Abstract:
A solid state dc-SQUID includes a superconducting loop containing a plurality of Josephson junctions, wherein an intrinsic phase shift is accumulated through the loop. In an embodiment of the invention, the current-phase response of the dc-SQUID sits in a linear regime where directional sensitivity to flux through the loop occurs. Changes in the flux passing through the superconducting loop stimulates current which can be quantified, thus providing a means of measuring the magnetic field. Given the linear and directional response regime of the embodied device, an inherent current to phase sensitivity is achieved that would otherwise be unobtainable in common dc-SQUID devices without extrinsic intervention.

Description:
BACKGROUND  
         [0001]    1. Field of the Invention  
           [0002]    This invention relates to dc-SQUID magnetometry and superconducting electronics and, in particular, to a magnetometer including a superconducting SQUID having an inherent phase shift without application of external magnetic fields.  
           [0003]    2. Discussion of Related Art  
           [0004]    Very precise measurements of small magnetic fields can be accomplished with a dc-SQUID magnetometer device. A conventional dc-SQUID magnetometer includes a superconducting loop containing a plurality of Josephson junctions, coupled to terminals. Any change in the magnetic field which penetrates the superconducting loop disturbs the current through the device, which is detectable at the terminals. Thus, the dc-SQUID can be used as a device for measuring changes in a magnetic field.  
           [0005]    Conventional dc-SQUID magnetometers lack inherent sensitivity. Furthermore, a conventional dc-SQUID magnetometer can only determine the magnitude of the change in a magnetic field, but cannot distinguish the direction of the change. In order to hyper-sensitize a standard dc-SQUID, flux-biasing can be used to shift the latent flux position in the SQUID loop into a linear response regime. A standard dc-SQUID loop behaves in accordance with a well defined current-phase relationship. The equilibrium position of the current-phase relation of a standard dc-SQUID lies in a region of sensitivity where the induced superconducting current is proportional to a small perturbation in the flux squared (I∝Φ 2 ), and resultingly there is no directional sensitivity. By biasing the SQUID loop with an applied flux, the equilibrium position can be shifted into a more sensitive linear response regime, thus introducing directional sensitivity into the current response as well. This can be accomplished by introducing a phase shift of the equilibrium position in the current-phase relation. The phase shift is realized in conventional dc-SQUID devices by application of an external magnetic field to the dc-SQUID device, a technique called flux biasing. In other words, with an externally applied magnetic flux on the SQUID device, a small perturbation in the flux induced by the magnetic field that is being measured will result in a linear response in the superconducting current from the SQUID device.  
           [0006]    Furthermore, by coupling multiple SQUID loops, it is possible to enhance the sensitivity of the dc-SQUID magnetometer. See U.S. Pat. No. 5,767,043, entitled “Multiple Squid Direct Signal Injection Device Formed On a Single Layer Substrate,” to Cantor et al., herein incorporated by reference in its entirety. One application of dc-SQUID magnetometry is as a non-destructive testing device in the field of semi-conductor electronics. In the electronics industry, each circuit that is manufactured must be non-destructively tested for correct operating parameters. This is accomplished by running current through the circuit to be tested and measuring the resulting magnetic fields. However, in order to detect flaws in the magnetic field a high degree of resolution is required, which cannot be achieved without flux biasing or coupling the dc-SQUIDs that make up the magnetometer. Thus, there is a necessity for increasing the latent sensitivity of the SQUID magnetometer.  
           [0007]    Further applications for dc-SQUID magnetometers range in practical uses. For example, dc-SQUID magnetometers are used in Magnetic Resonance Imaging, microscopic metal defect detection, mine detection, and submarine detection. Additional examples of uses for dc-SQUID magnetometers include analogue-to-digital converters and optical switches. Given the broad range of applications of dc-SQUID Magnetometers, there is a need for devices with increased sensitivity, including directional sensitivity, wherein the overall size and cost of a device is reduced.  
           [0008]    There are, however, practical limitations to current methods of dc-SQUID sensitizing. Biasing the loop introduces magnetic fields that may interfere with the fields or system being measured. Similarly, coupling dc-SQUIDs can lead to bulky measurement tools that increase the obtainable distance from the sample, thereby also decreasing the ability to measure magnetic fields in the sample.  
