scenario. 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: 2D helium; Fermi liquid; He 2D; Mott transition
1. Mott transition The description of the solidi"cation of bulk He as a Mott}Hubbard metal}insulator transition has been widely discussed [1}5]. Bulk liquid He is described in terms of versions of a lattice gas model, which must deal with the fact that there is no real lattice! In its simplest version, the Hubbard model is solved in the Gutzwiller approximation with the lattice at half-"lling. Tuning the density of the liquid varies the on-site repulsive potential energy ;. As ;P; , the e!ective mass ratio mH/mP R and F P!. The theory accounts for the weak pressure dependence of F observed in liquid He [1}3]. Experimentally, mH/m varies from 2.8 at zero pressure to 5.85 at 34 bar, at which pressure solidi"cation occurs via a "rst-order phase transition. In this paper we discuss the solidi"cation of 2D He adsorbed on graphite as a classic example of a Mott transition [6,7]. The key distinction from bulk, apart from dimensionality, is the fact that the He is exposed to a crystalline substrate potential. This is important since the &insulating' phase "rst forms a triangular lattice in commensuration with it. The exchange coupling of the S" nuclear spin &local moments' in this solid arises * Corresponding author. E-mail address: [email protected] (J. Saunders) Permanent address: Institute of Experimental Physics, Slovak Academy of Sciences, Kos\ ice, Slovak Republic.
from cyclic atomic permutations and there is mounting evidence that the ground state is a quantum spin liquid. Thus by varying the 2D density at ¹"0, we explore the Mott metal}insulator transition between a 2D Fermi liquid and a disordered spin system. This He system has the advantage of being truly two dimensional (no interlayer coupling), having simple short range van der Waals interactions, and no spin}orbit coupling (since exchange is between nuclear spins). 2. (7 ⴛ (7 commensurate solid The second layer of He adsorbed on bare graphite solidi"es at 6.4 nm\ [8]. This is consistent with the formation of a triangular lattice in (7;(7 commensuration with the He "rst layer, whose density from neutron scattering is 11.2 nm\. The ratio of these densities is close to the value expected. This structure is also found in PIMC calculations [9]. Experimentally, plating the graphite surface with a bilayer of HD (for which the density of each layer is 9.1 nm\) is found to reduce the density at which a He layer solidi"es to close to 5.2 nm\, further supporting the proposed structure. It is clear therefore that the periodic potential is crucial to the stability of this low-density 2D solid. 3. Strongly correlated 2D 6uid 3He The "rst heat capacity and magnetization studies of the second layer of He on graphite, as a function of
0921-4526/00/$ - see front matter 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 4 8 3 - 0
J. Saunders et al. / Physica B 280 (2000) 100}101
surface density [8,10], found values of mH/m up to 4.5 and an apparent saturation of F close to !. (The enhance ment of the low-temperature nuclear magnetization relative to that of an ideal Fermi gas is given by M/M " (mH/m)/(1#F ).) Later work explored more closely the density region near solidi"cation, where somewhat larger magnetization enhancements were observed, leading to the proposal of a highly correlated regime [11]. Recently, we have measured both heat capacity and magnetization of the #uid He on graphite preplated with an HD bilayer [12]. We "nd an apparent divergence of mH/m as n P5.1 nm\, a density close to that of the commensur ate solid phase. At 5.0 nm\, mH/m"13.1. The dramatic increase in magnetization as solidi"cation is approached is associated with this diverging e!ective mass, and consistent with F P!. These results indicate that localisation into the commensurate phase should be viewed as a Mott}Hubbard transition occurring via the Brinkman}Rice}Anderson} Vollhardt scenario [1}3]. In the present case we study the "lling controlled transition, as the density is tuned towards that of the (spin liquid) insulating phase, and "nd that the e!ective mass and magnetization diverge in the same way. Similar behaviour is observed in the titanate Sr La TiO as xP1 [13]. In this system e!ective \V V magnetic frustration reduces the antiferromagnetic ordering temperature in the insulating phase [14]. Associated with the mass diverging transition we "nd here a collapse of the Fermi-liquid regime, observed for ¹:0.05¹H, as the critical density is approached. $
101
Acknowledgements We thank A. Millis, M. Imada, G. Kotliar, P. Coleman for valuable discussions and correspondence. This work was supported by EPSRC (UK).
References [1] P.W. Anderson, W.F. Brinkman, in: K.H. Bennemann, J.B. Ketterson (Eds.), The Physics of Liquid and Solid Helium, Part II, Wiley, New York, 1978. [2] D. Vollhardt, Rev. Mod. Phys. 56 (1984) 99. [3] D. Vollhardt, P. WoK l#e, P.W. Anderson, Phys. Rev. B 35 (1987) 6703. [4] R.B. Laughlin, Adv. Phys. 47 (1998) 943. [5] P.W. Anderson, G. Baskaran, cond-mat/9711197. [6] M. Imada, J. Phys. Soc. Japan 64 (1995) 2954. [7] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70 (1998) 1039. [8] D.S. Greywall, Phys. Rev. B 47 (1990) 309. [9] M. Pierce, E. Manousakis, Phys. Rev. Lett. 81 (1998) 156. [10] C.P. Lusher, B.P. Cowan, J. Saunders, Phys. Rev. Lett. 67 (1991) 2497. [11] K.D. Morhard, C. BaK uerle, J. Bossy, Yu.M. Bunkov, S.N. Fisher, H. Godfrin, Phys. Rev. B 53 (1996) 2658. [12] A. Casey, H. Patel, J. NyeH ki, B.P. Cowan, J. Saunders, J. Low Temp. Phys. 113 (1998) 293. [13] Y. Tokura, Y. Taguchi, Y. Okada, Y. Fujishima, T. Arima, K. Kumagai, Y. Iye, Phys. Rev. Lett. 70 (1993) 2126. [14] H. Kajueter, G. Kotliar, G. Moeller, Phys. Rev. B 53 (1996) 16214.