           [0009]    The use of a phase shifter in order to sensitize the current-phase behavior in a superconducting loop is known; however, the inherent sensitization has been restricted to a π-phase shift. Thus there is a need for a device that can be used in dc-SQUID magnetometry with a high level of latent sensitivity, as well as directional sensitivity without the application of external magnetic fields.  
         SUMMARY  
         [0010]    In accordance with the present invention, a dc-SQUID magnetometer is presented which provides an inherent phase shift in a superconducting loop, i.e. a phase shift in the absence of an external magnetic field. Some embodiments of a dc-SQUID magnetometer according to the present invention include a high sensitivity, directional, superconducting Josephson device formed of a superconductive loop having a π/2-Josephson junction and a 0-Josephson junction. The superconductive loop is further coupled to at least two terminals by which a current may flow through the loop.  
           [0011]    The superconducting materials forming the superconducting loop and terminals can have dominant order pairing symmetry with non-zero angular momentum. In some embodiments, the superconducting material can be a high temperature, d-wave superconductor such as YBa 2 Cu 3   0   7−x , where x has values less than 0.4 and greater than 0.05, or Bi 2 Sr 2 Ca n−1  CuO 2+4 . In some other embodiments, a dc-SQUID magnetometer according to the present invention can include a p-wave superconducting material forming 0-junctions and π/2-junctions. An example of a p-wave superconducting material includes Sr 2 RuO 4 .  
           [0012]    Junctions having a π/2 phase shift or a 0 phase shift, for example, can be fabricated at the grain boundary of two d-wave superconducting materials. For example, in a junction formed at the grain boundary between two d-wave superconducting materials with a 45° misalignment in their crystal lattice structures, a π/2 phase shift results in a junction that is perpendicular to the terminals of the junction. Similarly, a 0° phase shift can be achieved in a grain boundary Josephson junction in which the misalignment in the crystal orientation between the superconductors on either side of the grain boundary is zero (in the trivial case) or, the 0° phase shift can be achieved in the case of a symmetric 22.5° grain boundary junction, where the a-axis of the order parameter of the two superconductors are rotated ±22.5° from parallel to the junction interface, respectively.  
           [0013]    The combination of a 0-junction and a π/2-junction induces an overall π/2-phase shift in the current as the superconducting loop is traversed, thus shifting the equilibrium position of the current-phase relation Resultingly, a π/2 dc-SQUID loop according to the present invention has a linear current-phase response with small changes in externally applied magnetic flux. The measured current is also sensitive to the direction of the flux through the loop. Further, the π/2 dc-SQUID loop does not require any externally applied flux biasing. This inherent phase shift allows for an order of 100 fold increase over the sensitivity of standard embodiments of dc-SQUID loops without the use of external means. Additionally, no external circuitry is required to bias the SQUID loop.  
           [0014]    An embodiment of a SQUID magnetometer according to the present invention can be fabricated by bi-epitaxial methods, although other deposition methods can also be utilized. For example, in the fabrication of a d-wave superconducting SQUID magnetometer according to the present invention, a seed layer may be deposited on a substrate and a first buffer layer may be deposited on the seed layer. In some embodiments, the seed layer may be MgO, the substrate SrTiO 3  or Sapphire, and the first buffer layer CeO 2 . The first buffer layer and the seed layer may be etched, for example by Xe-ion milling although any appropriate etching method can be used, to form a boundary. The boundary separates a first area having the seed layer and the first buffer layer from a second area where the seed layer and the first buffer layer have been removed. A second buffer layer can be deposited on the second area and the first buffer layer. A superconducting material may then be deposited on the second buffer layer and etched, for example by Xe-ion milling although any appropriate etching method can be used, to form a loop and terminals. Resultingly, Josephson junctions are formed along the boundary. The boundary can be shaped so that both a 0-junction and a π/2 junction are achieved at the boundary. The second buffer layer may also be of CeO 2 .  
           [0015]    The first buffer layer and the second buffer layer are deposited so that there is a lattice mismatch between the superconducting material deposited over the first area where the seed layer has been deposited and the superconducting material deposited over the second area, resulting in a grain boundary in the superconducting material at the boundary.  
           [0016]    A magnetometer according to the present invention may exhibit inherent phase shifts of any value. Phase shifts other than a π/2 phase shift can also result in a magnetometer operating in a linear region. These and other embodiments are further discussed below with respect to the following figures. 
       
    
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0017]    [0017]FIG. 1 shows a plan view of an embodiment of a SQUID Magnetometer according to the present invention.  
         [0018]    FIGS.  2  shows a plan view of an embodiment of a π/2 Josephson junction.  
         [0019]    [0019]FIG. 3 shows a plan view of a symmetric 22.5° Josephson junction.  
         [0020]    [0020]FIG. 4 shows a plan view of an embodiment of a 0 Josephson junction.  
         [0021]    [0021]FIGS. 5 a ,  5   b , and  5   c  show critical current—flux relations for a standard 0-phase shift dc-SQUID, a π-phase shift dc-SQUID, and a π/2-phase shift dc-SQUID, respectively.  
         [0022]    [0022]FIGS. 6 a  through  6   c  illustrate an example bi-epitaxial fabrication method.  
         [0023]    [0023]FIG. 7 shows a cross sectional view of an exemplary bi-epitaxial fabrication method.  
         [0024]    [0024]FIG. 8 shows a plan view of a 2-dimensional array of SQUID magnetometers according to the present invention.  
         [0025]    [0025]FIG. 9 shows a dc SQUID magnetometer according to the present invention utilized to measure a magnetic field. 
     
    
       [0026]    In the figures, elements with the same designation have similar or identical functions.  
       DETAILED DESCRIPTION  
       [0027]    [0027]FIG. 1 shows a plan view of an embodiment of a SQUID magnetometer  100  according to the present invention. SQUID magnetometer  100  of FIG. 1 includes loop  150 , junctions  110  and  120 , and terminals  140  and  141 . Loop  150  and terminals  140  and  141  can be formed of a d-wave superconducting material or a p-wave superconducting material deposited on areas  101  and  102 . Portion  151  of loop  150  is formed in area  102  and portion  152  of loop  150  is formed in area  101 .  
         [0028]    Loop  150  and junctions  110  and  120  provide an intrinsic phase shift to the current in magnetometer  100 . Intrinsic phase shifters are described in M. H. S. Amin, T. Duty, A. Omelyanchouk, G. Rose and A. Zagoskin, U.S. Provisional Application Serial No. No. 60/257,624, “Intrinsic Phase Shifter as an Element of a Superconducting Phase Quantum Bit”, filed Dec. 22, 2000, and the references therein, which is herein incorporated by reference in its entirety. A phase shifting structure with 0 and π-phase shifts in a two-terminal DC SQUID is described in R. R. Schulz, B. Chesca, B. Goetz, C. W. Schneider, A. Schmehl, H. Bielefeldt, H. Hilgenkamp, J. Mannhart and C. C. Tsuei, “Design and realization of an all d-wave dc pi-superconducting quantum interference device”, Appl. Phys. Lett. 76, 7 p.912 (2000), and the references therein, which is incorporated herein by reference in its entirety.  
         [0029]    Areas  101  and  102  indicate the surface of two misaligned crystal lattice structures. In some embodiments, the crystal lattice structure of the surface of area  101  is rotated about 45° with respect to the crystal lattice structure of the surface of area  102 . The areas  101  and  102  form grain boundaries  103  and  104  at their intersection. As a result of this misalignment, when the superconductor materials of terminals  140  and  141  and of SQUID loop  150  are deposited, the crystal orientation is determined by that of the material of areas  101  and  102  respectively. In other words, terminal  140  and portion  151  of loop  150  have a crystal lattice structure determined by the material of area  102  whereas terminal  141  and portion  152  of loop  150  have a crystal lattice structure determined by the material of area  101 . Examples of superconducting materials which may be included in a d-wave superconducting Josephson device  100  are Yba 2 Cu 3 O 7−x  and Bi 2 Sr 2 Ca n−1 Cu n O 2+4 , which both have d-wave order pairing symmetry. An example of a p-wave superconducting material which can be utilized to form device  100  includes Sr 2 RuO 4 . To achieve the π/2-phase shift in the p-wave superconductor case, the grain boundary rotation angle should be about 45°, and the order parameter should change to having a vertical alignment on one side of the grain boundary, and a horizontal alignment on the other side of the grain boundary. Any superconducting material with a dominant order pairing symmetry having a non-zero angular momentum can be used to form device  100 .  
         [0030]    Josephson junctions  110  and  120  are formed at grain boundaries  103  and  104 , respectively. In the embodiment shown in FIG. 1, grain boundary  103  (and hence junction  110 ) is formed parallel with a horizontal axis of the magnetometer. A vertical axis can be defined in device  100  along the directions of terminals  140  and  141  as shown in FIG. 1. Grain boundary  104 , however, is angled with respect to grain boundary  103  by an angle of Θ, such that the resulting junction on the SQUID loop is a zero or pi-phase shift Josephson junction, which in some embodiments can be a symmetric 22.5° Josephson junction.  
         [0031]    The current passing through junction  110  behaves according to the relationship I=I c  Sin 2 (θ−θ′), where θ is the phase of the superconducting region  151 , and  0 ′ is the phase in the superconducting region  152 . Furthermore, the current passing through junction  120  behaves according to the relationship I=I c  Sin (Ψ−Ψ′), where again, Ψ represents the phase of the superconductor in region  151 , and Ψ′ represents the phase of the superconductor in region  152 . The total current through the terminals  140  and  141  is just the sum of the currents through the junctions, which is dependent upon the embodiment of the invention. Specifically, variation in the width of the junctions or branches, the width of the overall loop, and the roughness of the junctions are the key factors involved in calculating the ratio of current in each branch of the loop. In an exemplary embodiment, the ratio is I 1 =2 1   2 =I c . Thus, the total current is given by I=I c  (Sin((φ 2 +φ e )−{fraction (1/2)} Sin 2φ2), where (φ 2 =θ−θ′, and φ e =φ 1 −φ 2 , and the dependence of φ 2  on φ e  can be easily calculated by taking the derivative of I with respect to φ 2  and finding the maximums and minimums. Furthermore, it is possible to derive from this the critical current—flux relationship (see FIG. 5 c ). In some embodiments, the angle of symmetry, Θ, can be about π/8 radians, such that junction  120  is a symmetric 22.5°-phase shift Josephson junction.  
         [0032]    [0032]FIG. 2 shows an example of a π/2-phase shift grain boundary Josephson junction  110 . Junction  110  is formed at grain boundary  103  (FIG. 1) by portion  152  and portion  151  separated by a junction boundary  210 . Boundary  210  can be a small gap between the two superconductors, or it can include an insulating material. As described above, portion  152  and portion  151  are each formed of a superconducting material having a dominant order pairing symmetry with non-zero angular moment. A lattice mismatch between the two superconducting materials in regions  151  and  152  introduces a phase shift in the quantum order parameter ψ as the junction is traversed. In some embodiments, the a-crystallographic direction of the superconducting material of portion  151  is rotated by π/4 from the a-crystallographic direction of the superconducting material of portion  151 . The order parameter of the superconducting material is directly related to the crystallographic orientation. Therefore, the phase shift of current that has traversed the grain boundary of FIG. 2, is θ−φ, where θ represents the phase of the supercurrent before crossing the grain boundary junction, and φ represents the phase incurred by the supercurrent in crossing the grain boundry junction. In FIG. 2, φ is π/2, and the overall phase shift of the junction  210  is π/2.  
         [0033]    The embodiment of junction  110  shown in FIG. 2 is an asymmetric junction. In that case, the a-crystallographic axis of portion  152  is rotated from boundary  212  by about 0° and the a crystallographic axis of portion  151  is rotated from boundary  211  by about 45°, yielding a total mismatch between the a-crystallographic axis between the superconducting materials of portions  151  and  152  of 45° (π/4). The a-crystallographic axis of the superconducting materials of portions  151  and  152  is indicated by arrows in FIG. 2. Additionally, the phase θ, and θ′ of the of the supercurrent is shown in each of portion  151  and  152 .  
         [0034]    A 0 phase shift grain boundary Josephson junction, embodied here as a symmetric 22.5° grain boundary Josephson junction,  300  is illustrated in FIG. 3. Junction  300  is symmetric because order parameter  149  in portion  152  is a mirror image of order parameter  149  in portion  151 . The supercurrent I 1  crossing grain boundary  310  from one direction has a dominant path that is the same regardless of the direction from which junction  300  is approached. Thus, the total phase incurred across grain boundary  310  is 0. Symmetric 22.5° Josephson junctions are further discussed in E. Il&#39;ichev, M. Grajcar, R. Hlubina, R. P. J. Ijsselsteijn, H. E. Hoenig, H. -G. Meyer, A. Golubov, M. H. S. Amin, A. M. Zagoskin, A. N. Omelyanchouk, and M. Yu. Kupriyanov, “Degenerate ground state in a mesoscopic YBa 2 Cu 3 O 7−x  grain boundary Josephson junction”, LANL, cond-mat/0102404 v2, 23 February, 2001, and the references therein, which is herein included by reference in its entirety.  
         [0035]    [0035]FIG. 4 shows an example of a 0-junction  120 . Again, the lattice mismatch between the a-crystallographic directions of the superconducting materials of portions  151  and  152  is the same as the lattice mismatch indicated in the discussion of FIG. 2 above. The a-crystallographic directions and the superconducting order parameter ψ and Ψ′ are shown in FIG. 4 for each of the superconducting materials of portions  151  and  152 , which shows a π/2 phase shift in the order parameter ψ′ with respect to the order parameter orientation of Ψ. Portions  151  and  152  are separated by junction boundary  320 . In junction  120  of FIG. 4, however, boundary  320  is not perpendicular to the direction of the superconducting current I. Instead, boundary  320  follows the grain boundary  104  and therefore is angled from the perpendicular direction by the angle of symmetry Θ. The angle of symmetry Θ can vary, but in an exemplary embodiment of the invention, Θ=22.5°, and the resulting junction is a symmetric 22.5° grain boundary Josephson junction, which, as shown in FIG. 3, results in a 0 phase shift in the supercurrent I across junction  120 .  
         [0036]    The widths of the junctions,  110  and  120 , L 1  and L 2 , respectively, are chosen to maximize the device sensitivity to flux threading in loop  150  by controlling the amount of supercurrent that travels along each branch of dc-SQUID  100 . In some embodiments where junction  110  is a π/2 junction and junction  120  is a O-junction, then widths L 1  and L 2  can be on the order of 1 μm. One skilled in the art will recognize that SQUID magnetometer  100  according to the present invention can have any combination of junctions  110  and  120  such that total intrinsic phase shift of loop  150  is realized. Sensitization of the dc-SQUID is realized for a range of phase shifts, where the phase shift can vary from 0&lt;φ&lt;π. Phase shifts of around π/2, as described above, further lead to directional sensitivity. Therefore, there is a hardy tolerance in the fabrication of the invention in terms of junction behavior, as well as allowing for a plurality of Josephson junctions that total a phase shift within the desired range.  
         [0037]    [0037]FIGS. 5 a  through  5   c  illustrate a comparison of the Critical Current-Flux relation for a 0-phase shift SQUID magnetometer, a π-phase shift SQUID magnetometer and a π/2-phase shift SQUID magnetometer according to the present invention. FIGS. 5 a  through  5   c  show that the critical current in the superconducting loop can be directly correlated with the flux through the loop. Characterization of the relationship can be found experimentally by controlling the supercurrent through dc-SQUID magnetometer  100  and measuring the flux in the loop with an instrument such as a magnetometer, or, in a contrary fashion, by applying a magnetic field through SQUID loop  100  and measuring the resulting supercurrent. In another experimental procedure, a constant current is applied across the terminals and the potential drop across the SQUID loop is measured.  
         [0038]    [0038]FIG. 5 a  shows the current-phase relationship for a 0 phase-shift SQUID loop. At 0 current and a normalized phase shift of 1, the response curve is at a peak. Therefore, a change in the flux through the loop results in a decrease in the supercurrent, that is independent of the direction of the flux in the loop. The response of a π dc-SQUID as shown in FIG. 5 b  is a useful variation of the response shown in FIG. 5 a  of the dc-SQUID as the sensitivity of the π dc-SQUID is linear with overall phase. As is clear from FIG. 5 b , a change in the flux in the loop results in a steep change in the current, but again, the change is positive in both cases and thus is independent of the direction of the flux in the loop. The response of a π/2 dc-SQUID is shown in FIG. 5 c . In the π/2 dc-SQUID, the equilibrium position (at 0 current) is also at a point where the sensitivity is linear with phase. However, a small perturbation in the flux through the loop causes a positive change in the current for one direction, and a negative change in the current for the other direction, thus allowing for directional sensitivity. An advantage of embodiments of a dc-SQUID magnetometer  100  in accordance with the present invention is a 2 fold increase in sensitivity over a conventional π dc-SQUID due to the sensitivity to direction of flux through the loop.  
         [0039]    [0039]FIGS. 6 a  through  6   c  illustrate an example of fabrication of a SQUID magnetometer according to the present invention. In this example, a bi-epitaxial fabrication method is employed, although one skilled in the art will recognize that other deposition methods can also be employed. Exemplary methods of bi-epitaxial fabrication are described in S. Nicoletti, H. Moriceau, J. C. Villegier, D. Chateigner, B. Bourgeaux, C. Cabanel, and J. Y. Laval, “Bi-epitaxial YBCO grain boundary Josephson junctions on SrTiO 3  and sapphire substrates,” Physica C, 269, p.255-267, 1996, and the references therein, which is hereby included by reference in its entirety. Further discussions regarding fabrication of a grain boundary between two d-wave semiconductor materials is further discussed in F. Tafuri, F. Carillo, F. Lombardi, F. Miletto Granozio, F. Ricci, U. Scotti di Uccio, A. Barone, G. Testa, E. Samelli, J. R. Kirtley, “Feasibility of Biepitaxial YBaCuO Josephson Junctions for Fundamental Studies and Potential Circuit Implementation, Los Alamos preprint server condmat/0010128, accepted for publication Phy. Rev. B (2000), which is herein incorporated by reference in its entirety. The behavior of such junctions on the phase shift of the order parameter is discussed in C. Bruder, A. van Otterlo, and G. T. Zimanyi, “Tunnel junctions of Unconventional Superconductors,” PRB 51, 12904 (1995); and C. C. Tsuei, “Design and realization of an all d-wave dc π-superconducting quantum interference device,” Applied Physics Letters, 76, p.912 (2000), each of which is included herein by reference in its entirety.  
         [0040]    In some embodiments, a seed layer followed by a buffer layer is deposited onto a substrate such as SrTiO 3  or Sapphire by means of pulsed laser deposition. The buffer layer forms on the substrate with a rotated crystallographic orientation (π/2 in some embodiments). Different crystallographic orientations can be achieved through the use of different buffer materials. A section of the seed and buffer layer can then be removed by a process such as Xe ion milling. The milling creates the weak link boundary (i.e., boundaries  103  and  104  of FIG. 1) for the device. Next, a second buffer layer followed by the high-T c  superconducting film are deposited, and the final structure is realized through further etching of the film. The buffer layers can be formed of CeO 2  for example.  
         [0041]    [0041]FIG. 6 a  shows an intermediate structure having a substrate layer  500  as a base for the bi-epitaxial fabrication process. Substrate layer  500  can be, for example, a layer of SrTiO 3  or Sapphire. A seed layer  510  is formed on substrate layer  500 . Seed layer  510 , for example, can be of MgO. In some embodiments, seed layer  510  can be about 5 nm thick. A buffer layer  515  can then be deposited on seed layer  510 . In some embodiments, buffer layer  515  can be of CeO 2  and can have a thickness of approximately 11 nm. Seed layer  510  and buffer layer  515  can then be milled away (for example by Xe-ion milling) from section  590 , as illustrated in FIG. 5A, such that a boundary  550  is formed. Angle Θ illustrates a bend in boundary  550 , corresponding to the bend between boundary  103  and boundary  104  of FIG. 1. In some embodiments, the angle Θ can be chosen as 22.5°. Boundary  550 , with a bend angle Θ, can be fabricated with smooth and sharp features using any of a number of etching techniques such as Xe ion milling.  
         [0042]    In some embodiments, boundary  550 , with bend angle Θ, is oriented with respect to the crystal structure of buffer layer  515  such that, once a d-wave crystal structure is deposited on top of buffer layer  515 , the d-wave crystal structure is oriented with it&#39;s a-axis at a 22.5° angle with respect to boundary  550  in one portion and at 0° in a second portion where the portions are separated by the bend at bend angle Θ. Reversly, boundary  550  can be arranged such that the a-axis of the superconducting crystal structure is oriented at 45° with respect to boundary  550  in one portion and 22.5° with respect to boundary  550  in a second portion.  
         [0043]    [0043]FIG. 6 b  shows deposition of a second buffer layer  530  on top of section  590 . Buffer layer  530  can have a thickness of approximately 18 nm and, again, can be of CeO 2 . The crystal orientation of buffer layer  515  differs from the crystal orientation of buffer layer  530  such that the intersection of layers  530  and  515  at boundary  550  creates a grain boundary.  
         [0044]    A superconducting layer  532  can then be deposited on buffer layer  515  and a superconducting layer  534  can be deposited on buffer layer  530  in such a way that boundary  550  remains clean and sharp. Superconducting layers  532  and  534  can be about 200 nm in thickness. The crystal orientations of the superconducting materials of layers  532  and  534  are determined by the crystal orientation of underlying seed layer  510  or substrate  500 , respectively. In some embodiments, a 45° lattice mismatch is arranged between the superconducting material of layer  532  and the superconducting material of layer  534 . In some embodiments the high-T c  superconducting material of layers  532  and  534  is a material such as YBa 2 Cu 3 O 7−x , where x is some value greater than 0 and less than 0.6.  
         [0045]    [0045]FIG. 6 c  shows SQUID magnetometer  100  completely fabricated. As illustrated in FIG. 6 c , superconducting layers  532  and  534  are etched into dc-SQUID  100  using, for example, a process such as Xe ion milling, with the resulting junctions  110  and  120  being a π/2-junction and 0-junction, respectively. The width of each of junctions  110  and  120  helps define the operation parameters of the SQUID by effecting the capacitance and critical current values. For example, having the width of junction  110  as twice that of junction  120  doubles the current in the  110  branch and halves the current in the  120  branch. In an exemplary embodiment, the width of branches  581  and  582 , in superconducting loop  150 , are on the order of 1 micrometer, which is much smaller than the width if the overall SQUID loop  150 . Furthermore, by tuning the widths of branches  581  and  582 , dc-SQUID  100  can be made substantially impervious with respect to the degree of cleanliness of junctions  110  and  120 . In one particular embodiment formed with superconducting material YBa 2 Cu 3 O 7−x , where x has values less than 0.6 and greater than 0.05, the widths of junctions  110  and  120  (L 1  and L 2 , respectively) are both about 1 μm respectively, the width of branches  581  and  582  are also approximately 1 μm as well, and the inside separation between branches  581  and  582  is approximately 10 μm.  
         [0046]    [0046]FIG. 7 shows a cross-sectional view of an example of a junction fabricated as described above with FIGS. 6 a  through  6   c . Each of the contributing layers are shown approximately to scale before any Ion milling. Substrate  500  can be SrTiO 3 , and can be approximately 50 nm in thickness. Seed layer  510  can be of MgO, and can be approximately 5 nm thick. Seed layer  510  has been milled away from the right hand side of the sample (under section  102 ) shown in FIG. 7. Buffer layer  515  can be of CeO 2  and can be approximately 11 nm thick. First buffer layer has also been milled away from the side under section  102 . Second buffer layer  530  can be of the same material as the first buffer layer, but with a thickness of approximately 18 nm. Further, second buffer layer  530  can be deposited over first buffer layer  515 . Finally, the supercodonductive material  532  and  534  is deposited onto the sample with a thickness of approximately 200 nm. The thickness values and materials given in this example are exemplary, and in no way limit the scope of the fabrication of the invention.  
         [0047]    [0047]FIG. 8 illustrates an embodiment of a 2-dimensional array  600  of dc-SQUID magnetometers according to the present invention. Array  600  includes SQUID magnetometers  620 - 1 , 1  through  620 -M,Q as shown in FIG. 6. In the embodiment of FIG. 8, each row can include a different number of magnetometers. Each of SQUID magnetometers  620 - 1 , 1  through  620 - 1 ,N is formed along a grain boundary  630 - 1  between regions  630 - 1  and  630 - 2 . Grain boundary  610 - 1  is shaped to provide positions for the formation of both O-junctions and π/2-junctions and conversely π-junctions and π/2 junctions. Each of grain boundaries  610 - 1  through  610 -M is shaped to provide for the fabrication of at least one O-junction or π-junction and at least one π/2-junction for each SQUID magnetometer  620 - 1 , 1  through  620 -M,Q formed along that grain boundary.  
         [0048]    Array  600  includes regions  610 ,  612  and  614 . In regions  610  and  614 , d-wave superconducting material can be deposited with a first crystallographic orientation and in region  612  d-wave superconducting material can be deposited with a second crystallographic orientation such that the lattice mismatch at the grain boundaries allows for creation of 0-junctions and π/2 junctions along the grain boundaries between regions  610  and  612  and between regions  612  and  614 . Furthermore, the shape of the grain boundary between regions  610  and  612  and regions  612  and  614  can be set in order to facilitate the production of a 0-junction and a π/2 junction in each SQUID magnetometer. SQUID magnetometers  620 - 1 , 1  through  620 -M,Q include 0 junctions  640 - 1 , 1  through  640 -M,Q, respectively, and π/2 junctions  642 - 1 , 1  through  642 -M,Q, respectively, as shown in FIG. 6. SQUID magnetometers  6201 , 1  through  620 -M,Q of array  600  can be fabricated as described above with respect to FIGS. 6 a  through  6   c . One skilled in the art will recognize that array  600  can be extended to an array including a plurality of dimensions and a plurality of π/2 dc-SQUID magnetometers. For example, a series of array  600  can be coupled to create a multi-dimensional array. In some embodiments, a series of array  600  magnetometers is stacked to form a three dimensional magnetometer.  
         [0049]    [0049]FIG. 9 illustrates the utilization of a π/2 SQUID magnetometer  702  according to the present invention. Magnetometer  702  can include a single SQUID loop or may be an array of SQUID loops such as array  600  illustrated in FIG. 8. Magnetometer  702  is positioned in proximity to a magnetic field source  701 .  
         [0050]    In some applications, source  701  can be a quantum qubit. In some other applications, source  701  can be an electronic circuit. In some further applications, source  701  can be a superconducting circuit. Source  701  can also be a magnetic resonance imaging system, a metallic sample being tested for defects, a mine, or a submarine. In general, source  701  can be any source of a magnetic field.  
         [0051]    Magnetometer  701  is coupled to a current device  703  in series and a voltmeter  704  in parallel. Current device  703  applies a constant current to the dc-SQUID Magnetometer. Any magnetic fields can be detected by the voltmeter. Embodiments of current device  703  are well known in the art. In an exemplary embodiment, the voltmeter  704  can be a radio-frequency single electron transistor. In operation, presence of an external magnetic field induces a superconducting current in magnetometer  701  which exceeds the critical current of the superconducting loop. Resultingly, a the junctions in the loop become resistive, and the voltmeter  704  registers a voltage. Since magnetometer  701  is direction sensitive, voltmeter  704  is capable of determining both the strength of the magnetic field {right arrow over (B)}, and any variation in the magnetic field {right arrow over (B)}, and the direction of the magnetic field {right arrow over (B)}.  
         [0052]    The above described embodiments are exemplary only and are not intended to be limiting. One skilled in the art will recognize variations from the particular embodiments described above that are intended to be within the spirit and scope of this invention. As such, the invention is limited only by the following claims.